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Full text of "Models of the Atom, Project Physics Text and Handbook Volume 5"

The Project Physics Course Text and Handbook 



Models of the Atom 



/•. •• 



The Project Physics Course 



Text and Handbook 



UNIT 



5 



Models of the Atom 



A Component of the 
Project Physics Course 




Published by 

HOLT, RINEHART and WINSTON, Inc. 

New York, Toronto 



Directors of Harvard Project Physics 

Gerald Holton, Department of Physics, Harvard 

University 
F. James Rutherford, Capuchino High School, 

San Bruno, Cahfornia, and Harvard University 
Fletcher G. Watson, Harvard Graduate School 

of Education 



Acknowledgments, Text Section 

The authors and publisher have made every effort 
to trace the ownership of all selections found in this 
book and to make full acknowledgment for their use. 
Many of the selections are in the public domain. 

Grateful acknowledgment is hereby made to the 
following authors, pubUshers, agents, and individ- 
uals for use of their copyrighted material. 



Special Consultant to Project Physics 

Andrew Ahlgren, Harvard Graduate School of 
Education 



A partial Ust of staff and consultants to Harvard 
Project Physics appears on page iv. 

This Text-Handbook, Unit 5 is one of the many in- 
structional materials developed for the Project 
Physics Course. These materials include Texts, 
Handbooks, Teacher Resource Books, Readers, 
Programmed Instruction booklets, Film Loops, 
Transparencies, 16mm films, and laboratory 
equipment. 



Copyright © 1970 Project Physics 

All Rights Reserved 

SBN 03-084501-7 

1234 039 98765432 

Project Physics is a registered trademark 



P. 3 Excerpts from The Way Things Are: The De 
Rerum Natura of Titus Lucretius Caius, a transla- 
tion by Rolfe Humphries, copyright © 1969 by 
Indiana University Press. 

P. 5 From 'The First Chapter of Aristotle's 
'Foundations of Scientij&c Thought' (Metaphysica, 
Liber A)," translated by Daniel E. Gershenson and 
Daniel A. Greenburg, in The Natural Philosopher, 
Vol. II, copyright © 1963 by the Blaisdell Pub- 
lishing Company, pp. 14—15. 

P. 7 From The Life of the Honorable Henry 
Cavendish, by George Wilson, printed for the 
Cavendish Society, 1851, pp. 186-187. 

Pp. 7-8 From "Elements of Chemistry" by Antoine 
Laurent Lavoisier, translated by Robert Kerr in Great 
Books of the Western World, Vol. 45, copyright 1952 
by Encyclopaedia Britannica, Inc., pp. 3-4. 

P. 11 From "The Atomic Molecular Theory" by 
Leonard K. Nash in Harvard Case Histories in 
Experimental Science, Case 4, Vol. 1, copyright 1950 
by Harvard University, p. 228. 

P. 21 From The Principles of Chemistry by Dmitri 
Mendeleev, translated by George Kamensky, copy- 
right 1905 by Longmans, Green and Company, 
London, p. 27. 

P. 22 Mendeleev, Dmitri, 1872. 

P. 29 From "Experimental Researches in Elec- 
tricity" by Michael Faraday from Great Books of the 
Western World, Vol. 45, copyright 1952 by 
Encyclopaedia Britannica, Inc., pp. 389-390. 

Pp. 43-44 Einstein, Albert, trans, by Professor 
Irving Kaplan, Massachusetts Institute of Tech- 
nology. 

P. 48 Roentgen, W. K. 

P. 57 From "Opticks" by Isaac Newton from Great 
Books of the Western World, Vol. 34, copyright 1952 
by Encyclopaedia Britannica, Inc., pp. 525-531. 

P. 67 From Background to Modeim Science, 
Needham, Joseph and Pagel, Walter, eds., copyright 
1938 by The Macmillan Company, pp. 68-69. 

P. 88 Letter from Rutherford to Bohr, March 1913. 

P. 91 From "Opticks" by Isaac Newton from Great 
Books of the Western World, Vol. 34, copyright 1952 
by Encyclopaedia Britannica, Inc., p. 541. 

P. 113 From Atom,ic Physics by Max Bom, copy- 
right 1952 by Blackie & Son, Ltd., p. 95. 



p. 114 Letter from Albert Einstein to Max Bom, 
1926. 

P. 119 From A Philosophical Essay on Possibilities 
by Pierre Simon Laplace, translated by Frederick W. 
Truscott and Frederick L. Emory, copyright 1951 
by Dover Publications, Inc., p. 4. 



Picture Credits, Text Section 

Cover photo: Courtesy of Professor Erwin W. 
Mueller, The Pennsylvania State University. 

P. 1 (top) Merck Sharp & Dohme Research 
Laboratories; (center) Loomis Dean, LIFE 
MAGAZINE, © Time Inc. 

P. 2 (charioteer) Hirmer Fotoarchiv, Munich; 
(architectural ruins) Greek National Tourist 
Office, N.Y.C. 

P. 4 Electrum pendant (enlarged). Archaic. 
Greek. Gold. Courtesy, Museum of Fine Arts, 
Boston. Henry Lillie Pierce Residuary Fund. 

P. 7 Fisher Scientific Company, Medford, Mass. 

P. 10 from Dalton, John, A New System of 
Chemical Philosophy, R. BickerstafF, London, 
1808-1827, as reproduced in A History of 
Chemistry by Charles-Albert Reichen, c 1963, 
Hawthorn Books Inc., 70 Fifth Ave., N.Y.C. 

P. 13 Engraved portrait by Worthington from a 
painting by Allen. The Science Museum, London. 

P. 15 (drawing) Reprinted by permission from 
CHEMICAL SYSTEMS by Chemical Bond Approach 
Project. Copyright 1964 by Earlham College Press, 
Inc. Published by Webster Division, McGraw-Hill 
Book Company. 

P. 20 Moscow Technological Institute. 

P. 26 (portrait) The Royal Society of London. 

P. 27 Courtesy of Aluminum Company of America. 

P. 32 Science Museum, London. Lent by J. J. 
Thomson, M.A., Trinity College, Cambridge. 

P. 35 Courtesy of Sir George Thomson. 

P. 39 (top) California Institute of Technology. 

P. 45 (left, top) Courtesy of The New York Times; 
(left, middle) American Institute of Physics; 
(middle, right) Courtesy of California Institute of 
Technology Archives; (left, bottom) Courtesy of 
Europa Verlag, Zurich. 

P. 47 (left, top) Dr. Max F. Millikan; (right, top) 
Harper Library, University of Chicago; (right 
margin) R. Diihrkoop photo. 

P. 48 The Smithsonian Institution. 

P. 49 Burndy Library, Norwalk, Conn. 

P. 51 Eastman Kodak Company, Rochester, N.Y. 

P. 52 High Voltage Engineering Corp. 

P. 53 (rose) Eastman Kodak Company; (fish) 



American Institute of Radiology; (reactor vessel) 
Nuclear Division, Combustion Engineering, Inc. 

P. 58 Science Museum, London. Lent by Sir 
Lawrence Bragg, F.R.S. 

P. 64 Courtesy of Dr. Owen J. Gingerich, 
Smithsonian Astrophysical Observatory. 

P. 67 Courtesy of Professor Lawrence Badash, 
Dept. of History, University of California, 
Santa Barbara. 

P. 76 (top) American Institute of Physics; 
(bottom, right) Courtesy of Niels Bohr Library, 
American Institute of Physics. 

P. 80 (ceremony) Courtesy of Professor Edward 
M. Purcell, Harvard University; (medal) Swedish 
Information Service, N.Y.C. 

P. 93 Science Museum, London. Lent by Sir 
Lawrence Bragg, F.R.S. 

P. 94 from the P.S.S.C. film Matter Waves. 

P. 100 American Institute of Physics. 

P. 102 Professor Harry Meiners, Rensselaer 
Polytechnic Institute. 

P. 106 American Institute of Physics. 

P. 107 (de Broglie) Academic des Sciences, Paris; 
(Heisenberg) Professor Werner K. Heisenberg; 
(Schrodinger) Ameriq^n Institute of Physics. 

P. 109 (top, left) Perkin-Elmer Corp. 

P. 112 Orear, Jay, Fundamental Physics, © 1961 
by John Wiley & Sons, Inc., New York. 

P. 115 The Graphic Work of M. C. Escher, 
Hawthorn Books Inc., N.Y. "Lucht en Water 2." 

Picture Credits, Handbook Section 

Cover: Drawing by Saul Steinberg, from 
The Sketchbook for 1967, Hallmark Cards, Inc. 

P. 130 These tables appear on pp. 122, 157 and 
158 of Types of Graphic Representation of the 
Periodic System of Chemical Elements by 
Edmund G. Mazurs, published in 1957 by the 
author. They also appear on p. 8 of Chemistry 
magazine, July 1966. 

P. 136 Courtesy L. J. Lippie, Dow Chemical 
Company, Midland. Michigan. 

P. 149 From the cover of The Science Teacher, 
Vol. 31, No. 8, December 1964, illustration for 
the article, "Scientists on Stamps; Reflections of 
Scientists' Public Image, " by Victor Showalter, 
The Science Teacher, December 1964, pp. 40—42. 

All photographs used with film loops courtesy 
of National Film Board of Canada. 

Photographs of laboratory equipment and of 
students using laboratory equipment were supplied 
with the cooperation of the Project Physics staff 
and Damon Corporation. 



Partial List of Staff and Consultants 

The individuals listed below (and on the following pages) have each contributed in some way to the 
development of the course materials. Their periods of participation ranged from brief consultations to 
full-time involvement in the team for several years. The affiliations indicated are those just prior to 
or during the period of participation. 



Advisory Committee 

E. G. Begle, Stanford University, Calif. 

Paul F. Brandwein, Harcourt, Brace & World, 

Inc., San Francisco, Calif. 
Robert Brode, University of California, Berkeley 
Erwin Hiebert, University of Wisconsin, Madison 
Harry Kelly, North Carolina State College, Raleigh 
William C. Kelly, National Research Council, 

Washington, D.C. 
Philippe LeCorbeiller, New School for Social 

Research, New York, N.Y. 
Thomas Miner, Garden City High School, New 

York. 
Philip Morrison, Massachusetts Institute of 

Technology, Cambridge 
Ernest Nagel, Columbia University, New York, 

N.Y. 
Leonard K. Nash, Harvard University 
I. I. Rabi, Columbia University, New York. N.Y. 

Staff and Consultants 

L. K. Akers, Oak Ridge Associated Universities, 

Tenn. 
Roger A. Albrecht, Osage Community Schools, 

Iowa 
David Anderson, Oberlin College, Ohio 
Gary Anderson, Harvard University 
Donald Armstrong, American Science Film 

Association, Washington, D.C. 
Arnold Arons, University of Washington 
Sam Ascher, Henry Ford High School, Detroit, 

Mich. 
Ralph Atherton, Talawanda High School, Oxford, 

Ohio 
Albert V. Baez, UNESCO, Paris 
William G. Banick, Fulton High School. Atlanta, 

Ga. 
Arthur Bardige, Nova High School, Fort 

Lauderdale, Fla. 
Rolland B. Bartholomew, Henry M. Gunn High 

School, Palo Alto, Calif. 
O. Theodor Benfey, Earlham College, Richmond, 

Ind. 
Richard Berendzen, Harvard College Observatory 
Alfred M. Bork, Reed College, Portland, Ore. 

F. David Boulanger, Mercer Island High School, 
Washington 

Alfred Brenner, Harvard University 
Robert Bridgham, Harvard University 
Richard Brinckerhoff, Phillips Exeter Academy, 
Exeter. N.H. 



Donald Brittain, National Film Board of Canada. 

Montreal 
Joan Bromberg, Harvard University 
Vinson Bronson, Newton South High School, 

Newton Centre, Mass. 
Stephen G. Brush, Lawrence Radiation Laboratory, 

University of California. Livermore 
Michael Butler. CIASA Films Mundiales. S. A.. 

Mexico 
Leon Callihan, St. Mark's School of Texas. Dallas 
Douglas Campbell, Harvard University 
J. Arthur Campbell, Harvey Mudd College, 

Claremont, California 
Dean R. Casperson. Harvard University 
Bobby Chambers. Oak Ridge Associated 

Universities. Tenn. 
Robert Chesley. Thacher School, Ojai, Calif. 
John Christensen. Oak Ridge Associated 

Universities, Tenn. 
David Clarke. Browne and Nichols School. 

Cambridge. Mass. 
Robert S. Cohen. Boston University. Mass. 
Brother Columban Francis. F.S.C.. Mater Christi 

Diocesan High School. Long Island City. N.Y. 
Arthur Compton. Phillips Exeter Academy, 

Exeter. N.H. 
David L. Cone, Los Altos High School, CaUf. 
William Cooley. University of Pittsburgh. Pa. 
Ann Couch. Harvard University 
Paul Cowan, Hardin-Simmons University. 

Abilene, Tex. 
Charles Davis. Fairfax County School Board. 

Fairfax. Va. 
Michael Dentamaro. Senn High School. Chicago, 

111. 
Raymond Dittman. Newton High School. Mass. 
Elsa Dorfman. Educational Services Inc.. 

Watertown. Mass. 
Vadim Drozin. Bucknell University. Lewisburg, 

Pa. 
Neil F. Dunn. Burlington High School. Mass. 
R. T. Ellickson. University of Oregon. Eugene 
Thomas Embry. Nova High School. Fort 

Lauderdale. Fla. 
Walter Eppenstein. Rensselaer Polytechnic 

Institute, Troy, N.Y. 
Herman Epstein. Brandeis University. Waltham. 

Mass. 
Thomas F. B. Ferguson. National Film Board of 

Canada. Montreal 
Thomas von Foerster. Harvard University 



(continued on p. 122) 



Science is an adventure of the whole human race to learn to live in and 
perhaps to love the universe in which they are. To be a part of it is to 
understand, to understand oneself, to begin to feel that there is a capacity 
within man far beyond what he felt he had, of an infinite extension of 
human possibilities . . . 

I propose that science be taught at whatever level, from the lowest to the 
highest, in the humanistic way. It should be taught with a certain historical 
understanding, with a certain philosophical understanding , with a social 
understanding and a human understanding in the sense of the biography, the 
nature of the people who made this construction, the triumphs, the trials, the 
tribulations. 

I. I. RABI 

Nobel Laureate in Physics 



Preface 



Background The Project Physics Course is based on the ideas and 
research of a national curriculum development project that worked in 
three phases. First, the authors — a high school physics teacher, a 
university physicist, and a professor of science education — collaborated 
to lay out the main goals and topics of a new introductory physics 
course. They worked together from 1962 to 1964 with financial support 
from the Carnegie Corporation of New York, and the first version of 
the text was tried out in two schools with encouraging results. 

These preliminary results led to the second phase of the Project 
when a series of major grants were obtained from the U.S. Office of 
Education and the National Science Foundation, starting in 1964. 
Invaluable additional financial support was also provided by the 
Ford Foundation, the Alfred P. Sloan Foundation, the Carnegie 
Corporation, and Harvard University. A large number of collaborators 
were brought together from all parts of the nation, and the group 
worked together for over four years under the title Harvard Project 
Physics. At the Project's center, located at Harvard University, 
Cambridge, Massachusetts, the staff and consultants included college 
and high school physics teachers, astronomers, chemists, historians 
and philosophers of science, science educators, psychologists, 
evaluation specialists, engineers, film makers, artists and graphic 
designers. The teachers serving as field consultants and the students 
in the trial classes were also of vital importance to the success of 
Harvard Project Physics. As each successive experimental version of 
the course was developed, it was tried out in schools throughout the 
United States and Canada. The teachers and students in those schools 
reported their criticisms and suggestions to the staff in Cambridge, 
and these reports became the basis for the subsequent revisions of 
the course materials. In the Preface to Unit 1 Text you will find a list of the 
major aims of the course. 



We wish it were possible to list in detail the contributions of each 
person who participated in some part of Harvard Project Physics. 
Unhappily it is not feasible, since most staff members worked on a 
variety of materials and had multiple responsibilities. Furthermore, 
every text chapter, experiment, piece of apparatus, film or other item 
in the experimental program benefitted from the contributions of a 
great many people. On the preceding pages is a partial list of 
contributors to Harvard Project Physics. There were, in fact, many 
other contributors too numerous to mention. These include school 
administrators in participating schools, directors and staff members 
of training institutes for teachers, teachers who tried the course after 
the evaluation year, and most of all the thousands of students who 
not only agreed to take the experimental version of the course, but 
who were also willing to appraise it critically and contribute their 
opinions and suggestions. 

The Project Physics Course Today. Using the last of the experimental 
versions of the course developed by Harvard Project Physics in 
1964-68 as a starting point, and taking into account the evaluation 
results from the tryouts, the three original collaborators set out to 
develop the version suitable for large-scale publication. We take 
particular pleasure in acknowledging the assistance of Dr. Andrew 
Ahlgren of Harvard University. Dr. Ahlgren was invaluable because 
of his skill as a physics teacher, his editorial talent, his versatility 
and energy, and above all, his commitment to the goals of Harvard 
Project Physics. 

We would also especially like to thank Miss Joan Laws whose 
administrative skills, dependability, and thoughtfulness contributed so 
much to our work. The publisher. Holt, Rinehart and Winston, Inc. 
of New York, provided the coordination, editorial support, and general 
backing necessary to the large undertaking of preparing the final 
version of all components of the Project Physics Course, including 
texts, laboratory apparatus, films, etc. Damon, a company located in 
Needham, Massachusetts, worked closely with us to improve the 
engineering design of the laboratory apparatus and to see that it was 
properly integrated into the program. 

In the years ahead, the learning materials of the Project Physics 
Course will be revised as often as is necessary to remove remaining 
ambiguities, clarify instructions, and to continue to make the materials 
more interesting and relevant to students. We therefore urge all 
students and teachers who use this course to send to us (in care of 
Holt, Rinehart and Winston, Inc., 383 Madison Avenue, New York, 
New York 10017) any criticism or suggestions they may have. 



F. James Rutherford 
Gerald Holton 
Fletcher G. Watson 



Contents 



TEXT SECTION, Unit 5 



Prologue 1 

Chapter 17 The Chemical Basis of Atomic Theory 

Dal ton's atomic theory and the laws of chemical combination 11 

The atomic masses of the elements 14 

Other properties of the elements: combining capacity 16 

The search for order and regularity among the elements 18 

Mendeleev's periodic table of the elements 19 

The modern periodic table 23 

Electricity and Matter: qualitative studies 25 

Electricity and matter: quantitative studies 28 

Chapter 18 Electrons and Quanta 

The idea of atomic structure 33 

Cathode rays 34 

The measurement of the charge of the electron: Millikan's experiment 37 

The photoelectric effect 40 

Einstein's theory of the photoelectric effect 43 

X rays 48 

Electrons, quanta and the atom 54 

Chapter 19 The Rutherford-Bohr Model of the Atom 

Spectra of gases 59 

Regularities in the hydrogen spectrum 63 

Rutherford's nuclear model of the atom 66 

Nuclear charge and size 69 

The Bohr theory : the postulates 71 

The size of the hydrogen atom 72 

Other consequences of the Bohr model 74 

The Bohr theory: the spectral series of hydrogen 75 

Stationary states of atoms: the Franck-Hertz experiment 79 

The periodic table of the elements 82 

The inadequacy of the Bohr theory and the state of atomic theory in the early 1920's 86 

Chapter 20 Some Ideas from Modern Physical Theories 

Some results of relativity theory 95 
Particle-hke behavior of radiation 99 
Wave-like behavior of particles 101 
Mathematical vs visuahzable atoms 104 
The uncertainty principle 108 
Probabihty interpretation 111 

Epilogue 116 

Contents — HandbookSection 125 

I ndex/Text Section 1 59 

Index/HandbookSection 163 

Answers to End-of-Section Questions 165 

Brief Answers to Study Guide Questions 168 






. * ^*". 







UNIT 



5 



Models of the Atom 



CHAPTERS 

17 The Chemical Basis of the Atomic Theory 

18 Electrons and Quanta 

19 The Rutherford-Bohr Model of the Atom 

20 Some Ideas from Modern Physical Theories 



PROLOGUE In the earlier units of this course we studied the motion 
of bodies: bodies of ordinary size, such as we deal with in everyday life, 
and very large bodies, such as planets. We have seen how the laws of 
motion and gravitation were developed over many centuries and how 
they are used. We have learned about conservation laws, about waves, 
about light, and about electric and magnetic fields. All that we have 
learned so far can be used to study a problem which has intrigued 
people for many centuries: the problem of the nature of matter. The 
phrase, "the nature of matter," may seem simple to us now, but its 
meaning has been changing and growing over the centuries. The kind 
of questions and the methods used to find answers to these questions 
are continually changing. For example, during the nineteenth century 
the study of the nature of matter consisted mainly of chemistry: in the 
twentieth century the study of matter has also moved into atomic and 
nuclear physics. 

Since 1800 progress has been so rapid that it is easy to forget that 
people have theorized about matter for more than 2,500 years. In fact 
some of the questions for which answers have been found only during 
the last hundred years began to be asked more than two thousand 
years ago. Some of the ideas we consider new and exciting, such as 
the atomic constitution of matter, were debated in Greece in the fifth 
and fourth centuries B.C. In this prologue we shall therefore review 
briefly the development of ideas concerning the nature of matter up to 
about 1800. This review will set the stage for the four chapters of Unit 5, 
which will be devoted, in greater detail, to the progress made since 
1800 on understanding the constitution of matter. It will be shown in 
these chapters that matter is made up of discrete particles that we call 
atoms, and that the atoms themselves have structure. 

Opposite: Monolith— The Face of Half Dome (Photo by Ansel Adams) 



The photographs on these two 
pages illustrate some of the variety 
of forms of matter: large and small, 
stable and shifting. 




microscopic crystals 




condensed water vapor 



Greek Ideas of Order 

The Greek mind loved clarity and order, expressed in 
a way that still touches us deeply. In philosophy, litera- 
ture, art and architecture it sought to interpret things in 
terms of humane and lasting qualities. It tried to discover 
the forms and patterns thought to be essential to an 
understanding of things. The Greeks delighted in show- 
ing these forms and patterns when they found them. Their 
art and architecture express beauty and intelligibility 
by means of balance of form and simple dignity. 

These aspects of Greek thought are beautifully ex- 
pressed in the shrine of Delphi. The theater, which could 
seat 5,000 spectators, impresses us because of the size 
and depth of the tiered seating structure. But even more 
striking is the natural and orderly way in which the theater 
is shaped into the landscape so that the entire landscape 
takes on the aspect of a giant theater. The Treasury build- 
ing at Delphi has an orderly system of proportions, with 
form and function integrated into a logical, pleasing 
whole. The statue of the charioteer found at Delphi, with 
its balance and firmness, represents a genuine ideal of 
male beauty at that time. After more than 2,000 years we 
are still struck by the elegance of Greek expression. 




v^'K^ 








r^. 



^5><^> 



Prologue 3 

The Roman poet Lucretius based his ideas of physics on the 
tradition of atomism dating back to the Greek philosophers Democritus 
and Leucippus. The following passages are from his poem De Rerum 
Natura (On the Nature of Things), an eloquent statement of atomism: 

... If you think 

Atoms can stop their course, refrain from movement, 

And by cessation cause new kinds of motion, 

You are far astray indeed. Since there is void 

Through which they move, all fundamental motes 

Must be impelled, either by their own weight 

Or by some force outside them. When they strike 

Each other, they bounce off; no wonder, either. 

Since they are absolute solid, all compact. 

With nothing back of them to block their path. 

... no atom ever rests 

Coming through void, but always drives, is driven 

In various ways, and their collisions cause. 

As the case may be, greater or less rebound. 

When they are held in thickest combination, 

At closer intervals, with the space between 

More hindered by their interlock of figure. 

These give us rock, or adamant, or iron. 

Things of that nature. (Not very many kinds 

Go wandering little and lonely through the void.) 

There are some whose alternate meetings, partings, are 

At greater intervals; from these we are given 

Thin air, the shining sunlight . . . 

* * * 

. . . It's no wonder 

That while the atoms are in constant motion, 

Their total seems to be at total rest, 

Save here and there some individual stir. 

Their nature lies beyond our range of sense. 

Far, far beyond. Since you can't get to see 

The things themselves, they're bound to hide their moves, 

Especially since things we can see, often 

Conceal their movements, too, when at a distance. 

Take grazing sheep on a hill, you know they move, 

The woolly creatures, to crop the lovely grass 

Wherever it may call each one, with dew 

Still sparkling it with jewels, and the lambs. 

Fed full, play little games, flash in the sunlight. 

Yet all this, far away, is just a blue, 

A whiteness resting on a hill of green. 

Or when great armies sweep across great plains 

In mimic warfare, and their shining goes 

Up to the sky, and all the world around 

Is brilliant with their bronze, and trampled earth 

Trembles under the cadence of their tread, 

White mountains echo the uproar to the stars, 

The horsemen gallop and shake the very ground, 

And yet high in the hills there is a place 

From which the watcher sees a host at rest. 

And only a brightness resting on the plain. 

[translated from the Latin by Rolfe Humphries] 



Models of the Atom 




This gold earring, made in Greece 
about 600 B.C., shows the great skill 
with which ancient artisans worked 
metals. [Museum of Fine Arts, Boston] 



Early science had to develop out of the ideas available before 
science started— ideas that came from experience with snow, wind, 
rain, mist and clouds; with heat and cold; with salt and fresh water; 
wine, milk, blood, and honey; ripe and unripe fruit; fertile and infertile 
seeds. The most obvious and most puzzling facts were that plants, 
animals, and men were born, that they grew and matured, and that they 
aged and died. Men noticed that the world about them was continually 
changing and yet, on the whole, it seemed to remain much the same. 
The unknown causes of these changes and of the apparent continuity 
of nature were assigned to the actions of gods and demons who were 
thought to control nature. Myths concerning the creation of the world 
and the changes of the seasons were among the earliest creative 
productions of primitive peoples everywhere, and helped them to come 
to terms with events man could see happening but could not rationally 
understand. 

Over a long period of time men developed some control over nature 
and materials: they learned how to keep warm and dry, to smelt ores, to 
make weapons and tools, to produce gold ornaments, glass, perfumes, 
and medicines. Eventually, in Greece, by the year 600 B.C., philosophers 
—literally "lovers of wisdom"— had started to look for rational explana- 
tions of natural events, that is, explanations that did not depend on the 
actions or the whims of gods or demons. They sought to discover the 
enduring, unchanging things out of which the world is made, and how 
these enduring things can give rise to the changes that we perceive, 
as well as the great variety of material things that exists. This was the 
beginning of man's attempts to understand the material world rationally, 
and it led to a theory of the nature of matter. 

The earliest Greek philosophers thought that all the different things 
in the world were made out of a single basic substance. Some thought 
that water was the fundamental substance and that all other substances 
were derived from it. Others thought that air was the basic substance; 
still others favored fire. But neither water, nor air, nor fire was satis- 
factory; no one substance seemed to have enough different properties 
to give rise to the enormous variety of substances in the world. According 
to another view, introduced by Empedocles around 450 B.C., there are 
four basic types of matter— earth, air, fire, and water— and all material 
things are made out of them. These four basic materials can mingle 
and separate and reunite in different proportions, and so produce 
the variety of familiar objects around us as well as the changes in 
such objects. But the basic four materials, called elements, were 
supposed to persist through all these changes. This theory was the 
first appearance in our scientific tradition of a model of matter, 
according to which all material things are just different arrangements 
of a few external elements. 

The first atomic theory of matter was introduced by the Greek 
philosopher Leucippus, born about 500 B.C., and his pupil Democritus, 
who lived from about 460 B.C. to 370 B.C. Only scattered fragments of 
the writings of these philosophers remain, but their ideas were dis- 
cussed in considerable detail by the Greek philosophers Aristotle 
(389-321 B.C.) and Epicurus (341-270 B.C.), and by the Latin poet 



Prologue 



Lucretius (100-55 B.C.). It is to these men that we owe most of our 
knowledge of ancient atomism. 

The theory of the atomists was based on a number of assumptions: 

(1) matter is eternal— no material thing can come from nothing, 
nor can any material thing pass into nothing; 

(2) material things consist of very small indivisible particles— the 
word "atom" meant "uncuttable" in Greek and, in discussing the ideas 
of the early atomists, we could use the word "indivisibles" instead of 
the word "atoms"; 

(3) atoms differ chiefly in their sizes and shapes; 

(4) the atoms exist in otherwise empty space (the void) which sepa- 
rates them, and because of this space they are capable of movement 
from one place to another; 

(5) the atoms are in ceaseless motion, although the nature and 
cause of the motion are not clear; 

(6) in the course of their motions atoms come together and form 
combinations which are the material substances we know; when the 
atoms forming these combinations separate, the substances decay or 
break up. Thus, the combinations and separations of atoms give rise to 
the changes which take place in the world; 

(7) the combinations and separations take place in accord with 
natural laws which are not yet clear, but do not require the action of 
gods or demons or other supernatural powers. 

With the above assumptions, the ancient atomists were able to 
work out a consistent story of change, of what they sometimes called 
"coming-to-be" and "passing away." They could not demonstrate 
experimentally that their theory was correct, and they had to be satis- 
fied with an explanation derived from assumptions that seemed 
reasonable to them. The theory was a "likely story." It was not 
useful for the prediction of new phenomena; but that became an 
important value for a theory only later. To these atomists, it was more 
significant that the theory also helped to allay the unreasonable fear 
of capricious gods. 

The atomic theory was criticized severely by Aristotle, who argued 
logically— from his own assumptions— that no vacuum or void could 
exist and that the ideas of atoms with their continual motion must be 
rejected. (Aristotle was also probably sensitive to the fact that in his 
time atomism was identified with atheism.) For a long time Aristotle's 
argument against the void was widely held to be convincing. One must 
here recall that not until the seventeenth century did Torricelli's 
experiments (described in Chapter 1 1 ) show that a vacuum could indeed 
exist. Furthermore, Aristotle argued that matter is continuous and 
infinitely divisible so that there can be no atoms. 

Aristotle developed a theory of matter as part of his grand scheme 
of the universe, and this theory, with some modifications, was thought 
to be satisfactory by most philosophers of nature for nearly two 
thousand years. His theory of matter was based on the four basic 
elements. Earth, Air, Fire, and Water, and four "qualities," Cold, Hot, 
Moist, and Dry. Each element was characterized by two qualities (the 



According to Aristotle in his Meta- 
physics, "There is no consensus 
concerning the number or nature of 
these fundamental substances. 
Thales, the first to think about such 
matters, held that the elementary 
substance is clear liquid. ... He 
may have gotten this idea from the 
observation that only moist matter 
can be wholly integrated into an 
object — so that all growth depends 
on moisture. . . . 

"Anaximenes and Diogenes held 
that colorless gas is more elemen- 
tary than clear liquid, and that in- 
deed, it is the most elementary of 
all simple substances. On the other 
hand Hippasus of Metpontum and 
Heraclitus of Ephesus said that the 
most elementary substance is heat. 
Empedocles spoke of four elemen- 
tary substances, adding dry dust to 
the three already mentioned . . . 
Anaxagoras of Clazomenae says 
that there are an infinite number of 
elementary constituents of mat- 
ter. . . ." [From a translation by 
D. E. Gershenson and D. A. Green- 
berg.] 



6 



Models of the Atom 



FIRE 




WATER 




Laboratory 
chemist. 



of a 16th-century al- 



nearer two to each side, as shown in the diagram at the left). Thus 
the element 

Earth is Dry and Cold, 

Water is Cold and Moist, 

Air is Moist and Hot, 

Fire is Hot and Dry. 

According to Aristotle, it is always the first of the two qualities which 
predominates. In his version the elements are not unchangeable; any 
one of them may be transformed into any other because of one or both 
of its qualities changing into opposites. The transformation takes place 
most easily between two elements having one quality in common; thus 
Earth is transformed into Water when dryness changes into moistness. 
Earth can be transformed into Air only if both of the qualities of earth 
(dry and cold) are changed into their opposites (moist and hot). 

As we have already mentioned in the Text Chapter 2, Aristotle was 
able to explain many natural phenomena by means of his ideas. Like 
the atomic theory, Aristotle's theory of coming-to-be and passing-away 
was consistent, and constituted a model of the nature of matter. It had 
certain advantages over the atomic theory: it was based on elements 
and qualities that were familiar to people; it did not involve atoms, 
which couldn't be seen or otherwise perceived, or a void, which was 
most difficult to imagine. In addition, Aristotle's theory provided some 
basis for further experimentation: it supplied what seemed like a 
rational basis for the tantalizing possibility of changing any material 
into any other. 

Although the atomistic view was not altogether abandoned, it found 
few supporters during the period 300 A.D. to about 1600 A.D. The atoms 
of Leucippus and Democritus moved through empty space, devoid of 
spirit, and with no definite plan or purpose. Such an idea remained 
contrary to the beliefs of the major religions. Just as the Athenians did 
in the time of Plato and Aristotle, the later Christian, Hebrew, and 
Moslem theologians considered atomists to be atheistic and "mate- 
rialistic" because they claimed that everything in the universe can be 
explained in terms of matter and motion. 

About 300 or 400 years after Aristotle, a kind of research called 
alchemy appeared in the Near and Far East. Alchemy in the Near East 
was a combination of Aristotle's ideas about matter with methods of 
treating ores and metals. One of the aims of the alchemists was to 
change, or "transmute" ordinary metals into precious metals. Although 
they failed to do this, the alchemists found and studied many of the 
properties of substances that are now classified as chemical properties. 
They invented some pieces of chemical apparatus, such as reaction 
vessels and distillation flasks, that (in modern form) are still common 
in chemical laboratories. They studied such processes as calcination, 
distillation, fermentation, and sublimation. In this sense alchemy may 
be regarded as the chemistry of the Middle Ages. But alchemy left 
unsolved the fundamental questions. At the opening of the eighteenth 
century the most important of these questions were: (1) what is a 
chemical element; (2) what is the nature of chemical composition and 
chemical change, especially burning; and (3) what is the chemical 



Prologue 



nature of the so-called elements, Earth, Air, Fire and Water. Until these 
questions were answered, it was impossible to make real progress in 
finding out the structure of matter. One result was that the "scientific 
revolution" of the seventeenth century, which clarified the problems of 
astronomy and mechanics, did not include chemistry. 

During the seventeenth century, however, some forward steps were 
made which supplied a basis for future progress on the problem of 
matter. The Copernican and Newtonian revolutions undermined the 
authority of Aristotle to such an extent that his ideas about matter 
were also more easily questioned. Atomic concepts were revived, and 
offered a way of looking at things that was very different from Aristotle's 
ideas. As a result, theories involving atoms (or "particles" or "corpus- 
cles") were again considered seriously. Boyle's models were based on 
the idea of "gas particles." Newton also discussed the behavior of a 
gas (and even of light) by supposing it to consist of particles. In 
addition, there was now a successful science of mechanics, through 
which one might hope to describe how the atoms interacted with each 
other. Thus the stage was set for a general revival of atomic theory. 

In the eighteenth century, chemistry became more quantitative; 
weighing in particular was done more frequently and more carefully. 
New substances were isolated and their properties examined. The 
attitude that grew up in the latter half of the century was exemplified by 
that of Henry Cavendish (1731-1810), who, according to a biographer, 
regarded the universe as consisting 



One of those who contributed 
greatly to the revival of atomism 
was Pierre Gassendi (1592 — 1655), a 
French priest and philosopher. He 
avoided the criticism of atomism 
as atheistic by saying that God also 
created the atoms and bestowed 
motion upon them. Gassendi ac- 
cepted the physical explanations of 
the atomists, but rejected their dis- 
belief in the immortality of the soul 
and in Divine Providence. He was 
thus able to provide a philosophical 
justification of atomism which met 
some of the serious religious 
objections. 



. . . solely of a multitude of objects which could be weighed, 
numbered, and measured; and the vocation to which he con- 
sidered himself called was to weigh, number, and measure 
as many of those objects as his alloted threescore years and 
ten would permit. ... He weighed the Earth; he analysed the 
Air; he discovered the compound nature of Water; he noted 
with numerical precision the obscure actions of the ancient 
element Fire. 



It was Cavendish, remember, who 
designed the sensitive torsional 
balance that made it possible to 
find a value for the gravitational 
constant G. (Text Sec. 8.8.) 



Eighteenth-century chemistry reached its peak in the work of 
Antoine Lavoisier (1743-1794), who worked out the modern views of 
combustion, established the law of conservation of mass, explained the 
elementary nature of hydrogen and oxygen, and the composition of 
water, and above all emphasized the quantitative aspects of chemistry. 
His famous book, Traite Elementaire de Chimie (or Elements of 
Chemistry), published in 1789, established chemistry as a modern 
science. In it, he analyzed the idea of an element in a way which is very 
close to our modern views: 

... if, by the term elements we mean to express those simple 
and indivisible atoms of which matter is composed, it is ex- 
tremely probable that we know nothing at all about them; but 
if we apply the term elements, or principles of bodies, to 
express our idea of the last point which analysis is capable 
of reaching, we must admit as elements all the substances 
into which we are capable, by any means, to reduce bodies 
by decomposition. Not that we are entitled to affirm that 



Lavoisier's work on the conserva- 
tion of mass was described in Text 
Chapter 9. 



Models of the Atom 



T R A I T E 

ELEMENTAIRE 

D E CHI MIE, 

PRfeSENTt DANS UN ORDRE NOUVEAU 

ET d'aPR^S LES D^COUVERTES UODERNES} 

Avec Figures : 

Tar M. Lavo ist EA , de CAcaJimU dit 
Sc'uncts, de la Socieii RoyaU de Medccme , dtt 
Socieus d' Agriculture de Paris O d'OrUan.s , de 
la Societe RoyaU de Londres , de I'lnftiiut de 
Bologiie , de la Societe Helvitique de Bajle , dt 
celtes de PhUadelphle , Harlem , Manchefler , 
Padoue , &c. 



|. 



TOME PREMIER. 




A PARIS, 

Ch« CuCHET, Libraire, rue & hotel Serpente. 

M. D C C. L X X X I X. 

Sma It PriviUgt de TAcaidrnit dtt Scieru-ei 6 dt U 
SociM RoyaU dt Midteint 

Title page of Lavoisier's Iratte Ele- 
mentaire de Chimie (1789) 



these substances we consider as simple may not be com- 
pounded of two, or even of a greater number of principles; 
but since these principles cannot be separated, or rather 
since we have not hitherto discovered the means of sepa- 
rating them, they act with regard to us as simple substances, 
and we ought never to suppose them compounded until ex- 
periment and observation have proved them to be so. 

During the latter half of the eighteenth century and the early years of 
the nineteenth century great progress was made in chemistry because 
of the increasing use of quantitative methods. Chemists found out more 
and more about the composition of substances. They separated many 
elements and showed that nearly all substances are compounds— 
combinations of a fairly small number of chemical elements. They 
learned a great deal about how elements combine to form compounds 
and how compounds can be broken down into the elements of which 
they are composed. This information made it possible for chemists to 
establish many empirical laws of chemical combination. Then chemists 
sought an explanation for these laws. 

During the first ten years of the nineteenth century, the English 
chemist John Dalton introduced a modified form of the old Greek 
atomic theory to account for the laws of chemical combination. It is 
here that the modern story of the atom begins. Dalton's atomic theory 
was an improvement over that of the Greeks because it opened the 
way for the quantitative study of the atom in the nineteenth century. 
Today the existence of the atom is no longer a topic of speculation. 
There are many kinds of experimental evidence, not only for the 
existence of atoms but also for their inner structure. In this unit we 
shall trace the discoveries and ideas that provided this evidence. 

The first convincing modern idea of the atom came from chemistry. 
We shall, therefore, start with chemistry in the early years of the nine- 
teenth century; this is the subject of Chapter 17. Then we shall see that 
chemistry raised certain questions about atoms which could only be 
answered by physics. Physical evidence, accumulated in the nineteenth 
century and the early years of the twentieth century, made it possible 
to propose models for the structure of atoms. This evidence will be 
discussed in Chapters 18 and 19. Some of the latest ideas about atomic 
theory will then be discussed in Chapter 20. 




Chemical laboratory of the 18th century 



17.1 Dalton's atomic theory and the laws of chemical combination 11 

17.2 The atomic masses of the elements 14 

17.3 Other properties of the elements: combining capacity 16 

17.4 The search for order and regularity among the elements 18 

17.5 Mendeleev's periodic table of the elements 19 

17.6 The modern periodic table 23 

17.7 Electricity and matter: qualitative studies 25 

17.8 Electricity and matter: quantitative studies 28 



OCD^O® 

oo®®© 



©®©®o 



Dalton's symbols for 'elements " (1808) 



CHAPTER SEVENTEEN 



The Chemical Basis of 
Atomic Theory 



17.1 Dalton's atomic theory and the laws of chemical combination 

The atomic theory of John Dalton appeared in his treatise, A 
New System of Chemical Philosophy, published in two parts, in 
1808 and 1810. The main postulates of his theory were: 

(1) Matter consists of indivisible atoms. 

. . . matter, though divisible in an extreme degree, is 
nevertheless not infinitely divisible. That is, there must 
be some point beyond which we cannot go in the division 
of matter. The existence of these ultimate particles of 
matter can scarcely be doubted, though they are probably 
much too small ever to be exhibited by microscopic im- 
provements. I have chosen the word atom to signify these 
ultimate particles. . . . 

(2) Each element consists of a characteristic kind of identical 
atoms. There are consequently as many different kinds of atoms as 
there are elements. The atoms of an element "are perfectly alike in 
weight and figure, etc." 

(3) Atoms are unchangeable. 

(4) When different elements combine to form a compound, the 
smallest portion of the compound consists of a grouping of a definite 
number of atoms of each element. 

(5) In chemical reactions, atoms are neither created nor 
destroyed, but only rearranged. 

Dalton's theory really grew out of his interest in meteorology 
and his research on the composition of the atmosphere. He tried to 
explain many of the physical properties of gases in terms of atoms 
(for example, the fact that gases readily mix, and the fact that the 
pressures of two gases add simply when both are combined in a 
fixed enclosure). He thought of the atoms of different elements as 
being different in size and in mass. In keeping with the quantitative 
spirit of the time, he tried to determine the numerical values for their 
relative masses. This was a crucial step forward. But before consider- 
ing how to determine the relative masses of atoms of the different 
elements, let us see how Dalton's postulates make it possible to ac- 
count for the experimentally known laws of chemical combination. 

11 



SG 17.1 



Meteorology is a science that deals 
with the atmosphere and its 
phenomena — weather forecasting 
is one branch of meteorology. 



12 



The Chemical Basis of the Atomic Theory 



Recall that empirical laws (such as 
these, or Kepler's laws of planetary 
motion) are just summaries of 
experimentally observed facts. They 
cry out for some theoretical base 
from which they can be shown to 
follow as necessary consequences. 
Physical science looks for these 
deeper necessities that describe 
nature, and is not satisfied with 
mere summaries of observation, 
useful though these may be initially. 



Dalton's atomic theory accounts in a simple and direct way for 
the law of conservation of mass. According to Dalton's theory 
(postulates 4 and 5), chemical changes are only the rearrangements 
of unions of atoms. Since atoms are unchangeable (according to 
postulate 3) rearranging them cannot change their masses. Hence, 
the total mass of all the atoms before the reaction must equal the 
total mass of all the atoms after the reaction. 

Another well known empirical law which could be explained 
easily with Dalton's theory is the law of definite proportions. This 
law states that any particular chemical compound always contains 
the same elements, and they are united in the same proportions of 
weight. For example, the ratio of the masses of oxygen and hy- 
drogen which combine to form water is always 7.94 to 1 : 

mass of oxygen _ 7.94 
mass of hydrogen 1 

If there is more of one element present than is needed for full 
combination in a chemical reaction, say 10 grams of oxygen and 
one gram of hydrogen, only 7.94 grams of oxygen will combine 
with the hydrogen. The rest of the oxygen, 2.06 grams, remains 
uncombined. 

The fact that elements combine in fixed proportions implies that 
each chemical compound will also decompose into definite propor- 
tions of elements. For example, the decomposition of sodium 
chloride (common salt) always gives the results: 39 percent 
sodium and 61 percent chlorine by weight. 

Now let us see how Dalton's model can be applied to a chemical 
reaction, say, to the formation of water from oxygen and hydrogen. 
According to Dalton's second postulate, all the atoms of oxygen 
have the same mass; and all the atoms of hydrogen have the same 
mass, which is different from the mass of the oxygen atoms. To 
express the total mass of oxygen entering into the reaction, we 
multiply the mass of a single oxygen atom by the number of oxygen 
atoms: 



SG 17.2, 17.3 



„ / mass of \ 

mass of oxygen = (oxygen atom ) 



number of ^ 
oxygen atoms, 



Similarly, for the total mass of hydrogen entering into the reaction: 

„ , , / mass of \ / number of \ 

mass of hydrogen - (^hydrogen atom] ^ \hydrogen atoms) 

We can find the ratio of the mass of oxygen to the mass of hydrogen 
by dividing the first equation by the second equation as shown at 
the top of the next page: 



Section 17.1 



13 



mass of 
mass of oxygen _ oxygen atom 



mass of hydrogen 



mass of 
hydrogen atom 



number of 

oxygen atoms 

number of 
hydrogen atoms 



If the masses of the atoms do not change (postulate 3), the first 
ratio on the right side of the equation has a certain unchangeable 
value. According to postulate 4, if the smallest portion of the com- 
pound water consists of a definite number of atoms of each element 
(postulate 4), the second ratio on the right side of the equation has 
a certain unchangeable value also. The product of the two ratios on 
the right side will always have the same value. This equation, 
based on an atomic theory, thus tells us that the ratio of the 
masses of oxygen and hydrogen that combine to form water will 
always have the same definite value. But this is just what the 
experimental law of definite proportions says. Dalton's theory 
accounts for this law of chemical combination— and this success 
tends to confirm Dalton's conception. Dalton's theory was also 
consistent with another empirical law of chemical combination, the 
law of multiple proportion. For some combinations of elements 
there are a set of possible values for their proportions in forming a 



SG 17.4 








^J^3r^ 








A page from Dalton's notebook, 
showing his representation of two 
adjacent atoms (top) and of a mole- 
cule or compound atom' (bottom) 



John Dalton (1766-1844). His first 
love was meteorology, and he kept 
careful daily weather records for 
46 years— a total of 200,000 observa- 
tions. He was the first to describe 
color blindness in a publication and 
was color-blind himself, not exactly 
an advantage for a chemist who had 
to see color changes in chemicals. 
(His color blindness may help to 
explain why Dalton is said to have 
been a rather clumsy experimenter.) 
However, his accomplishments rest 
not on successful experiments, but 
on his ingenious interpretation of 
the known results of others. Dalton's 
notion that all elements were com- 
posed of extremely tiny, indivisible 
and indestructible atoms, and that 
all substances are composed of 
combinations of these atoms was 
accepted soon by most chemists 
with surprisingly little opposition. 
There were many attempts to honor 
him, but being a Quaker he shunned 
any form of glory. When he received 
a doctor's degree from Oxford, his 
colleagues wanted to present him to 
King William IV. He had always 
resisted such a presentation be- 
cause he would not wear court 
dress. However, his Oxford robes 
satisfied the protocol. 




14 



The Chemical Basis of the Atomic Theory 




Dalton's visualization of the com- 
position of various compounds. 



set of compounds. Dalton showed that these cases could all be 
accounted for by different combinations of whole numbers of atoms. 

There are other laws of chemical combination which are 
explained by Dalton's theory. Because the argument would be 
lengthy and relatively little that is new would be added, we shall not 
elaborate on them here. 

Dalton's interpretation of the experimental facts of chemical 
combination made possible several important conclusions: (1) that 
the difference between one chemical element and another would 
have to be described in terms of the differences between the atoms 
of which these elements were made up; (2) that there were, there- 
fore, as many different types of atoms as there were chemical 
elements; (3) that chemical combination was the union of atoms of 
different elements into molecules of compounds. Dalton's theory 
also implied that the analysis of a large number of chemical com- 
pounds could make it possible to assign relative mass values to 
the atoms of different elements. This possibility will be discussed 
in the next section. 

Q1 What did Dalton assume about the atoms of an element? 
Q2 What two experimental laws did Dalton's theory explain? 
What follows from these successes? 



17.2 The atomic masses of the elements 



The first good estimates of 
molecular size came from the kinetic 
theory of gases and indicated that 
atoms (or molecules) had diameters 
of the order of 10'" meter. Atoms 
are thus much too small for ordinary 
mass measurements to be made on 
single atoms. 



SG 17.5 
SG 17.6 



One of the most important concepts to come from Dalton's work 
is that of atomic mass and the possibility of determining numerical 
values for the masses of the atoms of different elements. Dalton 
had no idea of the actual absolute mass of individual atoms. 
Reasonably good estimates of the size of atoms did not appear until 
about 50 years after Dalton published his theory. Nevertheless, as 
Dalton was able to show, relative values of atomic masses can be 
found by using the law of definite proportions and experimental 
data on chemical reactions. 

To see how this could be done we return to the case of water, 
for which, the ratio of the mass of oxygen to the mass of hydrogen 
is found by experiment to be 7.94:1. If one knew how many atoms 
of oxygen and hydrogen are contained in a molecule of water one 
could calculate the ratio of the mass of the oxygen atom to the mass 
of the hydrogen atom. But Dalton didn't know the numbers of 
oxygen and hydrogen atoms in a molecule of water so he made an 
assumption. As is done often, Dalton made the simplest possible 
assumption: that a molecule of water consists of one atom of 
oxygen combined with one atom of hydrogen. By this reasoning 
Dalton concluded that the oxygen atom is 7.94 times more massive 
than the hydrogen atom. Actually, the simplest assumption proved 
in this case to be incorrect: two atoms of hydrogen combine with 
one atom of oxygen to make a molecule of water. The oxygen atom 
has 7.94 times the mass of the two hydrogen atoms, and therefore 
has 15.88 times the mass of a single hydrogen atom. 

More generally, Dalton assumed that when only one compound 



Section 17.2 



15 



of any two elements is known to exist, molecules of the compound 
always consist of one atom of each. With this assumption Dalton 
could find values for the relative masses of different atoms — but 
later work showed that Dalton's assumption of one-to-one ratios was 
often as incorrect as it was for water. By studying the composition 
of water as well as many other chemical compounds, Dalton found 
that the hydrogen atom appeared to have a smaller mass than the 
atoms of any other element. Therefore, he proposed to express the 
masses of atoms of all other elements relative to the mass of the 
hydrogen atom. Dalton defined the atomic mass of an element as 
the mass of an atom of that element compared to the mass of a 
hydrogen atom. For example, the masses of chlorine and hydrogen 
gas that react to form hydrogen chloride (the only hydrogen and 
chlorine compound) are in the ratio of about 35V2 to 1 ; therefore 
the chlorine atom would be supposed to have an atomic mass of 
35 V2 atomic mass units. This definition could be used by chemists 
in the nineteenth century even before the actual values of the 
masses of individual atoms (say in kilograms) could be measured 
directly. 

During the nineteenth century chemists extended and improved 
Dalton's ideas. They studied many chemical reactions quantita- 
tively, and developed highly accurate methods for determining 
relative atomic and molecular masses. Because oxygen combined 
readily with many other elements chemists decided to use oxygen 
rather than hydrogen as the standard for atomic masses. Oxygen 
was assigned an atomic mass of 16 so that hydrogen would have 
an atomic mass close to one. The atomic masses of other elements 
could be obtained by applying the laws of chemical combination to 
the compounds of the elements with oxygen. Throughout the nine- 
teenth century more and more elements were identified and their 
atomic masses determined. For example, the table on the next page 
lists 63 elements found by 1872, together with the modern values 
for the atomic masses. This table contains much valuable informa- 
tion, which we shall consider at greater length in Sec. 17.4. (The 
special marks on the table— circles and rectangles— will be useful 
then.) 

Q3 Was the simplest chemical formula for the composition of 
a molecule necessarily the correct one? 

Q4 Why did Dalton choose hydrogen as the unit of atomic mass? 





SG 17.7 
SG 17.8 



The system of atomic masses used 
in modern physical science is based 
on this principle, although it differs 
in details (and the standard for 
comparison by international agree- 
ment is now carbon instead of 
hydrogen or oxygen.) 



The progress made in identifying 
elements in the 19th century may 
be seen in the following table. 

Total number of 



Year 


elements identified 


1720 


14 


1740 


15 


1760 


17 


1780 


21 


1800 


31 


1820 


49 


1840 


56 


1860 


60 


1880 


69 


1900 


83 



Some of the current representations 
of a water molecule. 



16 



The Chemical Basis of the Atomic Theory 



Elements known by 1872, in order of 
increasing relative atomic mass. 







Elements known by 1872 










Atomic 






Atomic 


Name 
hydrogen 


Symbol 
H 


Mass* 
1.0 


Name 


Symbol 


Mass* 


cadmium 


Cd 


112.4 


D lithium 


Li 


6.9 


indium 


In 


114.8(113) 


beryllium 


Be 


9.0 


tin 


Sn 


118.7 


boron 


B 


10.8 


antimony 


Sb 


121.7 


carbon 


C 


12.0 


tellurium 


Te 


127.6(125) 


nitrogen 


N 


14.0 


O iodine 


1 


126.9 


oxygen 





16.0 


D cesium 


Cs 


132.9 


O fluorine 


F 


19.0 


barium 


Ba 


137.3 


D sodium 


Na 


23.0 


didymium(**) 


Di 


(138) 


magnesium 


Mg 


24.3 


cerium 


Ce 


140.1 


aluminum 


Al 


27.0 


erbium 


Er 


167.3(178) 


silicon 


Si 


28.1 


lanthanum 


La 


138.9(180) 


phosphorus 


P 


31.0 


tantalum 


Ta 


180.9(182) 


sulfur 


S 


32.1 


tungsten 


W 


183.9 


O chlorine 


CI 


35.5 


osmium 


Os 


190.2(195) 


D potassium 


K 


39.1 


iridium 


Ir 


192.2(197) 


calcium 


Ca 


40.1 


platinum 


Pt 


195.1(198) 


titanium 


Ti 


47.9 


gold 


Au 


197.0(199) 


vanadium 


V 


50.9 


mercury 


Hg 


200.6 


chromium 


Cr 


52.0 


thallium 


TI 


204.4 


manganese 


Mn 


54.9 


lead 


Pb 


207.2 


iron 


Fe 


55.8 


bismuth 


Bi 


209.0 


cobalt 


Co 


58.9 


thorium 


Th 


232.0 


nickel 


Ni 


58.7 


uranium 


U 


238.0(240) 


copper 


Cu 


63.5 








zinc 


Zn 


65.4 








arsenic 
selenium 


As 

Se 


74.9 

79 


D alkaline metals 






O bromine 
n rubidium 


Br 
Rb 


79.9 
85.5 


O halogens 






strontium 


Sr 


87.6 


•Atomic masses g 


ven are modern values. Where 1 


yttrium 


Yt 


88.9 


these differ greatly from those 


accepted In 


zirconium 


Zr 


91.2 


1872. the old val 


ues are given In 


parentheses. 


niobium 
molybdenum 
ruthenium 
rhodium 


Nb 
Mo 
Ru 
Rh 


92.9 

95.9 
101.1(104) 
102.9(104) 


•*Didymium (Di) was later shown to be a mixture 
of two different elements, namely praseodym- 
ium (Pr; atomic mass 140.9) and neodymium 
(Nd: atomic mass 144.2). 


palladium 


Pd 


106.4 








silver 


Ag 


107.9 









The standard international chemical 
symbols are derived from languages 
other than English. The Latin name 
for sodium is natrium, hence the 
symbol is Na. 



17.3 Other properties of the elements: combining capacity 

As a result of studies of chemical compounds, chemists were 
able to design chemical formulas that indicate by a kind of symbolic 
shorthand the number of atoms in each molecule of a compound. 
For example, water has the familiar formula H2O, which indicates 
that a molecule of water contains two atoms of hydrogen (H) and 
one atom of oxygen (O). (Dalton thought it was HO.) Hydrogen 
chloride (hydrochloric acid when dissolved in water) had the formula 
HCl, signifying that one atom of hydrogen combines with one atom 
of chlorine (CI). Common salt may be represented by the formula 
NaCl; this indicates that one atom of sodium (Na) combines with 
one atom of chlorine to form one molecule of sodium chloride — 
common table salt. Another salt, calcium chloride (often used to 
melt ice on roads), has the formula CaCl,; one atom of calcium 
(Ca) combined with two atoms of chlorine to form this compound. 
Carbon tetrachloride, a common compound of chlorine used for dry 



Section 17.3 



17 



cleaning, has the formula CCI4 where C stands for a carbon atom 
that combines with four chlorine atoms. Another common sub- 
stance, ammonia, has the formula NH3; in this case one atom of 
nitrogen (N) combines with three atoms of hydrogen. 

There are especially significant examples of combining capacity 
among the gaseous elements. For example, the gas hydrogen occurs 
in nature in the form of molecules, each of which contains two 
hydrogen atoms. The molecule of hydrogen consists of two atoms 
and has the formula Hg. Similarly, chlorine has the molecular 
formula CI2. Chemical analysis always gives these results. It would 
be inconsistent with experiment to assign the formula H3 or H4 to a 
molecule of hydrogen, or CI, CI3, or CI4 to a molecule of chlorine. 
Moreover, each element shows great consistency in its combining 
proportions with other elements. For example, calcium and oxygen 
seem to have twice the combining capacity of hydrogen and 
chlorine — one atom of hydrogen is enough for one atom of chlorine, 
but two hydrogens are needed to combine with oxygen and two 
chlorines are required to combine with calcium. 

The above examples indicate that different elements have 
different capacities for chemical combination. It appeared that 
each species of atom is characterized by some definite combining 
capacity (which is sometimes called valence). At one time combin- 
ing capacity was considered as though it might represent the 
number of "hooks" possessed by a given atom, and thus the number 
of links that an atom could form with others of the same or different 
species. If hydrogen and chlorine atoms each had just one hook 
(that is, a combining capacity of 1) we would readily understand 
how it is that molecules like H2, CI2, and HCl are stable, while 
certain other species like H3, H2CI, HCI2, and CI3 don't exist at all. 
And if the hydrogen atom is thus assigned a combining capacity 
of 1, the formula of water (H2O) requires that the oxygen atom has 
two hooks or a combining capacity of 2. The formula NH3 for 
ammonia leads us to assign a combining capacity of three to nitro- 
gen; the formula CH4 for methane leads us to assign a capacity of 
4 to carbon; and so on. Proceeding in this fashion, we can assign 
a combining capacity number to each of the known elements. 
Sometimes complications arise as, for example, in the case of 
sulfur. In H2S the sulfur atom seems to have a combining capacity 
of 2, but in such a compound as sulfur trioxide (SO3), sulfur seems 
to have a combining capacity of 6. In this case and others, then, 
we may have to assign two (or even more) different possible capaci- 
ties to an element. At the other extreme of possibilities are those 
elements like helium and neon which have not been found as parts 
of compounds — and to these elements we may appropriately assign 
a combining capacity of zero. 

The atomic mass and combining capacities are numbers that 
can be assigned to an element; they are "numerical characteriza- 
tions" of the atoms of the element. There are other numbers which 
represent properties of the atoms of the elements, but atomic mass 
and combining capacity were the two most important to nineteenth- 



In the thirteenth century the 
theologian and philosopher Albert 
Magnus (Albert the Great) intro- 
duced the idea of affinity to denote 
an attractive force between sub- 
stances that causes them to enter 
into chemical combination. It was 
not until 600 years later that it 
became possible to replace this 
qualitative notion by quantitative 
concepts. Combining capacity is one 
of these concepts. 




Representations of molecules formed 
from "atoms with hooks. " Of course 
this conception is just a guide to the 
imagination. There are no such me- 
chanical linkages among atoms. 



SG 17.9 



Since oxygen combines with a 
greater variety of elements, 
combining capacity of an element 
was commonly determined by its 
combination with oxygen. For 
example, an element X that is found 
to have an "oxide formula" XO 
would have a combining capacity 
equal to oxygen's: 2. 



18 



The Chemical Basis of the Atomic Theory 



century chemists. These numbers were used in attempts to find 
order and regularity among the elements— a problem which will be 
discussed in the next section. 

Q5 At this point we have two numbers which are character- 
istic of the atoms of an element. What are they? 

Q6 Assume the combining capacity of oxygen is 2. In each of 
the following molecules, give the combining capacity of the atoms 
other than oxygen: CO, CO2, N2O5, Na^O and MnO. 



There were also many false trails. 
Thus in 1829 the German chemist 
Johann Wolfgang Dbbereiner 
noticed that elements often formed 
groups of three members with 
similar chemical properties. He 
identified the "triads": chlorine, 
bromine and iodine: calcium, 
strontium and barium: sulfur, 
selenium and tellurium: iron, cobalt 
and manganese. In each "triad," the 
atomic mass of the middle member 
was approximately the arithmetical 
average of the masses of the other 
two elements. But all this turned 
out to be of little significance. 



17.4 The search for order and regularity among the elements 

By 1872 sixty-three elements were known; they are listed in 
the table on p. 16 with their atomic masses and chemical symbols. 
Sixty-three elements are many more than Aristotle's four: and 
chemists tried to make things simpler by looking for ways of 
organizing what they had learned about the elements. They tried to 
find relationships among the elements — a quest somewhat like 
Kepler's earlier search for rules that would relate the motions of 
the planets of the solar system. 

In addition to relative atomic masses, many other properties of 
the elements and their compounds were determined. Among these 
properties were: melting point, boiling point, density, electrical 
conductivity, heat conductivity, heat capacity (the amount of heat 
needed to change the temperature of a sample of a substance by 1 
C) hardness, and refractive index. The result was that by 1870 an 
enormous amount of information was available about a large 
number of elements and their compounds. 

It was the English chemist J. A. R. Newlands who pointed out 
in 1865 that the elements could usefully be listed simply in the 
order of increasing atomic mass. When this was done, a curious fact 
became evident; similar chemical and physical properties appeared 
over and over again in the list. Newlands believed that there was 
in the whole list a periodic recurrence of elements with similar 
properties: ". . . the eighth element, starting from a given one, is a 
kind of repetition of the first, like the eighth note in an octave of 
music." Newlands' proposal was met with skepticism. One chemist 
even suggested that Newlands might look for a similar pattern in 
an alphabetical list of elements. 

Yet, existent relationships did indeed appear. There seemed to 
be families of elements with similar properties. One such family 
consists of the so-called alkali metals— hihium. sodium, potassium, 
rubidium and cesium. We have identified these elements by a D in 
the table on p. 16. All these metals are similar physically. They are 
soft and have low melting points. The densities of these metals are 
very low; in fact, lithium, sodium and potassium are less dense 
than water. The alkali metals are also similar chemically. They all 
have combining capacity 1. They all combine with the same other 
elements to form similar compounds. They form compounds readily 
with other elements, and so are said to be highly "reactive"; conse- 



Section 17.5 



19 



quently, they do not occur free in nature, but are always found in 
combination with other elements. 

Another family of elements, called the halogens, includes 
fluorine, chlorine, bromine and iodine. The halogens may be found 
in the table on p. 16 identified by small circles. 

Although these four halogen elements exhibit some marked 
dissimilarities (for example, at 25 °C the first two are gases, the 
third a liquid, the last a volatile solid), they also have much in com- 
mon. They all combine violently with many metals to form white, 
crystalline salts (halogen means "salt-former"); those salts have 
similar formulas, such as NaF, NaCl, NaBr and Nal, or MgFz, 
MgCla, MgBra and Mgla. From much similar evidence chemists 
noticed that all four members of the family seem to have the same 
valence with respect to any other particular element. All four ele- 
ments from simple compounds with hydrogen (HF, HCI, HBr, HI) 
which dissolve in water and form acids. All four, under ordinary 
conditions, exist as diatomic molecules; that is, each molecule 
contains two atoms. But notice: each halogen precedes an alkali 
metal in the list, although the listing was ordered simply by 
increasing atomic mass. It is as if some new pattern is coming out 
of a jig-saw puzzle. 

The elements which follow the alkali metals in the list also 
form a family, the one called the alkaline earth family; this family 
includes beryllium, magnesium, calcium, strontium and barium. 
Their melting points and densities are higher than those of the 
alkali metals. The alkaline earths all have a valence of two. They 
react easily with many elements, but not as easily as do the alkali 
metals. 

Recognition of the existence of these f amihes of elements 
encouraged chemists to look for a systematic way of arranging the 
elements so that the members of a family would group together. 
Many schemes were suggested; the most successful and far reach- 
ing was that of the Russian chemist D. I. Mendeleev. 

Q7 What are those properties of elements which recur system- 
atically with increasing atomic mass? 

17.5 Mendeleev's periodic table of the elements 

Mendeleev, examining the properties of the elements, reached 
the conclusion that the atomic mass was the fundamental "numeri- 
cal characterization" of each element. He discovered that if the 
elements were arranged in a table in the order of their atomic 
masses— but in a special way, a bit like cards laid out in the game 
of solitaire— the different chemical families turned out to fall into 
the different vertical columns of the table. There was no evident 
physical reason why this should be so, but it was a hint toward 
some remarkable connection among all elements. 



Modern chemists use the word 
'valence" less and less in the sense 
we use it here. They are more likely 
to discuss "combining number" or 
"oxidation number." Even the 
idea of a definite valence number 
for an element has changed, since 
combining properties can be dif- 
ferent under different conditions. 



Li 7 


Be 9.4 


B 11 


C 12 


N 14 


O 16 


F 19 


Ma 23 


Mg 24 


Al 27.4 


Si 28 


P 31 


S 32 


CI 35.3 


K39 


Ca 40 




Ti50 


V51 




...etc. 



Although the properties of elements 
do recur periodically with increasing 
atomic weight, Newlands had not 
realized that the separation of 
similar elements in the list becomes 
greater for the heavier elements. 



In this table, hydrogen was omitted 
because of its unique properties. 
Helium and the other elements of 
the family of "noble gases" had not 
yet been discovered. 



20 



The Chemical Basis of the Atomic Theory 




Dmitri Ivanovich Mendeleev (men- 
deh-lay>'-ef) (1834-1907) received his 
first science lessons from a political 
prisoner who had been previously 
banished to Siberia by the Czar. Un- 
able to get into college in Moscow, he 
was accepted in St. Petersburg, where 
a friend of his father had some in- 
fluence. In 1866 he became a profes- 
sor of chemistry there: in 1869 he pub- 
lished his first table of the sixty-three 
then known elements arranged ac- 
cording to increasing atomic mass. 
His paper was translated into German 
at once and so became known to sci- 
entists everywhere. Mendeleev came 
to the United States, where he studied 
the oil fields of Pennsylvania in order 
to advise his country on the develop- 
ment of the Caucasian resources. His 
liberal political views caused him 
often to be in trouble with the oppres- 
sive regime of the Czars. 



As in the table on the preceding page, Mendeleev set down 
seven elements, from lithium to fluorine, in order of increasing 
atomic masses, and then put the next seven, from sodium to 
chlorine, in the second row. The periodicity of chemical behavior is 
already evident before we go on to write the third row. In the first 
column on the left are the first two alkali metals. In the seventh 
column are the first two members of the family of halogens. Indeed, 
within each of the columns the elements are chemically similar, 
having, for example, the same characteristic combining capacity. 

When Mendeleev added a third row of elements, potassium (K) 
came below elements Li and Na, which are members of the same 
family and have the same oxide formula, X2O, and the same 
combining capacity 1. Next in the row is Ca, oxide formula XO as 
with Mg and Be above it. In the next space to the right, the element 
of next higher atomic mass should appear. Of the elements known 
at the time, the next heavier was titanium (Ti), and it was placed in 
this space, right below aluminum (Al) and boron (B) by various 
workers who had tried to develop such schemes. Mendeleev, how- 
ever, recognized that titanium (Ti) has chemical properties similar 
to those of carbon (C) and silicon (Si). For example, a pigment, 
titanium white, Ti02, has a formula comparable to CO2 and Si02. 
Therefore he concluded that titanium should be put in the fourth 
column. Then, if all this is not just a game but has deeper meaning. 
Mendeleev thought, there should exist a hitherto unsuspected ele- 
ment with atomic mass between that of calcium (40) and titanium 
(50), and with an oxide X2O3. Here was a definite prediction. 
Mendeleev found also other cases of this sort among the remaining 
elements when they were added to this table of elements with due 
regard to the family properties of elements in each column. 

The table below is Mendeleev's periodic system, or "periodic 
table" of the elements, as proposed in 1872. He distributed the 63 
elements then known (with 5 in doubt) in 12 horizontal rows or 
series, starting with hydrogen in a unique separated position at the 
top left, and ending with uranium at the bottom right. All elements 



Periodic classification of the ele- 
ments; Mendeleev, 1872. 



GROUP—* 


I 


II 


Ill 


IV 


V i VI 


VII VIII 


Higher oxides 
and hydrides 


R2O 


RO 


RjOa 


RO2 
H4R 


R205 
H3R 


RO3 
H2R 


R207 

HR 


RO, 


Ul 


1 


H(l) 
















2 


Li(7) 


Be(9.4) 


B(ll) 


C(12) 


N(14) 


0(16) 


F(19) 




3 


Na(23) 


Mg(24) 


Al(27.3) 


Si(28) 


P(3I) 


S(32) 


Cl(35.5) 




4 


K(39) 


Ca(40) 


-(44) 


Ti(48) 


V(SI) 


Cr(52) 


Mn(55) 


Fe(S6), Co(59). 
Ni(59). Cu(63) 


5 


iCu(63)l 


Zn(6S) 


-(68) 


-(72) 


A«(75) 


Se(78) 


Br{80) 




6 


Rb(85) 


Sr(87) 


?Yt(88) 


Zr(90) 


Nb(94) 


Mo(96) 


-(100) 


Ru(104),Rh(104), 
Pd(106)..\«(108) 


7 


lAg(108)! 


Cd(112) 


ln(ll3) 


Sn(118) 


Sb(122) 


Te(l25) 


1(127) 




8 


C8(133) 


Ba(I37) 


?Di(138) 


?Ce(140) 













9 

























10 








?Er(I78) 


?U(I80) 


Ta(l82) 


W(184) 





08(195), Ir(197), 
Pt(196). Au(199) 


11 


|Au(199)l 


Hg(200) 


Tl(204) 


Pb(207) 


Bi(208) 










12 










Th(231) 





U(240) 







Section 17.5 



21 



were listed in order of increasing atomic mass (Mendeleev's values 
given in parentheses), but were so placed that elements with similar 
chemical properties are in the same vertical column or group. 
Thus in Group VII are all the halogens; in Group VIII, only metals 
that can easily be drawn into wires; in Groups I and II, metals of 
low densities and melting points; and in I, the family of alkali 
metals. 

The table at the bottom of the previous page shows many gaps. 
Also, not all horizontal rows (series) have equally many elements. 
Nonetheless, the table revealed an important generalization; 
according to Mendeleev, 

For a true comprehension of the matter it is very impor- 
tant to see that all aspects of the distribution of the 
elements according to the order of their atomic weights 
express essentially one and the same fundamental depen- 
dence — periodic properties. 

There is gradual change in physical and chemical properties within 
each vertical group, but there is a more striking periodic change of 
properties in the horizontal sequence. 

This periodic law is the heart of the matter and a real novelty. 
Perhaps we can best illustrate it as Lothar Meyer did, by drawing 
a graph that shows the value of some measureable physical quantity 
as a function of atomic mass. Below is a plot of the relative 
atomic volumes of the elements, the space taken up by an atom in 
the liquid or solid state. Each circled point on this graph represents 
an element; a few of the points have been labeled with the 
identifying chemical symbols. Viewed as a whole, the graph 
demonstrates a striking periodicity: as the mass increases starting 
with Li, the atomic volume first drops, then increases to a sharp 
maximum, drops off again and increases to another sharp maximum, 
and so on. And at the successive peaks we find Li, Na, K, Rb, and 
Cs, the members of the family of alkali metals. On the left-hand 
side of each peak, there is one of the halogens. 



70 



I 50 



30! 



10 




50 70 90 

Atomic mass (amu) 



110 



130 



The 'atomic volume" is defined 
as the atomic mass divided by the 
density of the element in its liquid 
or solid state. 



In 1864, the German chemist Lothar 
Meyer wrote a chemistry textbook. 
In this book, he considered how the 
properties of the chemical elements 
might depend on their atomic 
masses. He later found that if he 
plotted atomic volume against the 
atomic mass, the line drawn through 
the plotted points rose and fell in 
two long periods. This was exactly 
what Mendeleev had discovered in 
connection with valence. Mendeleev 
published his first result in 1869; 
Meyer, as he himself later admitted, 
lacked the courage to include provi- 
sion for empty spaces that would 
amount to the prediction of the 
discovery of unknown elements. 
Nevertheless, Meyer should be 
given credit for the idea of the 
periodic table. 



The atomic volumes of elements 
graphed against their atomic masses. 



22 



The Chemical Basis of the Atomic Theory 



Mendeleev's periodic table of the elements not only provided a 
remarkable correlation of the elements and their properties, it also 
enabled him to predict that certain unknown elements should exist 
and what many of their properties should be. To estimate physical 
properties of a missing element, Mendeleev averaged the properties 
of its nearest neighbors in the table: those to right and left, above 
and below. A striking example of Mendeleev's success in using the 
table in this way is his set of predictions concerning the gap in 
Series 5, Group IV. Group IV contains silicon and elements re- 
sembling it. Mendeleev assigned the name "eka-silicon" (Es) to the 
unknown element. His predictions of the properties of this element 
are listed in the left-hand column below. In 1887, this element 
was isolated and identified (it is now called "germanium", Ge); its 
properties are listed in the right-hand column. Notice how remark- 
ably close Mendeleev's predictions are to the properties actually 
found. 



"The following are the 
properties which this 
element should have on 
the basis of the known 
properties of silicon, 
tin, zinc, and arsenic. 

Its atomic mass is 
nearly 72, its forms a 
higher oxide EsOa, . . . Es 
gives volatile organo- 
metallic compounds; for 
instance . . . Es (€2^2)4, 
which boils at about 160°, 
etc.; also a volatile and 
liquid chloride, EsCl^, 
boiling at about 90° and 
of specific gravity about 
1.9. .. . the specific gravity 
of Es will be about 5.5, 
and ESO2 will have a spe- 
cific gravity of about 4.7, 
etc " 



The predictions in the left 
column were made by 
Mendeleev in 1871. In 
1887 an element (german- 
ium) was discovered which 
was found to have the 
following properties: 

Its atomic mass is 72.5. 
It forms an oxide GeOa, 
and an organo- 
metallic compound 
Ge(C2H5)4 which boils at 
160° and forms a liquid 
chloride GeCl4 which 
boils at 83° C and has a 
specific gravity of 1.9. 
The specific gravity of 
germanium is 5.5 and the 
specific gravity of 
GeOi is 4.7. 



The daring of Mendeleev is shown in his willingness to venture 
detailed numerical predictions; the sweep and power of his system 
is shown above in the remarkable accuracy of those predictions. In 
similar fashion, Mendeleev described the properties to be expected 
for the then unknown elements that he predicted to exist in gaps in 
Group III, period 4, and in Group III. period 5— elements now called 
gallium and scandium — and again his predictions turned out to be 
remarkably accurate. 

Although not every aspect of Mendeleev's work yielded such 
successes, these were indeed impressive results, somewhat 



Section 17.6 



23 



reminiscent of the successful use of Newtonian laws to find an 
unknown planet. Successful numerical predictions like these are 
among the most desired results in physical science— even if in 
Mendeleev's case it was still mysterious why the table should work 
the way it did. 

Q8 Why is Mendeleev's table called "periodic table"? 
Q9 What was the basic ordering principle in Mendeleev's table? 
Q10 What reasons led Mendeleev to leave gaps in the table? 
Q11 What success did Mendeleev have in the use of the table? 



The discovery of Uranus and Nep- 
tune is described in Text Chapter 8. 



17.6 The modern periodic table 

The periodic table has had an important place in chemistry and 
physics for a century. It presented a serious challenge to any theory 
of the atom proposed after 1880: the challenge that the theory 
provide an explanation for the wonderful order among the elements 
as expressed by the table. A successful model of the atom must 
provide a physical reason why the table works as it does. In Chapter 
19 we shall see how one model of the atom— the Bohr model— met 
this challenge. 

Since 1872 many changes have had to be made in the periodic 
table, but they have been changes in detail rather than in general 
ideas. None of these changes has affected the basic periodic feature 
among the properties of the elements. A modern form of the table 
with current values is shown in the table below. 



A modern form of the periodic table 
of the chemical elements. The number 
above the symbol is the atomic mass, 
the number below the symbol is the 
atomic number. 



Group—* 
Period 

i 


I 


II 




III 


IV 


V 


VI 


VII 





1.0080 


































4.0026 


1 


H 


































He 




1 


































2 




6.939 


9.012 


10.811 


12.011 


14.007 


15.999 


18.998 


20.183 


2 


U 
3 


Be 

4 






















B 
5 



6 


N 

7 




8 


F 

9 


Ne 
10 




22.990 


24.31 


26.98 


28.09 


30.97 


32.06 


35.45 


39.95 


3 


Na 

n 


Mg 

12 






















Al 
13 


Si 
14 


P 
15 


S 
16 


Cl 

17 


Ar 

18 




39.10 


40.08 


44.96 


47.90 


50.94 


52.00 


54.94 


55.85 


58.93 


58.71 


63.54 


65.37 


69.72 


72.59 


74.92 


78.96 


79.91 


83.80 


4 


K 


Ca 


Sc 


Ti 


V 


Or 


M 


Fe 


Co 


Ni 


Cu 


Zd 


Ga 


Ge 


As 


Se 


Br 


Kr 




19 


20 


21 


22 


23 


24 


25 


26 


27 


28 


29 


30 


31 


32 


33 


34 


35 


36 




85.47 


87.62 


88.91 


91.22 


92.91 


95.94 


(99) 


101.07 


102.91 


106.4 


107.87 


112.40 


114.82 


118.69 


121.75 


127.60 


126.9 


131.30 


5 


Rb 


Sr 


Y 


Zr 


Nb 


Mo 


Tc 


Ru 


Rh 


Pd 


Ag 


Cd 


In 


Sd 


Sb 


Te 


I 


Xe 




37 


38 


39 


40 


41 


42 


43 


44 


45 


46 


47 


48 


49 


50 


51 


52 


53 


54 




132.91 


137.34 




178.49 


180.95 


183.85 


186.2 


190.2 


1922 


195.09 


196.97 


200.59 


204.37 


207.19 


208.98 


210 


(210) 


222 


6 


Cs 


Ba 


• 


Hf 


Ta 


W 


Re 


0» 


Ir 


Pt 


Au 


Hg 


Tl 


Pb 


Bi 


Po 


At 


Rn 




55 


56 


57-71 


72 


73 


74 


75 


76 


77 


78 


79 


80 


81 


82 


83 


84 


85 


86 




(223) 


226.05 




\ 






























7 


Fr 
87 


Ra 

88 


+ 
89-103 


) J 































•Rarc- 


138.91 


140.12 


140.91 


144.27 


(147) 


150.35 


151.96 


157.25 


158.92 


162.50 


164.93 


167.26 


168.93 


173.04 


174.97 


parth 


U 


Ce 


Pr 


Nd 


Pm 


Sm 


Eu 


Gd 


Tb 


Dy 


Ho 


Er 


Tm 


Yb 


Lu 


metals 


57 


58 


59 


60 


61 


62 


63 


04 


65 


66 


67 


68 


69 


70 


71 


t 


227 


232.04 


231 


238.03 


(237) 


(242) 


(243) 


(245) 


(249) 


(249) 


(253) 


(255) 


(256) 


(253) 


(257) 


\ctmide 


Ac 


Th 


Pa 


U 


Np 


Pu 


Am 


Cm 


Bk 


Of 


E 


Fm 


Mv 


No 


Lw 


metals 


89 


90 


91 


92 


93 


94 


95 


96 


97 


98 


99 


100 


101 


102 


103 



24 



The Chemical Basis of the Atomic Theory 



Although Mendeleev's table had 
eight columns, the column labelled 
VIII did not contain a family of 
elements. It contained the "transi- 
tion" elements which are now placed 
in the long series (periods) labelled 
4, 5 and 6 in the table on p. 23. The 
group labelled "O" in that table does 
consist of a family of elements, 
the noble gases, which do have 
similar properties in common. 



Helium was first detected in the 
spectrum of the sun in 1868 
(Chapter 19). Its name comes from 
helios, the Greek word for the sun. 

In chemistry, elements such as gold 
and silver that react only rarely with 
other elements were called "noble." 



One difference between the modern and older tables results from 
new elements having been found. Forty new elements have been 
identified since 1872, so that the table now contains 103 or more 
elements. Some of these new elements are especially interesting, 
and you will learn more about them in Unit 6. 

Comparison of the modern form of the table with Mendeleev's 
table shows that the modern table contains eight groups, or famihes, 
instead of seven. The additional group is labeled "zero." In 1894, 
the British scientists Lord Rayleigh and William Ramsay discovered 
that about 1 percent of our atmosphere consists of a gas that had 
previously escaped our detection. It was given the name argon 
(symbol Ar). Argon does not seem to enter into chemical combina- 
tion with any other elements, and is not similar to any of the groups 
of elements in Mendeleev's original table. Later, other elements 
similar to argon were also discovered: helium (He), neon (Ne), 
krypton (Kr), xenon (Xe), and radon (Rn). These elements are 
considered to form a new group or family of elements called the 
"noble gases." The molecules of the noble gases contain only one 
atom, and until recent years no compound of any noble gas was 
known. The group number zero was thought to correspond to the 
chemical inertness, or zero combining capacity of the members of 
the group. In 1963, some compounds of xenon and krypton were 
produced, so we now know that these elements are not really inert. 
These compounds are not found in nature, however, and some are 
very reactive, and therefore very difficult to keep. The noble gases 
as a group are certainly less able to react chemically than any other 
elements. 

In addition to the noble gases, two other sets of elements had to 
be included in the table. After the fifty-seventh element, lanthanum, 
room had to be made for a whole set of 14 elements that are almost 
indistinguishable chemically, known as the rare earths or lantha- 
nide series. Most of these elements were unknown in Mendeleev's 
time. Similarly, after actinium at the eighty-ninth place, there is a 
set of 14 very similar elements, forming what is called the actinide 
series. These elements are shown in two rows below the main table. 
No more additions are expected except, possibly, at the end of the 
table. There are no known gaps, and we shall see in Chapters 19 
and 20 that according to the best theory of the atom now available, 
no new gaps are expected to exist within the table. 

Besides the addition of new elements to the periodic table, there 
have also been some changes of a more general type. As we have 
seen, Mendeleev arranged most of the elements in order of 
increasing atomic mass. In the late nineteenth century, however, 
this basic scheme was found to break down in a few places. For 
example, the chemical properties of argon (Ar) and potassium (K) 
demand that they should be placed in the eighteenth and nineteenth 
positions, whereas on the basis of their atomic masses alone (39.948 
for argon, 39.102 for potassium), their positions should be reversed. 
Other reversals of this kind are also necessary, for example, for the 
fifty-second element, tellurium (atomic mass = 127.60) and the fifty- 
third, iodine (atomic mass = 126.90). 



Section 17.7 



25 



The numbers that place elements in the table with the greatest 
consistency in periodic properties are called the atomic numbers 
of the elements. The atomic numbers of all the elements are given 
in the table on p. 23. The atomic number is usually denoted by the 
symbol Z; thus for hydrogen, Z = 1, for chlorine, Z = 17, for 
uranium, Z = 92. In Chapter 19 we shall see that the atomic number 
has a fundamental physical meaning related to atomic structure, 
and that is the key to both the many puzzhng successes and few 
puzzUng failures of Mendeleev's scheme. Since he used atomic 
mass as the basis for the order of the elements, he preferred to 
believe that the apparent reversals were due to error in the values 
for the atomic masses. 

The need for reversals in mass order in the periodic table of the 
elements was apparent to Mendeleev. He attributed it to faulty 
atomic weight data. He confidently expected, for example, that the 
atomic mass of tellurium (which he placed fifty-second), when 
more accurately determined would turn out to be lower than that of 
iodine (which he placed fifty-third). And, in fact, in 1872 (see Table 
p. 20) he had convinced himself that the correct atomic mass of 
tellurium was 125! As the figures in the modern tables show how- 
ever, tellurium does have a greater atomic mass than iodine — the 
reversal is real. Mendeleev overestimated the applicability of the 
periodic law in every detail, particularly as it had not yet received 
a physical explanation. He did not realize that atomic mass was not 
the underlying ordering principle for atomic numbers — it was only 
one physical property (with slightly imperfect periodicity). Satis- 
factory explanations for these reversals have been found in modern 
atomic physics, and will be explained in Unit 6. 

Q1 2 What is the "atomic number" of an element? Give examples 
of the atomic number of several elements. 



SG 17.10-17.12. 



17.7 Electricity and matter: qualitative studies 



While chemists were applying Dalton's atomic theory in the 
first decade of the nineteenth century, another development was 
taking place which opened an important path to our understanding 
of the atom. Humphry Davy and Michael Faraday made discoveries 
which showed that electricity and matter are intimately related. 
Their discoveries in "electrochemistry" had to do with decomposing 
chemical compounds by passing an electric current through them. 
This process is called electrolysis. 

The study of electrolysis was made possible by the invention of 
the electric cell in 1800 by the Italian scientist Alessandro Volta. As 
we saw in Unit 4, Volta's cell consisted of disks of different metals 
separated from each other by paper moistened with a weak solution 
of salt. As a result of chemical changes occurring in such a cell, an 
electric potential difference is established between the metals. A 
battery is a set of several similar cells connected together. A battery 
usually has two terminals, one charged positively and the other 



Some liquids conduct electricity. 
Pure distilled water is a poor con- 
ductor; but when certain substances 
such as acids or salts are dissolved 
in water, the resulting solutions are 
good electrical conductors. Gases 
are not conductors under normal 
conditions, but can be made 
electrically conducting in the 
presence of strong electric fields, or 
by other methods. The conduction of 
electricity in gases, vital to the story 
of the atom, will be discussed in 
Chapter 18. 



26 



The Chemical Basis of the Atomic Theory 





Humphry Davy (1778-1829) was the 
son of a farmer. In his youth he worl<ed 
as an assistant to a physician, but was 
discharged because of his lil<ing for 
explosive chemical experiments. He 
became a chemist, discovered nitrous 
oxide (laughing gas), which was later 
used as an anaesthetic, and developed 
a safety lamp for miners as well as an 
arc light. His work in electrochemistry 
and his discovery of several elements 
made him world-famous; he was 
knighted in 1812. In 1813 Sir Hum- 
phry Davy hired a young man, Michael 
Faraday, as his assistant and took 
him along on an extensive trip through 
France and Italy. It became evident to 
Davy that young Faraday was a man of 
scientific genius. Davy is said to have 
been envious, at first, of Faraday's 
great gifts. He later said that he be- 
lieved his greatest discovery was 
Faraday. 



charged negatively. When the terminals are connected to each other 
by means of wires or other conducting materials, there is an electric 
current in the battery and the materials. Thus, the battery can 
produce and maintain an electric current. It is not the only device 
that can do so, but it was the first source of steady currents. 

Within a few weeks after Volta's announcement of his discovery 
it was found that water could be decomposed into oxygen and 
hydrogen by the use of electric currents. At the left is a diagram of 
an electrolysis apparatus. The two terminals of the battery are 
connected, by conducting wires, to two thin sheets of platinum 
("electrodes"). When these platinum sheets are immersed in ordinary 
water, bubbles of oxygen appear at one sheet and bubbles of 
hydrogen at the other. Adding a small amount of certain acids 
speeds up the reaction without changing the products. Hydrogen 
and oxygen gases are formed in the proportion of 7.94 grams of 
oxygen to 1 gram of hydrogen, which is exactly the proportion in 
which these elements combine to form water. Water had previously 
been impossible to decompose, and had long been regarded as an 
element. Thus the ease with which water was separated into its 
elements by electrolysis dramatized the chemical use of electricity, 
and stimulated many other investigations of electrolysis. 

Among these investigations, some of the most successful were 
those of the young English chemist Humphry Davy. Perhaps the 
most striking of Davy's successes were those he achieved in 1807 
when he studied the effect of the current from a large electric 
battery upon soda and potash. Soda and potash were materials of 
commercial importance (for example, in the manufacture of glass, 
soap, and gunpowder) and had been completely resistant to every 
earlier attempt to decompose them. Soda and potash were thus 
regarded as true chemical elements— up to the time of Davy's work. 
(See Dalton's symbols for the elements on p. 10.) When electrodes 
connected to a large battery were touched to a solid lump of soda, 
or to a lump of potash, part of the solid was heated to its melting 
point. At one electrode small globules of molten metal appeared 
which burned brightly and almost explosively in air. When the 
electrolysis was done in the absence of air, the metalhc material 
could be collected and studied. The metallic elements discovered in 
this way were called sodium and potassium. Sodium was obtained 
from soda (now called sodium hydroxide), and potassium was 
obtained from potash (now called potassium hydroxide). In the 
immediately succeeding years, electrolysis experiments made on 
several previously undecomposed "earths" yielded the first samples 
ever obtained of such metallic elements as magnesium, strontium, 
and barium. There were also many other demonstrations of the 
striking changes produced by the chemical activity of electricity. 

Q13 Why was the first electrolysis of water such a surprising 
achievement? 

Q14 What were some other unexpected results of electrolysis? 



Electrolysis 





Student laboratory apparatus like 
that shown in the sketch above can be 
used for experiments in electrolysis. 
This setup allows nneasurement of the 
amount of electric charge passing 
through the solution in the beaker, 
and of the mass of metal deposited 
on the suspended electrode. 

The separation of elements by 
electrolysis is important in industry, 
particularly in the production of alumi- 
num. These photographs show the 
large scale of a plant where aluminum 
is obtained from aluminum ore in 
electrolytic tanks. 

(a) A row of tanks where alumi- 
num is separated out of aluminum ore. 

(b) A closer view of the front of 
some tanks, showing the thick copper 
straps that carry the current for 
electrolysis. 

(c) A huge vat of molten alumi- 
num that has been siphoned out of 
the tanks is poured into molds. 



28 



The Chemical Basis of the Atomic Theory 



By chemical change we mean here 
the breaking up of molecules during 
electrolysis, as by gas bubbles 
rising at the electrodes, or by metal 
deposited on it. 



Mass « current x time 

charge 
"^^ —r: — 5— > time 
time 

<^ charge transferred 



17.8 Electricity and matter: quantitative studies 

Davy's work on electrolysis was mainly qualitative. But 
quantitative questions were also asked. How much chemical change 
can be produced when a certain amount of electric charge is passed 
through a solution? If the same amount of charge is passed through 
different solutions, how do the amounts of chemical change com- 
pare? Will doubling the amount of electricity double the chemical 
change effected? 

The first answers to these questions were obtained by Michael 
Faraday, who discovered two fundamental and simple empirical 
laws of electrolysis. He studied the electrolysis of a solution of the 
blue salt copper sulfate in water. The electric current between 
electrodes placed in the solution caused copper from the solution 
to be deposited on the negative electrode and oxygen to be liberated 
at the positive electrode. Faraday determined the amount of copper 
deposited on the cathode by weighing the cathode before the elec- 
trolysis started and again after a known amount of current had 
passed through the solution. He found that the mass of copper de- 
posited depends on only two things: the magnitude of the electric 
current (measured, say, in amperes), and the length of time that the 
current was maintained. In fact, the mass of copper deposited is 
directly proportional to both the current and the time. When either 
was doubled, the mass of copper deposited was doubled. When both 
were doubled, four times as much copper was deposited. Similar 
results were found in experiments on the electrolysis of many 
different substances. 

Faraday's results may be described by stating that the amount 
of chemical change produced in electrolysis is proportional to the 
product of the current and the time. Now, the current (in amperes) 
is the quantity of charge (in coulombs) transferred per unit time 
(in seconds). The product of current and time therefore gives the 
total charge in coulombs that has moved through the cell during the 
given experiment. We then have Faraday's first law of electrolysis: 



The mass of an element liberated at an electrode during 
electrolysis is proportional to the amount of charge which 
has passed through the electrode. 

Next Faraday measured the mass of different elements liberated 
from chemical compounds by equal amount of electric charge. He 
found that the amount of an element liberated from the electrolyte 
by a given amount of electricity depends on the element's atomic 
mass and on its combining capacity (valence). His second law of 
electrolysis states: 



This experimentally determined 
amount of electric charge, 96,540 
coulombs, is now called a faraday. 



If A is the atomic mass of an element, and if v is its 
valence, a transfer of 96,540 coulombs of electric charge 
liberate Alv grams of the element. 



SG 17.13-17.16 



The table on the next page gives examples of Faraday's second 



Section 17.8 



29 



Masses of elements that would be electrolyzed 


from compounds by 




96,540 coulombs of electric charge. 








COMBINING 




MASS OF ELEMENT 


ELEMENT 


ATOMIC MASS A 


CAPACITY V 




LIBERATED (grams) 


Hydrogen 


1.008 


1 




1.008 


Chlorine 


35.45 


1 




35.45 


Oxygen 


16.00 


2 




8.00 


Copper 


63.54 


2 




31.77 


Zinc 


65.37 


2 




32.69 


Aluminum 


26.98 


3 




8.99 



The values of atomic mass in this 
table are based on a value of 
exactly 16 for oxygen. 



law of electrolysis. In each case the mass of the element produced 
by electrolysis is equal to its atomic mass divided by its combining 
capacity. 

The quantity Alv was recognized to have significance beyond 
just electrolysis experiments. For example, the values for Alv are 
8.00 for oxygen and 1.008 for hydrogen. The ratio is 8.00/1.008 = 
7.94. But as we have found before, this is just the ratio of masses 
of oxygen and hydrogen that combine to produce water. In general, 
when two elements combine, the ratio of their combining masses 
is equal to the ration of their values for Alv. 

Faraday's second law of electrolysis has an important implica- 
tion. It shows that a given amount of electric charge is somehow 
closely connected with the atomic mass and valence of an element. 
The mass and valence are characteristic of the atoms of the 
element. Perhaps, then, a certain amount of electricity is somehow 
connected with an atom of the element. The implication is that 
electricity may also be atomic in character. This possibility was 
considered by Faraday, who wrote cautiously: 

... if we adopt the atomic theory or phraseology, then the 
atoms of bodies which are equivalents to each other in 
their ordinary chemical action have equal quantities of 
electricity naturally associated with them. But I must 
confess that I am jealous of the term atom; for though it 
is very easy to talk of atoms, it is very difficult to form a 
clear idea of their nature, especially when compound 
bodies are under consideration. 



In Chapter 18 you will read about the details of the research 
that did establish the fact that electricity itself is atomic in 
character, and that the "atoms" of electricity are part of the atoms 
of matter. This research, for which Faraday's work and his cautious 
guess prepared, helped make possible the exploration of the structure 
of the atom. 

Q15 The amount of an element deposited in electrolysis 
depends on three factors. What are they? 

Q16 What are the significances of the quantity Alv for an 
element? 



SG 17.17-17.20 



STUDY GUIDE 



17.1 The Project Physics learning materials 
particularly appropriate for Chapter 17 include 
the following: 

Experiment 

Electrolysis 
Activities 

Dalton's Puzzle 
Electrolysis of Water 
Periodic Table 
Single-electrode Plating 
Activities from the Scientific American 
Film Loops 

Production of Sodium by Electrolysis 
Articles of general interest in Reader 5 are: 
The Island of Research 
The Sentinel 
Although most of the articles in Reader 5 are 
related to ideas presented in Chapter 20, you 
may prefer to read some of them earlier. 

17.2 The chemical compound zinc oxide (molec- 
ular formula ZnO) contains equal numbers of 
atoms of zinc and oxygen. Using values of atomic 
masses from the modern version of the periodic 
table (on page 23), find the percentage by mass of 
zinic in zinic oxide. What is the percentage of 
oxygen in zinc oxide? 

17.3 The chemical compound zinc chloride 
(molecular formula ZnCla) contains two atoms of 
chlorine for each atom of zinc. Using values of 
atomic masses from the modern version of the 
periodic table, find the percentage by mass of 
zinc in zinc chloride. 

17.4 During the complete decomposition of a 
5.00-gram sample of ammonia gas into its com- 
ponent elements, nitrogen and hydrogen, 4.11 
grams of nitrogen were obtained. The molecular 
formula of ammonia is NH3. Find the mass of a 
nitrogen atom relative to that of a hydrogen 
atom. Compare your result with the one you 
would get by using the values of the atomic 
masses in the modern version of the periodic 
table. If your result is different from the latter 
result, how do you account for the difference? 

17.5 From the information in Problem 17.3, 
calculate how much nitrogen and hydrogen are 
needed to make 1.2 kg of ammonia. 

17.6 // the molecular formula of ammonia were 
falsely thought to be NH^, and you used the result 
of the experiment in Problem 17.3, what value 
would you get for the ratio of the mass of a 
nitrogen atom relative to that of a hydrogen 
atom? 

17.7 A sample of nitric oxide gas, weighing 
1.00 g, after separation into its components, is 
found to have contained 0.47 g of nitrogen. 
Taking the atomic mass of oxygen to be 16.00, 
find the corresponding numbers that express the 
atomic mass of nitrogen relative to oxygen on the 
respective assumptions that the molecular formula 
of nitric oxide is (a) NO; (b) NO^; (c) N.O. 



17.8 Early data yielded 8.2 8.0 for the mass ratio 
of nitrogen and oxygen atoms, and 17 for the 
mass ratio of hydrogen and oxygen atoms. Show 
that these results lead to a value of 6 for the 
relative atomic mass of nitrogen, provided that 
the value 1 is assigned to hydrogen. 

17.9 Given the molecular formulae HCl. NaCl. 
CaCl.,, AICI3, SnCL,, PCI,, finf possible combining 
capacities of sodium, calcium, aluminum, tin and 
phosphorus. 

17.10 (a) Examine the modem periodic table of 

elements and cite all reversals of order 
of increasing atomic mass. 

(b) Restate the periodic law in your own 
words, not forgetting about these 
reversals. 

17.11 On the next page is a table of the melting 
and boiling temperatures of the elements. 

(a) Plot these quantities against atomic 
number in two separate graphs. Comment 
on any periodicity you observe in the 
plots. 

(b) Predict the values for melting and boiling 
points of the noble gases, which were 
unknown in 1872. Compare your predic- 
tions with the modern values given in. 
say, the Handbook of Chemistry and 
Physics. 

17.12 In recent editions of the Handbook of 
Chemistry and Physics there are printed in or 
below one of the periodic tables the valence 
numbers of the elements. Neglect the negative 
valence numbers and plot (to element 65) a 
graph of maximum valences observed vs. atomic 
mass. What periodicity is found? Is there any 
physical or chemical significance to this 
periodicity? 

17.13 According to the table on p. 29, when about 
96,500 coulombs of charge pass through a water 
solution, how much of oxygen will be released 

at the same time when (on the other electrode) 
1.008 g of hydrogen are released? How much 
oxygen will be produced when a current of 
3 amperes is passed through water for 60 minutes 
(3600 seconds)? 

17.14 If a current of 0.5 amperes is passed 
through molten zinc chloride in an electrolytic 
apparatus, what mass of zinc will be deposited in 

(a) 5 minutes (300 seconds); 

(b) 30 minutes; 

(c) 120 minutes? 

17.15 (a) For 20 minutes (1200 seconds), a cur- 

rent of 2.0 amperes is passed through 
molten zinc chloride in an electrolytic 
apparatus. What mass of chlorine will 
be released at the anode? 



30 



(b) If the current had been passed through 
molten zinc iodide rather than molten 
zinc chloride what mass of iodine 
would have been released at the anode? 

(c) Would the quantity of zinc deposited in 
part (b) have been different from what 
it was in part (a)? Why? 

(d) How would you set up a device for 
plating a copper spoon with silver? 

17.16 What may be the relation of Faraday's 
speculation about an "atom of electricity" to the 
presumed atomicity in the composition of chemical 
elements? 

17.17 96,540 coulombs in electrolysis frees A 
grams of a monovalent element of atomic mass 
A such as hydrogen when hydrochloric acid is 
used as electrolyte. How much chlorine will be 
released on the other electrode? 

17.18 If 96,540 coulombs in electrolysis always 
frees A grams of a monovalent element, A/2 
grams of a divalent element, etc., what relation 
does this suggest between valence and "atoms" 
of electricity? 

17.19 The idea of chemical elements composed 
of identical atoms makes it easier to correlate 
the phenomena discussed in this chapter. Could 
the phenomena be explained without using the 
idea of atoms? Are chemical phenomena, which 
usually involve a fairly large quantity of material 
(in terms of the number of "atoms"), sufficient 
evidence for Daltons belief that an element 
consists of atoms, all of which are exactly 
identical with each other? 

17.20 A sociologist recently wrote a book about 
the place of man in modern society, called 
Multivalent Man. In general, what validity is 
there for using such terms for sociological or 
other descriptions? 

17.21 Which of Dalton's main postulates (pp. 
11-12) were similar to those in Greek atomism 
(pp. 4-5)? Which are quite different? 

Melting and Boiling Temperatures of the 
Elements Known by 1872 



Melting and Boiling Temperatures of the 
Elements Known by 1872 (cont.) 



ATOMIC 




NUMBER 


NAME 


1 


hydrogen 


3 


lithium 


4 


beryllium 


5 


boron 


6 


carbon 


7 


nitrogen 


8 


oxygen 


9 


fluorine 


11 


sodium 



MELTING 


BOILING 


POINT 


POINT 


-259°C 


-253°C 


186 


1340 


1280 


2970 


2300 


2550 


>3350 


4200 


-210 


-196 


-218 


-183 


-223 


-188 


98 


880 



ATOMIC 




MELTING 


BOILING 


NUMBER 


NAME 


POINT 


POINT 


12 


magnesium 


651 


1107 


13 


aluminum 


660 


2057 


14 


silicon 


1420 


2355 


15 


phosphorus 


44 


280 


16 


sulfur 


113 


445 


17 


chlorine 


-103 


-35 


19 


potassium 


62 


760 


20 


calcium 


842 


1240 


22 


titanium 


1800 


>3000 


23 


vanadium 


1710 


3000 


24 


chromium 


1890 


2480 


25 


manganese 


1260 


1900 


26 


iron 


1535 


3000 


27 


cobalt 


1495 


2900 


28 


nickel 


1455 


2900 


29 


copper 


1083 


2336 


30 


zinc 


419 


907 


33 


arsenic 


814 


615 


34 


selenium 


217 


688 


35 


bromine 


-7 


59 


37 


rubidium 


39 


700 


38 


strontium 


774 


1150 


39 


yttrium 


1490 


2500 


40 


zirconium 


1857 


>2900 


41 


niobium 


2500 


3700 


42 


molybdenum 


2620 


4800 


44 


ruthenium 


2450 


2700 


45 


rhodium 


1966 


2500 


46 


palladium 


1549 


2200 


47 


silver 


961 


1950 


48 


cadmium 


321 


767 


49 


indium 


156 


2000 


50 


tin 


232 


2270 


51 


antimony 


631 


1380 


52 


tellurium 


452 


1390 


53 


iodine 


114 


184 


55 


cesium 


29 


670 


56 


barium 


725 


1140 


57 


lanthanum 


826 




58 


cerium 


804 


1400 


68 


erbium 






73 


tantalum 


3000 


4100 


74 


tungsten 


3370 


5900 


76 


osmium 


2700 


>5300 


77 


iridium 


2454 


>4800 


78 


platinum 


1774 


4300 


79 


gold 


1063 


2600 


80 


mercury 


-39 


357 


81 


thallium 


302 


1460 


82 


lead 


327 


1620 


83 


bismuth 


271 


1560 


90 


thorium 


1845 


4500 


92 


uranium 


1133 


ignites 



31 



18.1 The idea of atomic structure 

18.2 Cathode rays 

18.3 The measurement of the charge of the electron: 
Millikan's experiment 

18.4 The photoelectric effect 

18.5 Einstein's theory of the photoelectric effect 

18.6 X rays 

18.7 Electrons, quanta, and the atom 



33 
34 

37 
40 
43 
48 
54 



The tube used by J. J. Thomson to determine the charge-to-mass ratio of electrons. 




CHAPTER EIGHTEEN 



Electrons and Quanta 



18.1 The idea of atomic structure 



The successes of chemistry in the nineteenth century, in ac- 
counting for combining proportions and in predicting chemical 
reactions, had proved to the satisfaction of most scientists that 
matter is composed of atoms. 

But there remained a related question: are atoms really 
indivisible, or do they consist of still smaller particles? We can see 
the way in which this question arose by thinking a little more about 
the periodic table. Mendeleev had arranged the elements in the 
order of increasing atomic mass. But the atomic masses of the 
elements cannot explain the periodic features of Mendeleev's table. 
Why, for example, do the 3rd, 11th, 19th, 37th, 55th, and 87th 
elements, with quite different atomic masses, have similar chemical 
properties? Why are these properties somewhat different from those 
of the 4th, 12th, 20th, 38th, 56th, and 88th elements in the hst, but 
greatly different from the properties of the 2nd, 10th, 18th, 36th, 
54th, and 86th elements? 

The periodicity in the properties of the elements led to specula- 
tion about the possibility that atoms might have structure, that 
they might be made up of smaller pieces. The gradual changes of 
properties from group to group might suggest that some unit of 
atomic structure is added, in successive elements, until a certain 
portion of the structure is completed. The completed condition 
would occur in the atom of a noble gas. In an atom of the next 
heavier element, a new portion of the structure may be started, 
and so on. The methods and techniques of classical chemistry 
could not supply experimental evidence for such structure. In the 
nineteenth century, however, discoveries and new techniques in 
physics opened the way to the proof that atoms do, indeed, consist 
of smaller pieces. Evidence piled up that suggested the atoms of dif- 
ferent elements differ in the number and arrangement of these pieces. 

In this chapter, we shall discuss the discovery of one structural 
element which all atoms contain: the electron. Then we shall see 
how experiments with light and electrons led to a revolutionary 



SG 18.1 



These elements burn when exposed 
to air; they decompose water, often 
explosively. 

These elements react slowly with 
air or water. 

These elements rarely combine with 
any others. 



33 



34 



Electrons and Quanta 



idea — that light energy is transmitted in discrete amounts. In 
Chapter 19, we shall describe the discovery of another part of the 
atom, the nucleus. Finally we shall show how Niels Bohr combined 
these pieces to create a workable model of the atom. The story 
starts with the discovery of cathode rays. 

18.2 Cathode rays 




■^ J-- 



Cathode ray apparatus 

Substances which glow when 
exposed to light are called 
fluorescent. Fluorescent lights are 
essentially Geissler tubes with an 
inner coating of fluorescent powder. 



cathode 




Bent Geissler tube. The most intense 
green glow appeared at g 




A Crookes tube 



In 1855 the German physicist Heinrich Geissler invented a 
vacuum pump which could remove enough gas from a strong glass 
tube to reduce the pressure to 0.01 percent of normal air pressure. 
It was the first major improvement in vacuum pumps after 
Guericke's invention of the air pump, two centuries earlier. It 
turned out to be a critical technical innovation that opened new 
fields to pure scientific research. Geissler's friend Julius Pliicker 
connected one of Geissler's evacuated tubes to a battery. He was 
surprised to find that at the very low pressure that could be obtained 
with Geissler's pump, electricity flowed through the tube. Pliicker 
used apparatus similar to that sketched in the margin. He sealed a 
wire into each end of a strong glass tube. Inside the tube, each wire 
ended in a metal plate, called an electrode. Outside the tube, each 
wire ran to a source of high voltage. (The negative plate is called 
the cathode, and the positive plate is called anode.) A meter 
indicated the current in the tube. 

Pliicker and his student, Johann Hittorf, noticed that when an 
electric current passes through the low-pressure gas in a tube, the 
tube itself glows with a pale green color. Several other scientists 
observed these effects, but two decades passed before anyone under- 
took a thorough study of the glowing tubes. By 1875, Sir William 
Crookes had designed new tubes for studying the glow produced 
when an electric current passes through an evacuated tube. When 
he used a bent tube, (see figure at the left) the most intense green 
glow appeared on the part of the tube which was directly opposite 
the cathode (at g). This suggested that the green glow was produced 
by something which comes out of the cathode and travels down the 
tube until it hits the glass. Another physicist, Eugen Goldstein, who 
was studying the effects of passing an electric current through a 
gas at low pressure, named whatever it was that appeared to be 
coming from the cathode, cathode rays. For the time being, it was 
quite mysterious just what these cathode rays were. 

To study the nature of the rays, Crookes did some ingenious 
experiments. He reasoned that if cathode rays could be stopped 
before they reached the end of the tube, the intense green glow 
would disappear. He therefore introduced barriers (for example, in 
the form of a Maltese cross, as in the sketch in the margin). A 
shadow of the barrier appeared in the midst of the green glow at 
the end of the tube. The cathode seemed to act like a source which 
radiates a kind of light; the cross acted like a barrier blocking the 
light. Because the shadow, cross, and cathode appeared along one 
straight line, Crookes concluded that the cathode rays, like light 
rays, travel in straight lines. Next, Crookes moved a magnet near 



Section 18.2 



35 



the tube, and the shadow moved. Thus he found that magnetic 
fields deflected the paths of cathode rays (which does not happen 
with light). 

In the course of many experiments, Crookes found the following 
properties of cathode rays: 

(a) No matter what material the cathode is made of, it produces 
rays with the same properties. 

(b) In the absence of a magnetic field, the rays travel in straight 
lines perpendicular to the surface that emits them. 

(c) A magnetic field deflects the path of the cathode rays. 

(d) The rays can produce some chemical reactions similar to the 
reactions produced by light; for example, certain silver salts change 
color when hit by the rays. 

In addition, Crookes suspected (but did not succeed in showing) 
that (e) charged objects deflect the path of cathode rays. 

Physicists were fascinated by the cathode rays. Some thought 
that the rays must be a form of light, because they have so many 
of the properties of light: they travel in straight lines, and produce 
chemical changes and fluorescent glows just as light does. Accord- 
ing to Maxwell's theory of electricity and magnetism, light consists 
of electromagnetic waves. So the cathode rays might, for example, 
be electromagnetic waves of frequency much higher than that of 
visible light. 

However, magnetic fields do not bend light; they do bend the 
path of cathode rays. In Chapter 14 we described how magnetic 
fields exert forces on currents, that is, on moving electric charges. 
Since a magnetic field deflects cathode rays in the same way that it 
deflects negative charges, some physicists believed that cathode 
rays consisted of negatively charged particles. 

The controversy over whether cathode rays are a force of 
electromagnetic waves or a stream of charged particles continued 
for 25 years. Finally, in 1897, J. J. Thomson made a series of 
experiments which convinced physicists that the cathode rays are 
negatively charged particles. Details of Thomson's experiment and 
calculations are given on page 36. 

It was then well-known that the paths of charged particles are 
affected by both magnetic and electric fields. By assuming that 
the cathode rays were negatively charged particles, Thomson could 
predict what should happen to the cathode rays when they passed 
through such fields. For example, it should be possible to balance 
the deflection of a beam of cathode rays by a magnetic field by 
turning on an electric field of just the right magnitude and 
direction. As page 36 indicates, the predictions were verified, and 
Thomson could therefore conclude that the cathode rays were 
indeed made up of negatively charged particles. He was then able 
to calculate, from the experimental data, the ratio of the charge of 
a particle to its mass. This ratio is denoted by qlm, where q is the 
charge and m is the mass of the particle. 

Thomson found that the rays coming from cathodes made of 
different materials all had the same value of qlm, namely 1.76 x 
10'' coulombs per kilogram. 



J. J. Thomson later observed this 
to be possible. 




Sir Joseph John Thomson (1856- 
1940), one of the greatest British 
physicists, attended Owens College 
in Manchester, England and then 
Cambridge University. He worked 
on the conduction of electricity 
through gases, on the relation be- 
tween electricity and matter and on 
atomic models. His greatest single 
contribution was the discovery of the 
electron. He was the head of the fa- 
mous Cavendish Laboratory at Cam- 
bridge University, where one of his 
students was Ernest Rutherford. 



Thomson's q/m Experiment 



J. J. Thomson measured the ratio of charge q to mass m for cathode-ray particles by means of the 
evacuated tube shown in the photograph on page 32. A high voltage applied between two electrodes in the 
left end of the tube produced cathode rays. Those rays that passed through both slotted cylinders in the 
narrow neck of the tube formed a nearly parallel beam. The beam produced a spot of light on a fluorescent 
coating inside the large end of the tube at the right. 






The path of the beam was deflected by an electric field applied between two horizontal plates in the 
mid-section of the tube; (note that direction of electric field '^ \s upward along plane of page): 






G^~*^ -f. 



The beam's path was also deflected when there was no electric field but when a magnetic field was set 
up by means of a pair of current-carrying wire coils placed around the midsection of the tube; (the direction 
of the magnetic field ^ is into the plane of the page): 




When only the magnetic field ^ is turned on, particles in the beam, having charge q and speed v, would 
experience a force Bqv; because the force is always perpendicular to the direction of the velocity vector, 
the beam would be deflected in a nearly circular arc of radius R as long as it is in the nearly uniform 
magnetic field. If the particles in the beam have mass m, they must be experiencing a centripetal force 
mv'/R while moving in a circular arc. Since the centripetal force is provided by the magnetic force Bqv. 
we can write Bqv = mv'-R. Rearranging terms: q/m = v/BR- 

B can be calculated from the geometry of the coils and the electric current in them. R can be found 
geometrically from the displacement of the beam spot on the end of the tube. To determine v, Thomson 
applied the electric field and the magnetic field at the same time, and arranged the directions and strengths 
of the two fields so that the electric field ^exerted a downward force Eq on the beam particles exactly equal 
to the upward force Bqv due to the magnetic field -as seen by the fact that the beam, acted on by both 
fields in opposing ways, goes along a straight line. 



If the magnitudes of the forces due to the electric and magnetic fields are equal, then Eq = Bqv. Solving 
for V we have: v ^ E/B. E can be calculated from the separation of the two plates and the voltage between 
them; so the speed of the particles v can be determined. Now all the terms on the right of the earlier equation 

for n/m arp knn\A/n anH n/m ran V\p rnmn\iior{ 



Section 18.3 37 

Thus, it was clear that cathode rays must be made of something 
all materials have in common. Thomson's negatively charged 
particles were later called electrons. The value of qlm for the 
cathode ray particles was about 1800 times larger than the values 
of qlm for hydrogen ions, 9.6 x 10' coulombs per kilogram as 
measured in electrolysis experiments of the kind we discussed in 
Sec. 17.8. (See table on p. 29.) Thomson concluded from these results SG 18.2 
that either the charge of the cathode ray particles is much greater 
than that of the hydrogen ion, or the mass of the cathode ray 
particles is much less than the mass of the hydrogen ion. 

Thomson also made measurements of the charge q on these 
negatively charged particles with methods other than those 
involving deflection by electric and magnetic fields. Although these 
experiments were not very accurate, they were good enough to 
indicate that the charge of a cathode ray particle was the same or 
not much diff"erent from that of the hydrogen ion in electrolysis. In 
view of the small value of qlm, Thomson was therefore able to 
conclude that the mass of cathode ray particles is much less than 
the mass of hydrogen ions. 

In short, the cathode ray particles, or electrons, were found to 
have two important properties: (1) they were emitted by a wide 
variety of cathode materials, and (2) they were much smaller 
in mass than the hydrogen atom, which has the smallest known 
mass. Thomson therefore concluded that the cathode ray particles 
form a part of all kinds of matter. He suggested that the atom is 
not the ultimate hmit to the subdivision of matter, and that the 
electron is part of an atom, that it is. perhaps even a basic building 
block of atoms. We now know that this is correct: the elctron — 
whose existence Thomson had first proved by quantitative experi- 
ment—is one of the fundamental or "elementary" particles of which 
matter is made. 

In the article in which he published his discovery, Thomson also 
speculated on the ways in which such particles might be arranged 
in atoms of different elements, in order to account for the periodicity 
of the chemical properties of the elements. Although, as we shall 
see in the next chapter, he did not say the last word about the 
arrangement and number of electrons in the atom, he did say the 
first word about it. 

Q1 What was the most convincing evidence that cathode rays 
were not electromagnetic radiation? 

Q2 What was the reason given for the ratio qlm for electrons 
being 1800 times larger than qlm for hydrogen ions? 

Q3 What were two main reasons for Thomson's beUef that 
electrons may be "building blocks" from which all atoms are made? 



18.3 The measurement of the charge of the electron: Millikan's 
experiment 

After the ratio of charge to the mass (qlm) of the electron had 
been determined, physicists tried to measure the value of the 



38 



Electrons and Quanta 



From now on we denote the magni- 
tude of the charge of the electron 
by q,: 

q, = ^.6x 10 ''coul. 

The sign of the charge is negative 
for the electron. 



SG 18.3 



In 1964, an American physicist, 
Murray Gell-Mann, suggested that 
particles with charge equal to 1/3 
or 2/3 of q might exist. He named 
these particles "quarks"— the word 
comes from James Joyce's novel 
Finnegan's Wake. Quarks are now 
being looked for in cosmic-ray and 
bubble-chamber experiments. 



Thomson found that 

q,./m = 1.76 X 10" coul/kg. 

According to Millikan's experiment 
the magnitude of q,. is 1.6 x 10 '" coul. 

Therefore, the mass of an electron is: 

_ 1.6 X 10'" coul 
"^ 1.76 X 10" coul/kg 

= 0.91 X 10 '" kg 

(Mass of a hydrogen ion is 1.66 x 
10 -" kg. This is approximately the 
value of one "atomic mass unit.") 



charge q itself in a variety of ways. If the charge could be deter- 
mined, the mass of the electron could be found from the known 
value of qlm. In the years between 1909 and 1916, the American 
physicist Robert A. Milhkan succeeded in measuring the charge of 
the electron. This quantity is one of the fundamental constants of 
physics; it comes up again and again in atomic and nuclear physics 
as well as in electricity and electromagnetism. 

Millikan's "oil-drop experiment" is still one of the nicest 
experiments that students can do, and is described in general out- 
line on page 39. He found that the electric charge that a small 
object such as an oil drop can pick up is always a simple multiple 
of a certain minimum value. For example, the charge may have 
the value -4.8 x 10"'^ coulombs, or -1.6 x 10~'^ coulombs, or -6.4 x 
10"'^ coulombs, or -1.6 x 10"'^ coulombs. But it never has a charge 
of, say, —2.4 x 10~'^ coulombs, and it never has a value smaller 
than —1.6 x 10""* coulombs. In other words, electric charges always 
come in multiples (I, 2, 3 . . .) of 1.6 x 10"'^ coulombs, a quantity 
often symbolized by q^. Milhkan took this minimum charge to be 
the amount of charge of a single electron. 

The magnitude of the charge of nuclei or atomic and molecular 
ions has also turned out always to come in multiples of the electron 
charge q^. For example, when a chemist refers to a "doubly charged 
oxygen ion," he means that the magnitude of the charge of the ion 
is 2qg, or 3.2 x 10"'* coulombs. 

Note that Milhkan's experiments did not prove that no charges 
smaller than q^ can exist. All we can say is that no experiment has 
yet proved the existence of smaller charges. There are recent 
theoretical reasons to expect that in some very high-energy experi- 
ments, another elementary particle of charge of j q^ may 
eventually be discovered; but no such "fractional" charge is 
expected to be found on nuclei, ions, or droplets. 

In everyday life, the electric charge one meets is so large 
compared to that on one electron that one can think of such charges 
or currents as being continuous— just as one usually thinks of the 
flow of water in a river as continuous rather than as a flow of 
individual molecules. A current of one ampere, for example, is 
equivalent to the flow of 6.25 x 10"* electrons per second. The 
"static" electric charge one accumulates by shuffling over a rug on 
a dry day consists of something like 10'^ electron charges. 

Since the work of Millikan, a wide variety of other experiments 
involving many diff'erent fields within physics have all pointed to 
the same basic unit of charge as being fundamental in the structure 
and behavior of atoms, nuclei, and particles smaller than these. For 
example, it has been shown directly that cathode ray particles carry 
this basic unit of charge — that they are, in other words, electrons. 

By combining Millikan's value for the electron charge q^ with 
Thomson's value for the ratio of charge to mass {qjm.), we can 
calculate the mass of a single electron (see margin). The result 
found is that the mass of the electron is about 10"''" kilograms. 
From electrolysis experiments (see Sec. 17.8) we know that the 




vAciftBte 



Millikan's Oil-drop Experiment 

R. A. Millikan's own apparatus (about 1910) 
for measuring the charge of the electron is seen 
in the photograph above. A student version of 
Millikan's apparatus shown in the lower 
photograph was taken in a laboratory period 
of the Projects Physics Course. 

In principle Millikan's experiment is simple; 
the essential part of the apparatus is sketched 
above. When oil is sprayed into the 
chamber containmg two horizontal plates, 
the minute droplets formed are electrically 
charged as they emerge from the spray nozzle. 
The charge of a droplet is what must be 
measured. Consider a small oil drop of mass m 
carrying an electric charge Q. It is situated 
between the two horizontal plates that are 
separated by a distance d and at an electrical 
potential difference V. There will be a uniform 
electric field ^ between the plates, of strength 
V/6 (see Sec. 14.8). This field can be adjusted 
so that the electrical force qE' exerted upward 



on the drop's charge will balance the force maf, 
exerted downward by gravity. In this balanced 
situation, 



therefore 
or 



el 'grav 



qE = mag 
q = ma,j/E 



The mass of the drop can, in principle, be 
determined from its radius and the density of 
the oil from which it was made. Millikan had to 
measure these quantities by an indirect method, 
but it is now possible to do the experiment 
with small manufactured polystyrene spheres 
instead of oil drops. Their mass is known, so 
that some of the complications of the original 
experiment can be avoided. Millikan's remark- 
able result was that the charge q on objects 
such as an oil drop is always a multiple (1, 2, 
3 . . .) times a smallest charge, which he 
identified with the charge of one electron (Qp). 



40 Electrons and Quanta 

charge-to-mass ratio of a hydrogen ion is 1836 times smaller than 
the charge-to-mass ratio of an electron. Since an electron and a 
hydrogen ion form a neutral hydrogen atom when they combine, it 
is reasonable to expect that they have equal and opposite charges. 
We may therefore conclude that the mass of the hydrogen ion is 
1836 times as great as the mass of the electron: that is the mass 
of the hydrogen ion is 1836 x 0.91 x IQ-^o kg = 1.66 x IQ-' kg. This 
is approximately the value of one atomic mass unit. 

Q4 Oil drops pick up different amounts of electric charge. On 
what basis did Millikan decide that the lowest charge he found was 
actually just one electron charge? 



18.4 The photoelectric effect 

In 1887 the German physicist Heinrich Hertz was testing 
Maxwell's theory of electromagnetic waves. He noticed that a 
metalhc surface can emit electric charges when hght of very short 
wavelength falls on it. Because light and electricity are both 
involved, the name photoelectric effect was given to this phenome- 
non. When the electric charges so produced passed through electric 
and magnetic fields, the direction of their paths was changed in 
the same rays as the path of cathode rays. It was therefore deduced 
that the electric charges consist of negatively charged particles. In 
1898, J. J. Thomson measured the value of the ratio qlm for these 
photoelectrically emitted particles with the same method that he 
used for the cathode ray particles. He got the same value for the 
particles ejected in the photoelectric effect as he had earlier for 
the cathode-ray particles. By means of these experiments (and 
others) the photoelectric particles were shown to have the same 
properties as electrons. In fact, we must consider them to be 
ordinary electrons, although they are often referred to as photo- 
electrons, to indicate their origin. Later work showed that all 
substances, sohds, Uquids and gases, exhibit the photoelectric effect 
under appropriate conditions. It is, however, convenient to study the 
effect with metallic surfaces. 

The photoelectric effect, which we shall be stud\ing in greater 
detail, has had an important place in the development of atomic 
physics. The effect could not be explained in terms of the ideas of 
physics we have studied so far. New ideas had to be introduced to 
account for the experimental results. In particular, a revolutionary 
concept was introduced — that of quanta. A new branch of physics — 
quantum t/ieor?y — developed at least in part because of the 
explanation provided for the photoelectric effect. 

The basic inforination for studying the photoelectric effect 
comes from two kinds of measurements: measurements of the 
photoelectric current (the number of photoelectrons emitted per 
unit time); and measurements of the kinetic energies with which 
the photoelectrons are emitted. 



Section 18.4 



41 



The photoelectric current can be studied with an apparatus 
like that sketched in Fig. (a) in the margin. Two metal plates, C and 
A, are sealed inside a well-evacuated quartz tube. (Quartz glass is 
transparent to ultraviolet light as well as visible light.) The two 
plates are connected to a source of potential difference (for 
example, a battery). In the circuit is also an ammeter. As long as 
light strikes plate C, as in Fig. (b), electrons are emitted from it. If 
the potential of plate A is positive relative to plate C, these emitted 
photoelectrons will accelerate to plate A. (Some emitted electrons 
will reach plate A even if it is not positive relative to C.) The result- 
ing "photoelectric" cun-ent is indicated by the ammeter. The result 
of the experiment is that the stronger the beam of light of a given 
color (frequency), the greater the photoelectric current. 



The best way to study this part -as 
most other parts — of physics is 
really by doing the experiments 
discussed! 





Schematic diagram of apparatus for 
photoelectric experiments. 



(a) L_3 



Any metal used as the plate C shows a photoelectric effect, but 
only if the light has a frequency greater than a certain value. This 
value of the frequency is called the threshold frequency for that 
metal. Different metals have different threshold frequencies. If the 
incident Ught has a frequency lower than the threshold frequency, 
no photoelectrons are emitted, no matter how great the intensity of 
the light is or how long the light is left on! This is the first of a set 
of surprising discoveries. 

The kinetic energies of the electrons can be measured in a 
shghtly modified version of the apparatus, sketched in Fig. (c) 
below. The battery is reversed so that the plate A now tends to repel 
the photoelectrons. The voltage can be changed from zero to a value 
just large enough to keep any electrons from reaching the plate A, 
as indicated in Fig. (d). 





42 



Electrons and Quanta 



SG 18.4 



In Sec. 14.8, we saw that the change 
in potential energy of a charge is 
given by Vxq. In Unit 3 we saw that 
(in the absence of friction) the 
decrease in kinetic energy in a 
system is equal to the increase 
in its potential energy. 




^/Ce^uevry of it^oe*Jr n^^r 



Photoelectric effect: maximum kinetic 
energy of the electrons as a function 
of the frequency of the incident light; 
different metals yield lines that are 
parallel, but have different threshold 
frequencies. 



When the voltage across the plates is zero, the meter will 
indicate a current, showing that the photoelectrons emerge from 
the metallic surface with kinetic energy and so can reach plate A. 
As the repelling voltage is increased the photoelectric current 
decreases until a certain voltage is reached at which the current 
becomes zero, as indicated in Fig. (d) above. This voltage, which is 
called the stopping voltage, is a measure of the maximum kinetic 
energy of the emitted photoelectrons (KE,„qj.). If the stopping voltage 
is denoted by Vgi^p, this maximum kinetic energy is given by the 
relation: 

XF =V a 

'■^'-'max ' stop rie 

The results may be stated more precisely. For this purpose let 
us now number the important experimental results to make it more 
convenient to discuss their theoretical interpretation later. 

(1) A substance shows a photoelectric effect only if the incident 
light radiation has a frequency above a certain value called the 
threshold frequency (symbol /„). 

(2) If Ught of a given frequency does produce a photoelectric 
effect, the photoelectric current from the surface is proportional to 
the intensity of the light falling on it. 

(3) If Ught of a given frequency liberates photoelectrons, the 
emission of these electrons is immediate. The time interval between 
the incidence of the Ught on the metallic surface and the appear- 
ance of electrons has been found to be at most 3 x 10~" sec. and is 
probably much less. In some experiments, the light intensity used 
was so low that, according to the classical theory, it should take 
several hundred seconds for an electron to accumulate enough 
energy from the Ught to be emitted. But even in these cases 
electrons are sometimes emitted about a bilUonth of a second after 
the light strikes the surface. 

(4) The maximum kinetic energy of the photoelectrons increases 
in direct proportion to the frequency of the Ught which causes 
their emission, and is independent of the intensity of the incident 
light. The way in which the maximum kinetic energy of the 
electrons varies with the frequency of the incident light is shown in 
the margin where the symbols (/o)i, (/o)2 and (/„)3 stand for the 
different threshold frequencies of three different substances. For 
each substance, the experimental data points fall on a straight Une. 
All the lines have the same slope. 

What is most astonishing about the results is that photo- 
electrons are emitted if the light frequencies are a little above the 
threshold frequency, no matter how weak the beam of light is; but 
if the light frequencies are just a bit below the threshold frequency, 
no electrons are emitted no matter how great the intensity of the 
light beam is. 

Findings (1), (3) and (4) could not be explained on the basis of 
the classical electromagnetic theory of light. There was no way in 
which a low-intensity train of light waves spread out over a large 
number of atoms could, in a very short time interval, concentrate 



Section 18.5 



43 



enough energy on one electron to knock the electron out of the 
metal. 

Furthermore, the classical wave theory was unable to account 
for the existence of a threshold frequency. There seemed to be no 
reason why a sufficiently intense beam of low-frequency radiation 
would not be able to produce photoelectricity, if low-intensity 
radiation of higher frequency could produce it. Similarly, the classi- 
cal theory was unable to account for the fact that the maximum 
kinetic energy of the photoelectrons increases linearly with the 
frequency of the light but is independent of the intensity. Thus, 
the photoelectric effect posed a challenge which the classical wave 
theory of light could not meet. 

Q5 Light falling on a certain metal surface causes electrons to 
be emitted. What happens to the photoelectric current as the in- 
tensity of the light is decreased? 

Q6 What happens as the frequency of the light is decreased? 

Q7 Sketch a rough diagram of the equipment and circuit used 
to demonstrate the main facts of photoelectricity. 



18.5 Einstein's theory of the photoelectric effect 

The explanation of the photoelectric effect was the major work 
cited in the award to Albert Einstein of the Nobel Prize in physics 
for the year 1921. Einstein's theory, proposed in 1905, played a 
major role in the development of atomic physics. The theory was 
based on a daring proposal. Not only were most of the experimental 
details still unknown in 1905, but the key point of Einstein's 
explanation was contrary to the classical ideas of the time. 

Einstein assumed that energy of hght is not distributed evenly 
over the whole expanding wave front (as is assumed in the classical 
theory), but rather remains concentrated in separate "lumps." 
Further, the amount of energy in each of these regions is not just 
any amount, but a definite amount of energy which is proportional 
to the frequency / of the wave. The proportionaUty factor is a 
constant, denoted by h, and is called Planck's constant, for reasons 
which will be discussed later. Thus, in this model, the Hght energy 
in a beam of frequency / comes in pieces, each of amount h x f. 
The amount of radiant energy in each piece is called a quantum 
of energy. It represents the smallest quantity of energy of light of 
that frequency. The quantum of hght energy was later called a 
photon. 

There is no explanation clearer or more direct than Einstein's. 
We quote from his first paper (1905) on this subject, changing only 
the notation used there to make it coincide with usual current 
practice (including our own notation): 

. . . According to the idea that the incident hght consists 
of quanta with energy hf, the ejection of cathode rays by 
light can be understood in the following way. Energy 



See the articles "Einstein" and 
"Einstein and some Civilized Dis- 
contents" in Reader 5. 



/] = 6.6 X 10" joule-sec 



44 



Electrons and Quanta 



SG 18.5 



Each electron must be given a 
minimum energy to emerge from the 
surface because it must do woric 
against the forces of attraction as it 
leaves the rest of the atoms. 



This equation is usually called 
Einstein's photoelectric equation. 



SG 18.6-18.8. 



How Einstein's theory explains the 
photoelectric effect: 

(1) No photoelectric emission below 
threshold frequency. Reason: low- 
frequency photons don't have 
enough energy to provide electrons 
with KE sufficient to leave the metal. 

(2) Current ^•- light intensity. Reason: 
one photon ejects one electron. 

SG 18.9, 18.10 




quanta penetrate the surface layer of the body, and their 
energy is converted, at least in part, into kinetic energy of 
electrons. The simplest picture is that a light quantum 
gives up all its energy to a single electron; we shall 
assume that this happens. The possibiUty is not to be ex- 
cluded, however, that electrons receive their energy only 
in part from the light quantum. An electron provided with 
kinetic energy inside the body may have lost part of its 
kinetic energy by the time it reaches the surface. In addi- 
tion, it is to be assumed that each electron, in leaving the 
body, has to do an amount of work W (which is character- 
istic of the body). The electrons ejected directly from the 
surface and at right angles to it will have the greatest 
velocities perpendicular to the surface. The maximum kinetic 
energy of such an electron is 



KE, 



hf-W 



If the body plate C is charged to a positive potential, 
V,,„,, just large enough to keep the body from losing 
electric charge, we must have 



KE, 



h/-W = V, 



where q^ is the magnitude of the electronic charge . . . 

If the derived formula is correct, then V,,op, when 
plotted as a function of the frequency of the incident light, 
should yield a straight line whose slope should be inde- 
pendent of the nature of the substance illuminated. 

We can now compare Einstein's photoelectric equation with the 
experimental results to test whether or not his theory accounts for 
the results. According to the equation, the kinetic energy is greater 
than zero only when hf is greater than W. Hence, the equation says 
that an electron can be emitted only when the frequency of the 
incident light is greater than a certain lowest value/,, (where 
hf„ = W.) 

Next, according to Einstein's photon model, it is an individual 
photon that ejects an electron. The intensity of the light is propor- 
tional to the number of the photons in the light beam, and the 
number of photoelectrons ejected is proportional to the number of 
photons incident on the surface. Hence the number of electrons 
ejected (and with it the photoelectric current) is proportional to 
the intensity of the incident light. 

According to Einstein's model the light energy is concentrated 
in the quanta (photons). So, no time is needed for collecting light 

Student apparatus for photoelectric 
experiments often includes a vacuum 
phototube, like the one shown at the 
left. The collecting wire corresponds 
to A in Fig. (a) on p. 41. and is at the 
center of a cylindrical photosensitive 
surface that corresponds to C. The 
frequency of the light entering the 
tube is selected by placing colored 
filters between the tube and a white 
light source, as shown at the right. 




detector 





Albert Einstein (1879-1955) was born in the city of 
Dim, in Germany. Like Newton he showed no particu- 
lar intellectual promise as a youngster. He received 
his early education in Germany, but at the age of 17, 
dissatisfied with the regimentation in school and 
militarism in the nation, he left for Switzerland. After 
graduation from the Polytechnic School, Einstein (in 
1901) found work in the Swiss Patent Office in Berne. 
This job gave Einstein a salary to live on and an op- 
portunity to use his spare time for working in physics 
on his own. In 1905 he published three papers of 
epoch-making importance. One dealt with quantum 
theory and included his theory of the photoelectric 
effect. Another treated the problem of molecular mo- 
tions and sizes, and worked out a mathematical anal- 
ysis of the phenomenon of "Brownian motion." 
Einstein's analysis and experimental work by Jean 
Perrin, a French physicist, provided a strong argu- 
ment for the molecular motions assumed in the kinetic 
theory. Einstein's third 1905 paper provided the theory 
of special relativity which revolutionized modern 
thought about the nature of space, time, and physical 
theory. 




In 1915, Einstein published a paper on the theory 
of general relativity in which he provided a new theory 
of gravitation that included Newton's theory as a 
special case. 

When Hitler and the Nazis came to power in Ger- 
many, in 1933, Einstein came to the United States and 
became a member of the Institute for Advanced Stu- 
dies at Princeton. He spent the rest of his working 
life seeking a unified theory which would include 
gravitation and electromagnetics. Near the beginning 
of World War II, Einstein wrote a letter to President 
Roosevelt, warning of the war potential of an "atomic 
bomb," for which the Germans had all necessary 
knowledge and motivation to work. After World War 
II, Einstein devoted much of his time to promoting 
world agreement to end the threat of atomic warfare. 



46 



Electrons and Quanta 



(3) Immediate emission. Reason: 

a single photon provides the energy 
concentrated in one place. 

(4) KE,„„.r increases linearly with 
frequency above f„. Reason: the 
work needed to remove the electron 
is IV = hf„; any energy left over 
from the original photon is now 
available for kinetic energy of the 
electron. 



The equation K£„,„, -^ hf - IV can 
be said to have led to two Nobel 
prizes: one to Einstein, who derived 
it theoretically, and one to Millikan, 
who verified it experimentally. This 
equation is the subject of a Project 
Physics laboratory experiment. 

SG 18.11 



energy; the quanta transfer their energy immediately to the 
photoelectrons, which emerge after the very short time required for 
them to escape from the surface. 

Finally, the photoelectric equation predicts that the greater 
the frequency of the incident light, the greater is the maximum 
kinetic energy of the ejected electrons. According to the photon 
model, the photon's energy is directly proportional to the hght 
frequency. The minimum energy needed to eject an electron is the 
energy required for the electron to escape from the metal surface — 
which explains why light of frequency less than some frequency 
fg cannot eject any electrons. The kinetic energy of the escaping 
electron is the difference between the energy of the absorbed photon 
and the energy lost by the electron in passing through the surface. 

Thus, Einstein's photoelectric equation agreed quahtatively with 
the experimental results. There remained two quantitative tests to 
be made: (1) does the maximum energy vary in direct proportion to 
the light frequency? (2) is the proportionality factor h really the 
same for all substances? For some 10 years, experimental physicists 
attempted these quantitative tests. One of the experimental 
difficulties was that the value of W for a metal is greatly changed 
if there are impurities (for example, a layer of oxidized metal) on 
the surface. It was not until 1916 that it was estabhshed. by Robert A. 
Milhkan, that there is indeed a straight-line relationship between 
the frequency of the absorbed light and the maximum kinetic 
energy of the photoelectrons (as in the graph on p. 42). To obtain 
his data Millikan designed an apparatus in which the metal photo- 
electric surface was cut clean while in a vacuum. A knife inside the 
evacuated volume was manipulated by an electromagnet outside 
the vacuum to make the cuts. This rather intricate arrangement 
was required to achieve an uncontaminated metal surface. 

Millikan also showed that the straight line graphs obtained for 
different metals all had the same slope, even though the threshold 
frequencies were different. The value of h could be obtained from 
Milhkan's measurements; it was the same for each metal surface, 
and, it agreed very well with a value obtained by means of other, 
independent methods. So Einstein's theory of the photoelectric 
effect was verified quantitatively. 

Historically, the first suggestion that the energy in electro- 
magnetic radiation is "quantized" (comes in definite quanta) came 
not from the photoelectric effect, but from studies of the heat and 
light radiated by hot solids. The concept of quanta of energy was 
introduced by Max Planck, a German physicist, in 1900. five years 
before Einstein's theory, and the constant h is known as Planck's 
constant. Planck was trying to account for the way heat (and light) 
energy radiated by a hot body is related to the frequency of the 
radiation. Classical physics (nineteenth-century thermodynamics 
and electromagnetism) could not account for the experimental 
facts. Planck found that the facts could be interpreted only by 
assuming that atoms, on radiating, change their energy discontin- 
uously, in quantized amounts. Einstein's theory of the photoelectric 
effect was actually an extension and application of Planck's quan- 



Section 18.5 



47 




Robert Andrews Millikan (1868-1953), 
an American physicist, attended Ober- 
lin College, where his interest in phys- 
ics was only mild. After his graduation 
he became more interested in physics, 
taught at Oberlin while taking his 
master's degree, and then obtained 
his doctor's degree from Columbia 
University in 1895. After post-doctoral 
work in Germany he went to the Uni- 
versity of Chicago, where he became a 
professor of physics in 1910. His work 
on the determination of the electronic 
charge took place from 1906 to 1913. 
He was awarded the Nobel Prize in 
physics in 1923 for this research, and 
for the very careful experiments which 
resulted in the verification of the Ein- 
stein photoelectric equation (Sec. 
18.4). In 1921, Millikan moved to the 
California Institute of Technology, 
eventually to become its president. 



turn theory of thermal radiation: Einstein postulated that the 
quantum change in the atom's energy is carried off as a localized 
photon rather than being spread continuously over the light wave. 

The experiments and the theory on radiation are much more 
difficult to describe than the experiments and the theory of the 
photoelectric effect. That is why we have chosen to introduce the 
new concept of quanta of energy by means of the photoelectric 
effect. By now, there have been many ways of checking both 
Planck's and Einstein's conceptions. In all these cases, Planck's 
constant h has now the same basic position in quantum physics 
that Newton's universal constant G has in the physics of 
gravitation. 

The photoelectric effect presented physicists with a real 
dilemma. According to the classical wave theory, light consists of 
electromagnetic waves extending continuously throughout space. 
This theory was highly successful in explaining optical phenomena 
(reflection, refraction, polarization, interference), but could not 
account for the photoelectric effect. Einstein's theory, in which 
the existence of separate lumps of light energy was postulated, 
accounted for the photoelectric effect; it could not account for the 
other properties of hght. The result was that there were two models 
whose basic concepts seemed to be mutually contradictory. Each 
model had its successes and failures. The problem was: what, if 
anything, could be done about the contradictions between the two 
models? We shall see later that the problem and its treatment have 
a central position in modern physics. 

Q8 Einstein's idea of a quantum of light had a definite relation 
to the wave model of light. What was it? 

Q9 Why does the photoelectron not have as much energy as 
the quantum of light which causes it to be ejected? 




Max Planck (1858-1947), a German 
physicist, was the originator of the 
quantum theory, one of the two great 
revolutionary physical theories of the 
20th century. (The other is Einstein's 
relativity theory.) Planck won the 
Nobel Prize in 1918 for his quantum 
theory. He tried for many years to 
show that this theory can be under- 
stood in terms of the classical physics 
of Newton and Maxwell, but this 
attempt did not succeed. Quantum 
physics is fundamentally different, 
through its postulate that energy in 
light and matter is not continuously 
divisible into any arbitrarily small 
quantity, but exists in quanta of defi- 
nite amount. 



48 



Electrons and Quanta 




Wilhelm Konrad Rontgen (1845-1923) 



The discovery of x rays was nar- 
rowly missed by several physicists, 
including Hertz and Lenard (another 
well-known German physicist). An 
English physicist, Frederick Smith, 
found that photographic plates 
kept in a box near a cathode-ray 
tube were liable to be fogged — so 
he told his assistant to keep them 
in another place! 



Q10 What does a "stopping voltage" of, say. 2.0 volts indicate 
about the photoelectrons emerging from a metal surface? 



18.6 X rays 

In 1895. a surprising discovery was made which, hke the 
photoelectric effect, did not fit in with accepted ideas about electro- 
magnetic waves and eventually needed quanta for its explanation. 
The discovery was that of x rays by the German physicist. Wilhelm 
Rontgen; its consequences for atomic physics and technology are 
dramatic and important. 

On November 8. 1895. Rontgen was experimenting with the 
newly found cathode rays, as were many physicists all over the 
world. According to a biographer. 

... he had covered the all-glass pear-shaped tube [Crookes 
tube — see Sec. 18.2] with pieces of black cardboard, and 
had darkened the room in order to test the opacity of the 
black paper cover. Suddenly, about a yard from the tube, 
he saw a weak light that shimmered on a little bench he 
knew was nearby. Highly excited, Rontgen Ut a match 
and, to his great surprise, discovered that the source of 
the mysterious light was a httle barium platinocyanide 
screen lying on the bench. 

Barium platinocyanide, a mineral, is one of the many chemicals 
known to fluoresce, that is, to emit visible light when illuminated 
with ultraviolet hght. But no source of ultraviolet hght was present 
in Rontgen's experiment. Cathode rays had not been observed to 
travel more than a few centimeters in air. So, neither ultraviolet 
light nor the cathode rays themselves could have caused the 
fluorescence. Rontgen therefore deduced that the fluorescence he 
had observed was due to rays of a new kind, which he named 
X rays, that is, rays of an unknown nature. During the next seven 
weeks he made a series of experiments to determine the properties 
of this new radiation. He reported his results on December 28. 1895 
to a scientific society in a paper whose title (translated) is "On a 
New Kind of Rays." 

Rontgen's paper described nearly all of the properties of x rays 
that are known even now. It included an account of the method of 
producing the rays, and proof that they originated in the glass wall 
of the tube, where the cathode rays struck it. Rontgen showed that 
the X rays travel in straight lines from their place of origin and 
that they darken a photographic plate. He reported in detail the 
ability of x rays to penetrate various substances — paper, wood, 
aluminum, platinum and lead. Their penetrating power was greater 
through light materials (paper, wood, flesh) than through dense 
materials (platinum, lead, bone). He described photographs showing 
"the shadows of bones of the hand, of a set of weights inside a 
small box, and of a piece of metal whose inhomogeneity becomes 
apparent with x rays." He gave a clear description of the shadows 

Opposite: One of the earliest x-ray photographs made in the United 
States (1896). The man x-rayed had been hit by a shotgun blast. 





/ 



^ 




50 



Electrons and Quanta 



X rays were often referred to as 
Rontgen rays, after their discoverer. 



It is easy to see why a charged 
electroscope will be discharged 
when the air around it is ionized: 
It attracts the ions of the opposite 
charge from the air. 



Such a particle -the neutron— was 
discovered in 1932. You will see in 
Chapter 23 (Unit 6) how hard it was 
to identify. But the neutron has 
nothing to do with x rays. 



SG 18.12 



cast by the bones of the hand on the fluorescent screen. Rontgen 
also reported that the x rays were not deflected by a magnetic field, 
and showed no reflection, refraction or interference effects in 
ordinary optical apparatus. 

One of the most important properties of x rays was discovered 
by J. J. Thomson a month or two after the rays themselves had 
become known. He found that when the rays pass through a gas 
they make it a conductor of electricity. He attributed this effect to 
"a kind of electrolysis, the molecule being spHt up, or nearly spHt 
up by the Rontgen rays." The x rays, in passing through the gas. 
knock electrons loose from some of the atoms or molecules of the 
gas. The atoms or molecules that lose these electrons become 
positively charged. They are called ions because they resemble the 
positive ions in electrolysis, and the gas is said to be ionized. The 
freed electrons may also attach themselves to previously neutral 
atoms or molecules, thereby leaving them negatively charged. 

Rontgen and Thomson found, independently, that electrified 
bodies are discharged when the air around them is ionized by 
X rays. The rate of discharge was shown to depend on the intensity 
of the rays. This property was therefore used as a convenient 
quantitative means of measuring the intensity of an x-ray beam. 
As a result, careful quantitative measurements of the properties 
and effects of x rays could be made. 

One of the problems that aroused keen interest during the years 
following the discovery of x rays was that of the nature of the 
mysterious rays. They did not act like charged particles — electrons 
for example — because they were not deflected by magnetic or 
electric fields. Therefore it seemed that they had to be either neutral 
particles or electromagnetic waves. It was difficult to choose 
between these two possibilities. On the one hand, no neutral 
particles of atomic size (or smaller) were then known which had 
the penetrating power of x rays. The existence of neutral particles 
with high penetrating power would be extremely hard to prove in 
any case, because there was no way of getting at them. On the 
other hand, if the x rays were electromagnetic waves, they would 
have to have extremely short wavelengths: only in this case, 
according to theory, could they have high penetrating power and 
show no refraction or interference effects with ordinary optical 
apparatus. 

As we have already discussed in Chapters 12 and 13, distinctly 
wavelike properties become apparent only when waves interact 
with objects (like slits in a barrier) that are smaller than several 
wavelengths across. The wavelength hypothesized for x rays would 
be on the order of 10~'" meter. So to demonstrate their wave 
behavior, it would be necessary to see, say, a diff'raction grating 
with slits spaced about 10"'" meter apart. Several lines of evidence, 
from kinetic theory and from chemistry, indicated that atoms were 
about 10~'° meter in diameter. It was suggested, therefore, that 
X rays might be diff'racted noticeably by crystals, in which the 
atoms are arranged in orderly layers about 10~'° meter apart. In 
1912, such experiments succeeded; the layers of atoms do act like 



Section 18.6 



51 




X-ray diffraction patterns from a metal 
crystal. The black spots are produced 
by constructive interference of x rays. 



diffraction gratings, and x rays do, indeed, act like electromagnetic 
radiations of very short wavelength — like ultra ultraviolet light. 
These experiments are more complicated to interpret than diffraction 
of a beam of light by a single, two-dimensional optical grating. Now 
the diffraction effect occurs in three dimensions instead of two. 
Hence the diffraction patterns are far more elaborate (see the 
illustration above). 

In addition to wave properties, x rays were also found to have 
quantum properties: they can, for example, cause the emission of 
electrons from metals. These electrons have greater kinetic energies 
than those produced by ultraviolet hght. (The ionization of gases by 
X rays is also an example of the photoelectric effect; in this case 
the electrons are freed from the atoms and molecules of the gas.) 
Thus, X rays also require quantum theory for the explanation of 
some of their behavior. So, like Hght, x rays were shown to have 
both wave and particle properties. 

Rontgen's initial discovery of x rays excited intense interest 
throughout the entire scientific world. His experiments were 
immediately repeated — and extended in many laboratories in both 
Europe and America. The scientific journals during the year 1896 
were filled with letters and articles describing new experiments or 
confirming the results of earUer experiments. (This widespread 
experimentation was made possible by the fact that, during the 
years before Rontgen's discovery, the passage of electricity through 
gases had been a popular topic for study by physicists — many 
physics laboratories had cathode-ray tubes, and could produce 
X rays easily.) 

Intense interest in x rays was generated by the spectacular use 
of these rays in medicine. Within three months of Rontgen's 



SG 18.13 



SG 18.14-18.16 



Originally, x rays were produced in Rbntgen's 
laboratory when cathode rays (electrons) struck 
a target (the glass wall of the tube). Nowadays 
X rays are commonly produced by directing a beam 
of high energy electrons onto a metal target. As 
the electrons are deflected and stopped, x rays of 
various energies are produced. The maximum 
energy a single ray can have is the total kinetic 
energy the incident electron is giving up on being 
stopped. So the greater the voltage across which 
the electron beam is accelerated, the more ener- 
getic- and penetrating -are the x rays. One type 
of X ray tube is shown in the sketch below, where 
a stream of electrons is emitted from a cathode C 
and accelerated to a tungsten target T by a strong 
electric field (high potential difference). 




In the photograph at the right is the inner part of 
a high voltage generator which can be used to 
provide the large potential differences required 
for making energetic x rays. This Van de Graaf 
type generator (named after the American physi- 
cist who invented it), although not very different 
in principle from the electrostatic generators of 
the 18th century, can produce an electric potential 
difference of 4,000,000 volts between the top and 
ground. 








Above left is a rose, photographed 
with X rays produced when the po- 
tential difference between the elec- 
tron-emitting cathode and the target 
in the x-ray tube is 30,000 volts. 

Below the rose is the head of a 
dogfish shark; its blood vessels have 
been injected with a fluid that absorbs 
X rays in order to study the blood 
vessels. 

In the photograph at the bottom of 
the page, x rays are being used to 
inspect the welds of a 400-ton tank 
for a nuclear reactor. 

Immediately above is illustrated the 
familiar use of x rays in dentistry and 
the resulting records. Because x rays 
are injurious to tissues, a great deal 
of caution is required in using them. 
For example, the shortest possible 
pulse of X rays is used, lead shielding 
is provided for the body, and the tech- 
nician stands behind a wall of lead and 
lead glass. 



54 Electrons and Quanta 

discovery, x rays were being put to practical use in a hospital in 
Vienna in connection with surgical operations. The use of this new 
aid to surgery spread rapidly. Since Rontgen's time, x rays have 
revolutionized some phases of medical practice, especially the 
diagnosis of some diseases, and the treatment of some forms of 
cancer. In other fields of applied science, both physical and 
biological, uses have been found for x rays which are nearly as 
important as their use in medicine. Among these are the study of 
the crystal structure of materials; "industrial diagnosis," such as 
the search for possible defects in materials and engineering 
structures; the study of old paintings and sculptures; and many 
others. 

Q11 X rays were the first "ionizing" radiation discovered. 
What does "ionizing" mean? 

Q12 What were three properties of x rays that led to the 
conclusion that x rays were electromagnetic waves? 

Q13 What was the evidence that x rays had a very short 
wavelength? 

18.7 Electrons, quanta and the atom 

By the beginning of the twentieth century enough chemical 
and physical information was available so that many physicists 
devised models of atoms. It was known that negative particles 
with identical properties — electrons could be obtained from many 
different substances and in different ways. This suggested the 
notion that electrons are constituents of all atoms. But electrons 
are negatively charged, while samples of an element are ordinarily 
electrically neutral and the atoms making up such samples are 
also presumably neutral. Hence the presence of negative electrons 
in an atom would seem to require the presence also of an equal 
amount of positive charge. 

Comparison of the values of qlm for the electron and for 
charged hydrogen atoms indicated, as mentioned in Sec. 18.2, that 
hydrogen atoms are nearly two thousand times more massive than 
electrons. Experiments (which will be discussed in some detail in 
Chapter 22) showed that electrons constitute only a very small part 
of the atomic mass in any atom. Consequently any model of an 
atom must take into account the following information: (a) an 
electrically neutral atom contains equal amounts of positive and 
negative charge; (b) the negative charge is associated with only a 
small part of the mass of the atom. Accordingly, any atomic model 
should answer at least two questions: (1) how many electrons are 
there in an atom, and (2) how are the electrons and the positive 
charge arranged in an atom? 

During the first ten years of the twentieth century, several 
atomic models were proposed, but none was satisfactory. The 
early models were all based entirely upon classical physics, that is, 
upon the physics of Newton and Maxwell. No one knew how to 
invent a model that also took account of the theory of Planck which 



Section 18.7 



55 



incorporated the quantization of energy. There was also need for 
more detailed experimental facts — for example, this was the period 
during which the charge on the electron and the main facts of 
photoelectricity were still being found. Nevertheless physicists 
cannot and should not wait until every last fact is in — that will 
never happen, and you can't even know what the missing facts are 
unless you have some sort of model. Even an incomplete or a partly 
wrong model will provide clues on which to build a better one. 

Until 1911 the most popular model for the atom was one 
proposed by J. J. Thomson in 1904. Thomson suggested that an 
atom consisted of a sphere of positive electricity in which was 
distributed an equal amount of negative charge in the form of 
electrons. Under this assumption, the atom was like a pudding 
of positive electricity with the negative electricity scattered in it 
like raisins. The positive "fluid" was assumed to act on the negative 
charges, holding them in the atom by means of electric forces only. 
Thomson did not specify how the positive "fluid" was held together. 
The radius of the atom was taken to be of the order of 10"'° m, on 
the basis of information from the kinetic theory of gases and other 
considerations (see SG 18.13). With this model Thomson was able 
to calculate that certain arrangements of electrons would be stable, 
the first requirements for explaining the existence of stable atoms. 
Thomson's theory also suggested that chemical properties might be 
associated with particular groupings of electrons. A systematic 
repetition of chemical properties might then occur among groups 
of elements. But it was not possible to deduce the detailed structure 
of the atoms of particular elements, and no detailed comparison 
with the actual periodic table could be made. 




I 








£»/ Z'2. Z-3 l-A 

In Chapter 19 we shall discuss some additional experimental 
information that provided valuable clues to improved models of the 
structure of atoms. We shall also see how one of the greatest 
physicists of our time, Niels Bohr, was able to combine the experi- 
mental evidence then available with the new concept of quanta 
into a successful theory of atomic structure. Although Bohr's model 
was eventually replaced by more sophisticated ones, it provided the 
clues that led to the presently accepted theory of the atom, and to 
this day is in fact quite adequate for explaining most of the main 
facts with which we shall be concerned in this course. 

Q14 Why was most of the mass of an atom beheved to be 
associated with positive electric charge? 

Q15 Why don't physicists wait until "all the facts are in" before 
they begin to theorize or make models? 



See the Project Physics film loop 
Thomson Model of the Atom. 




2-S- 



Z^4, 



Some stable (hypothetical) arrange- 
ments of electrons in Thomson atoms. 
The atomic number Z is interpreted 
as equal to the number of electrons. 



STUDY GUIDE 



18.1 The Project Physics learning materials 
particularly appropriate for Chapter 18 include 
the following: 

Experiments 

The charge-to-mass ratio for an electron 
The measurement of elementary charge 
The photoelectric effect 

Activities 

Writings by and about Einstein 

Measuring qlm for the electron 

Cathode rays in a Crookes tube 

X rays from a Crookes tube 

Lighting a bulb photoelectrically with a 

match 

Reader Articles 

Failure and Success 
Einstein 

Transparencies 

Photoeler trie experiment 
Photoelectric equation 

18.2 In Thomson's experiment on the ratio of 
charge to mass of cathode ray particles (p. 36), 
the following might have been typical values for 
B, V and d: with a magnetic field B alone, the 
deflection of the beam indicated a radius of 
curvature of the beam within the field of 0.114 
meters for B = 1.0 x 10"' tesla.* With the same 
magnetic field, the addition of an electric field in 
the same region (V = 200 volts, plate separation 
d = 0.01 meter) made the beam go on straight 
through. 

(a) Find the speed of the cathode ray particles 
in the beam. 

(b) Find qlm for the cathode ray particles. 

18.3 Given the value for the charge on the 
electron, show that a current of one ampere is 
equivalent to the movement of 6.25 x 10"* 
electrons per second past a given point. 

18.4 In the apparatus of Fig. 18.7, an electron is 
turned back before reaching plate A and 
eventually arrives at electrode C from which it 
was ejected. It arrives with some kinetic energy. 
How does this final energy of the electron compare 
with the energy it had as it left the electrode C? 

18.5 It is found that at light frequencies below 
the threshold frequency no photoelectrons are 
emitted. What happens to light energy? 

18.6 For most metals, the work function W is 
about 10"'" joules. Light of what frequency will 
cause photoelectrons to leave the metal with 
virtually no kinetic energy? In what region of 
the spectrum is this frequency? 

18.7 What is the energy of a Ught photon which 

*The MKSA unit lor B is N/ampm and is now 
called the tesla. (after the electrical engineer 
Nikola Tesla). 



corresponds to a wavelength of 5 x 10 ' m? 
5 X 10"" m? 

18.8 The minimum or threshold frequency of 
light from emission of photoelectrons for copper 
is 1.1 X 10'^ cycles/sec. When ultraviolet Ught of 
frequency 1.5 x 10'-^ cycles/sec shines on a copper 
surface, what is the maximum energy of the 
photoelectrons emitted, in joules? In electron 
volts? 

18.9 What is the lowest-frequency bght that will 
cause the emission of photoelectrons from a 
surface whose work function is 2.0 eV (that is, 
an energy of at least 2.0 eV is needed to eject an 
electron)? 

18.10 Monochromatic light of wavelength 5000 
A falls on a metal cathode to produce photo- 
electrons. (lA = 10"'" meter) The Ught intensity 
at the surface of the metal is 10- joules/m^ 

per sec. 

(a) What is the frequency of the Ught? 

(b) What is the energy (in joules) of a single 
proton of the light? 

(c) How many photons fall on 1 m- in one sec? 

(d) If the diameter of an atom is about 1 A. 
how many photons fall on one atom in one 
second, on the average? 

(e) How often would one photon fall on one 
atom, on the average? 

(f ) How many photons fall on one atom in 
10"'" sec, on the average? 

(g) Suppose the cathode is a square 0.05 m on 
a side. How many electrons are released 
per second, assuming every photon releases 
a photoelectron? How big a current would 
this be in amperes? 

18.11 Roughly how many photons of visible Ught 
are given off per second by a 1-watt flashlight? 
(Only a bout 5 percent of the electric energy input 
to a tungsten-filament bulb is given off" as \ isible 
Ught.) 

Hint: first find the energy, in joules, of an average 
photon of visible Ught. 

18.12 Recall from Sec. 17.8 that 96.540 coulombs 
of charge will deposit 31.77 grams of copper in 
the electrolysis of copper sulfate. In Sec. 18.3. the 
charge of a single electron was reported to be 1.6 
X 10"'-' coulomb. 

(a) How many electrons must be transferred 
to deposit 31.77 grams of copper? 

(b) The density of copper is 8.92 grams per 
cm'. How many copper atoms would 
there be in the 1 cm^? (Actually copper 
has a coiTibining number of 2. which 
suggests that 2 electrons are required to 
deposit a single copper atom.) 

(c) What is the approximate volume of each 
copper atom? 

(d) What is the approximate diameter of a 
copper atom? (For this rough approxima- 
tion, assume that the atoms are cubes.) 



56 



18.13 The approximate size of atoms can be 
calculated in a simple way from x-ray scattering 
experiments. The diagram below represents the 
paths of two portions of an x-ray wavefront, part 
of which is scattered from the first layer of atoms 
in a CFN'stal, and part of which is scattered from 
the second layer. The part reflected from the 
second layer travels a distance 2x further before 
it emerges from the crystal. 




IqOO a^<i^ O O 

(a) Under what conditions will the scattered 
wavefronts reinforce one another (that 
is, be in phase)? 

(b) Under the conditions, will the scattered 
wavefronts cancel one another? 

(c) Use trigonometr^' to express the relation- 
ship among wavelength K the distance d 
between layers, and the angle of reflection 
6„„j. that will have maximum intensity. 

18.14 The highest frequency, /^^j, of the x rays 
produced by an x ray tube is given by the relation 

where h is Planck's constant, q^ is the charge of 
an electron, and V is the potential diff'erence at 
which the tube operates. If V is 50,000 volts, 
what is/„a_r? 



18.15 The equation giving the maximum energy 
of the X rays in the preceding problem looks hke 
one of the equations in Einstein's theory of the 
photoelectric effect. How would you account for 
this similarity? For the difference? 

18.16 What potential difference must be applied 
across an x-ray tube for it to emit x rays with 

a minimum wavelength of 10"" m? What is the 
energy of these x rays in joules? In electron volts? 

18.17 A glossary is a collection of terms Umited 
to a special field of knowledge. Make a glossary of 
terms that appeared for the first time in this 
course in Chapter 18. Make an informative 
statement or definition for each term. 

18.18 In his Opticks, Newton proposed a set of 
hypotheses about light which, taken together, 
constituted a fairly successful model of hght. 
The hypotheses were stated as questions. Three of 
the hypotheses are given below: 

Are not all hypotheses erroneous, in which 
light is supposed to consist in pression or 
motion waves . . . ? [Quest. 28] 

Are not the rays of light very small bodies 
emitted from shining substances? [Quest. 29] 

Are not gross bodies and light convertible 
into one another, and may not bodies receive 
much of their activity from the particles of 
hght which enter their composition? 
[Quest. 30] 

(a) In what respect is Newton's model similar 
to and different from the photon model of 
hght? 

(b) Why would Newton's model be insufficient 
to explain the photoelectric effect? What 
predictions can we make with the photon 
model that we cannot with Newton's? 



57 



19.1 Spectra of gases 59 

19.2 Regularities in the hydrogen spectrum 63 

19.3 Rutherford's nuclear model of the atom 66 

19.4 Nuclear charge and size 69 

19.5 The Bohr theory: the postulates 71 

19.6 The size of the hydrogen atom 72 

19.7 Other consequences of the Bohr model 74 

19.8 The Bohr theory: the spectral series of hydrogen 75 

19.9 Stationary states of atoms: the Franck-Hertz experiment 79 

19.10 The periodic table of the elements 82 

19.11 The inadequacy of the Bohr theory, and the state of 

atomic theory in the early 1920's 86 




Sculpture representing the Bohr 
model of a sodium atom. 



CHAPTER NINETEEN 



The Rutherford-Bohr Model of the Atom 



19.1 Spectra of gases 

One of the first real clues to our understanding of atomic 
structure was provided by the study of the emission and absorption 
of light by samples of the elements. The results of this study are so SG 19.1 

important to our story that we shall review the history of their 
development in some detail. 

It had long been known that light is emitted by gases or vapors 
when they are excited in any one of several ways: by heating the 
gas to a high temperature, as when a volatile substance is put into a 
flame; by an electric discharge through gas in the space between 
the terminals of an electric arc; by a continuous electric current 
in a gas at low pressure (as in the now familiar "neon sign"). 

The pioneer experiments on light emitted by various excited 
gases were made in 1752 by the Scottish physicist Thomas Melvill. 
He put one substance after another in a flame; and "having placed 
a pasteboard with a circular hole in it between my eye and the 
flame . . . , I examined the constitution of these different lights with 
a prism." Melvill found the spectrum of light from a hot gas to be 
different from the well-known continuum of rainbow colors found 
in the spectrum of a glowing solid or liquid. Melvill's spectrum 
consisted, not of an unbroken stretch of color continuously graded 
from violet to red, but of individual patches, each having the color 
of that part of the spectrum in which it was located, and with dark 
gaps (missing colors) between the patches. Later, when more 
general use was made of a narrow slit through which to pass the 
light, the emission spectrum of a gas was seen as a set of bright 
lines (see the figure in the margin on p. 61); the bright lines are in 
fact colored images of the slit. The existence of such spectra shows 
that light from a gas is a mixture of only a few definite colors or 
narrow wavelength regions of light. 

Melvill also noted that the colors and locations of the bright 
spots were different when different substances were put in the 
flame. For example, with ordinary table salt in the flame, the 

59 




Hot solids emit all wavelengths of light, producing a continu- 
ous spectrum on the screen at right. The shorter-wavelength 
portions of light are refracted more by the prism than are long 
wavelengths. 




Hot gases emit only certain wavelengths of light, producing a 
"bright line" spectrum. If the slit had a different shape, so 
would the bright lines on the screen. 




1 



Cool gases absorb only certain wavelengths of light, produc- 
ing a "dark line" spectrum when "white" light from a hot 
solid is passed through the cool gas. 



Section 19.1 



61 



predominant color was "bright yellow" (now known to be character- 
isitic of the element sodium). In fact, the line emission spectrum is 
markedly different for each chemically different gas because each 
chemical element emits its own characteristic set of wavelengths 
(see the figure in the margin). In looking at a gaseous source with- 
out the aid of a prism or a grating, the eye combines the separate 
colors and perceives the mixture as reddish for glowing neon, pale 
blue for nitrogen, yellow for sodium vapor, and so on. 

Some gases have relatively simple spectra. Thus the most 
prominent part of the visible spectrum of sodium vapor is a pair of 
bright yellow lines. Some gases or vapors have exceedingly complex 
spectra. Iron vapor, for example, has some 6000 bright lines in the 
visible range alone. 

In 1823 the British astronomer John Herschel suggested that 
each gas could be identified from its unique line spectrum. By the 
early 1860's the physicist Gustave R. Kirchhoff and the chemist 
Robert W. Bunsen, in Germany, had jointly discovered two new 
elements (rubidium and cesium) by noting previously unreported 
emission lines in the spectrum of the vapor of a mineral water. This 
was the first of a series of such discoveries; it started the develop- 
ment of a technique making possible the speedy chemical analysis 
of small amounts of materials by spectrum analysis. 

In 1802 the English scientist William Wollaston saw in the 
spectrum of sunlight something that had been overlooked before. 
Wollaston noticed a set of seven sharp, irregularly spaced dark lines 
across the continuous solar spectrum. He did not understand why 
they were there, and did not carry the investigation further. A dozen 
years later, the German physicist, Joseph von Fraunhofer, used 
better instruments and detected many hundreds of such dark lines 
To the most prominent dark lines, Fraunhofer assigned the letters 
A, B, C, etc. These dark lines can be easily seen in the sun's 
spectrum with even quite simple modem spectroscopes, and his 
letters A. B, C . . . are still used to identifv them. 



^o! 




Parts of the line emission spectra 
of mercury (Hg) and helium (He), 
redrawn from photographic records. 



Spectroscope: A device for 
examining the spectrum by eye. 

Spectrometer or spectrograph: 
A device for measuring the wave 
length of the spectrum and for 
recording the spectra (for example 
on film). 




The Fraunhofer dark lines in the 
visible part of the solar spectrum: 
only a few of the most prominent 
lines are represented. 



In the spectra of several other bright stars, Fraunhofer found 
similar dark lines; many of them, although not all, were in the same 
positions as those in the solar spectrum. 

The key observations toward a better understanding of both 
the dark-line and the bright-line spectra of gases were made by 
Kirchhoff in 1859. By that time it was known that the two promi- 
nent yellow lines in the emission spectrum of heated sodium vapor 
in the laboratory had the same wavelengths as two neighboring 
prominent dark lines in the solar spectrum to which Fraunhofer had 



62 



The Rutherford-Bohr Model of the Atom 



absorption 
spectrum 



emission 
spectrum 



assigned the letter D. It was also known that the light emitted by a 
glowing solid forms a perfectly continuous spectrum that shows no 
dark hnes. Kirchhoff now demonstrated that if the light from a 
glowing solid, as on page 60. is allowed first to pass through cooler 
sodium vapor and is then dispersed by a prism, the spectrum 
exhibits two prominent dark lines at the same place in the spectrum 
as the D-lines of the sun's spectrum. It was therefore reasonable 
to conclude that the light from the sun, too, was passing through a 
mass of sodium gas. This was the first evidence of the chemical 
composition of the gas envelope around the sun. 

■MM ■■■—■■ 



ultraviolet 



visible 



>4 infrared 



Comparison of the line absorption 
spectrum and line emission spectrum 
of sodium vapor. 



SG 19.2 



When Kirchhoff 's experiment was repeated with other relatively 
cool gases placed between a glowing solid and the prism, each gas 
was found to produce its own characteristic set of dark lines. 
Evidently each gas in some way absorbs light of certain wave- 
lengths from the passing "white" light. More interesting still, 
Kirchhoff showed that the wavelength corresponding to each 
absorption line is equal to the wavelength of a bright line in the 
emission spectrum of the same gas. The conclusion is that a gas 
can absorb only light of these wavelengths which, when excited, it 
can emit. But note that not every emission line is represented in 
the absorption spectrum. (Soon you will see why.) 

Each of the various Fraunhofer lines across the spectrum of the 
sun and also of far more distant stars have now been identified with 
the action of some gas as tested in the laboratory, and thereby the 
whole chemical composition of the outer region of the sun and other 
stars has been determined. This is really quite breathtaking from 
several points of view: (a) that it could be possible to find the 
chemical composition of immensely distant objects; (b) that the 
chemical materials there are the same as those in our own sur- 
roundings on earth, as shown by the fact that even the most 
complex absorption spectra are faithfully reproduced in the star 
spectra; and (c) that therefore the physical processes in the atom 
that are responsible for absorption must be the same here and 
there. In these facts we have a hint of how universal physical law 
really is: even at the outermost edges of the cosmos from which we 
get any light with absorbed wavelengths, the laws of physics appear 
to be the same as for common materials close at hand in our 
laboratory! This is just what GaUleo and Newton had intuited when 



Section 19.2 



63 



they proposed that there is no difference between terrestrial and 
celestial physics. 

Q1 What can you infer about the source if its light gives a 
bright line spectrum? 

Q2 What can you infer about the source if its light gives a dark 
line spectrum? 

Q3 What evidence is there that the physics and chemistry of 
materials at great distances from us is the same as of matter close 
at hand? 



19.2 Regularities in the hydrogen spectrum 



Of all the spectra, the line emission spectrum of hydrogen is 
especially interesting for both historical and theoretical reasons. In 
the visible and near ultraviolet regions, the emission spectrum 
consists of an apparently systematic series of Hnes whose positions 
are indicated at the right. In 1885, a Swiss school teacher, Johann 
Jakob Balmer, found a simple formula- an empirical relation- 
which gave the wavelengths of the lines known at the time. The 
formula is: 



Johann Jakob Balmer (1825-1898), 
a teacher at a girls' school in 
Switzerland, came to study wave- 
lengths of spectra listed in tables 
through his interest in mathematical 
puzzles and numerology. 



\ = b 



n' 



n^-2^ 



Where b is a constant which Balmer determined empirically and 
found to be equal to 3645.6 A, and n is a whole number, different for 
each line. Specifically, to give the observed value for the wave- 
length, n must be 3 for the first (red) line of the hydrogen emission 
spectrum (named HJ; n = 4 for the second (green) line (H^); n == 5 
for the third (blue) line (H;,); and n = 6 for the fourth (violet) line 
(Hg). The table below shows excellent agreement (within 0.02%) 
between the values Balmer computed from his empirical formula 
and previously measured values. 



NAME 
OF LINE 



Wavelength A (in A) 

FROM BALMER'S BY ANGSTROM'S 

FORMULA MEASUREMENT 



DIFFERENCE 



H„ 


3 


6562.08 


6562.10 


+0.02 


H, 


4 


4860.8 


4860.74 


-0.06 


H. 


5 


4340 


4340.1 


+ 0.1 


H« 


6 


4101.3 


4101.2 


-0.1 




The Balmer lines of hydrogen; re- 
drawn from a photograph made with 
a film sensitive to ultraviolet light as 
well as visible. The lines get more 
crowded as they approach the series 
limit in the ultraviolet. 



Data on hydrogen spectrum (as given 
in Balmer's paper of 1885). 



It took nearly 30 years before anyone understood why Balmer's 
empirical formula worked so well -why the hydrogen atom emitted 
light whose wavelength made such a simple sequence. But this did 
not keep Balmer from speculating, that there might be other series of 



■H.o 



64 The Rutherford-Bohr Model of the Atom 

hither-to unsuspected lines in the hydrogen spectrum, and that their 
wavelengths could be found by replacing the 2'^ in the denominator 
of his equation by other numbers such as P, 3^, 4-, and so on. This 
suggestion, which stimulated many workers to search for such 
additional spectral series, turned out to be fruitful, as we shall 
discuss shortly. 

To use modern notation, we first rewrite B aimer's formula in a 
form that will be more useful. 



1-^ 



In this equation, which can be derived from the first one, R^ is 
a constant, equal to 4/b. (It is called the Rydberg constant for 
hydrogen, in honor of the Swedish spectroscopist J. R. Rydberg 
who, following B aimer, made great progress in the search for 
various spectral series.) The series of Unes described by B aimer's 
formula are called the Balmer series. While Balmer constructed his 
formula from known X of only four lines, his formula predicted that 
there should be many more lines in the same series (indeed, 
infinitely many such lines as n takes on values such as n = 3, 4, 5, 
6, 7, 8, . . . oo). The figure in the margin indicates that this has 
indeed been observed — and every one of the lines is correctly pre- 
dicted by Balmer's formula with considerable accuracy. 

If we follow Balmer's speculative suggestion of replacing 2^ 
by other numbers, we obtain the possibilities: 



k~^"{v~n^ 



X'^'^fe 1? 



1- 



"W nV 



and so on. Each of these equations describes a possible series. All 
these hypothetical series of lines can then be summarized in one 
overall formula: 



k ^"[n/ n,V 



Part of the absorption spectrum 
of the star Rigel ()3 Orion). The 
dark lines are at the same loca- 
tion as lines due to absorption 
by hydrogen gas in the ultra- 
violet region; they match the 
lines of the Balmer series as 
indicated by the H numbers 
(where H, would be H„, H^ would 
be H;, etc.). This indicates the 
presence of hydrogen in the 
star. 



where n^ is a whole number that is fixed for any one series for 
which wavelengths are to be found (for example, it is 2 for all lines 
in the Balmer series). The letter n, stands for integers that take on 
the values n^^ + 1, w^^ + 2, n^^ + 3, . . . for the successive individual 
lines in a given series (thus, for the first two lines of the Balmer 
series, n, is 3 and 4.) The constant R„ should have the same value 
for all of these hydrogen series. 

So far, our discussion has been merely speculation. No series, 
no single line fitting the formula in the general formula, need exist 
( — except for the observed Bahner series, where nf = 2). But when 
physicists began to look for these hypothetical lines with good 
spectrometers — they found that they do exist! 

In 1908. F. Paschen in Germany found two hydrogen lines in 
the infrared whose wavelengths were correctly given by setting 
71/ = 3 and n, = 4 and 5 in the general formula; many other lines 



Section 19.2 65 

in this "Paschen series" have since been identified. With improve- 
ments of experimental apparatus and techniques, new regions of 
the spectrum could be explored, and thus other series gradually 
were added to the Balmer and Paschen series. In the table below 
the name of each series listed is that of the discoverer. 

Series of lines in the hydrogen spectrum 



NAME OF 


DATE OF 


REGION OF 


VALUES IN 


SERIES 


DISCOVERY 


SPECTRUM 


BALMER EQUATION 


Lyman 


1906-1914 


ultraviolet 


n^ = 1 , n, = 2, 3, 4, 


Balmer 


1885 


ultraviolet-visible 


rif = 2, n,. = 3, 4, 5, 


Paschen 


1908 


infrared 


rif = 3, n,. = 4, 5, 6 


Brackett 


1922 


infrared 


Pf = 4, n,. = 5, 6, 7 


Pfund 


1924 


infrared 


n^= 5, H; = 6, 7, 8 



Balmer had also hoped that his formula for hydrogen spectra 
might be a pattern for finding series relationships in the observed 
spectra of other gases. This suggestion bore fruit also. While his 
formula itself did not work directly in describing spectra of gases 
other than hydrogen, it inspired formulas of similar mathematical 
form that were useful in expressing order in portions of a good 
many complex spectra. The Rydberg constant Rh also reappeared 
in such empirical formulas. 

For three decades after Balmer's success, physicists tried to 
account for spectra by constructing models of the atom that would 
radiate light of the right wavelengths. But the great number and 
variety of spectral lines, emitted even by the simplest atom, 
hydrogen, made it difiicult to find a successful model. Eventually 
models were made that succeeded in revealing the origin of 
spectra and in this chapter and the next one, you will see how it 
was done. 

What you have already learned in Chapter 18 about quantum SG 19.3-19.5 

theory suggests one line of attack: the emission and absorption of 
light from an atom must correspond to a decrease and an increase 
of the amount of energy the atom has. If atoms of an element emit 
light of only certain frequencies, then the energy of the atoms must 
be able to change only by certain amounts. These changes of energy 
must belong to some rearrangement of the parts of the atom. 

Q4 What evidence did Balmer have that there were other 
series of lines in the hydrogen spectrum, with terms 3^, 4^, etc. 
instead of 2^? 

Q5 Often discoveries result from grand theories (like 
Newton's) or from a good intuitive grasp of phenomena (like 
Faraday's). What led Balmer to his relation for spectra? 

Q6 What accounts for the success of Balmer's overall formula 
in predicting new series of the emission spectrum of hydrogen? 



66 



The Rutherford-Bohr Model of the Atom 



SG 19.6 







HCTAu 



In somewhat the same way, you 
could, in principle, use a scattering 
experiment to discover the size and 
shape of an object hidden from view 
in a cloud or fog — by directing a 
series of projectiles at the unseen 
object and tracing their paths back 
after deflection. 




19.3 Rutherford's nuclear model of the atom 

A new basis for atomic models was provided during the period 
1909 to 1911 by Ernest Rutherford, a New Zealander who had 
already shown ability as an experimentalist at McGill University in 
Montreal, Canada. He had been invited in 1907 to Manchester 
University in England where he headed a productive research 
laboratory. Rutherford was specially interested in the rays emitted 
by radioactive substances, in particular in a (alpha) rays. As we 
shall see in Chapter 21, a rays consist of positively charged particles. 
These particles are positively charged helium atoms with masses 
about 7500 times greater than the electron mass. Some radioactive 
substances emit a particles at rates and energies great enough for 
the particles to be used as projectiles to bombard samples of ele- 
ments. The experiments that Rutherford and his colleagues did 
with a particles are examples of a highly important kind of 
experiment in atomic and nuclear physics — the scattering 
experiment. 

In a scattering experiment, a narrow, parallel beam of projec- 
tiles (for example, a particles, electrons, x rays) is aimed at a target 
that is usually a thin foil or film of some material. As the beam 
strikes the target, some of the projectiles are deflected, or scattered 
from their original direction. The scattering is the result of the 
interaction between the particles in the beam and the atoms of the 
material. A careful study of the projectiles after they have been 
scattered can yield information about the projectiles, the atoms, 
or both — or the interaction between them. Thus if we know the 
mass, energy and direction of the projectiles, and see what happens 
to them in a scattering experiment, we can deduce properties of 
the atoms that scattered the projectiles. 

Rutherford noticed that when a beam of a particles passed 
through a thin metal foil, the beam spread out. The scattering of a 
particles can be imagined to be caused by the electrostatic forces 
between the positively charged a particles and the charges that 
make up atoms. Since atoms contain both positive and negative 
charges, an a particle is subjected to both repulsive and attractive 
forces as it passes through matter. The magnitude and direction of 
these forces depend on how near the particle happens to approach 
to the centers of the atoms among which it moves. When a particu- 
lar atomic model is proposed, the extent of the expected scattering 
can be calculated and compared with experiment. In the case of the 
Thomson model of the atom, calculation showed that the probability 
is so negligibly small that an a particle would be scattered through 
an angle of more than a few degrees. 

The breakthrough to the modern model of the atom came when 
one of Rutherford's assistants, Hans Geiger, found that the number 
of particles scattered through angles of 10° or more was much 
greater than the number predicted on the basis of the Thomson 
model. In fact, one out of about every 8000 a particles was scattered 
through an angle greater than 90°. Thus a significant number of a 
particles virtually bounced right back from the foil. This result was 
entirely unexpected on the basis of Thomson's model of the atom. 



Section 19.3 



67 




Ernest Rutherford (1871-1937) was born, grew up. and 
received most of his education in New Zealand. At 
age 24 he went to Cambridge, England to work at 
the Cavendish Laboratory under J. J. Thomson. From 
there he went to McGill University in Canada, then 
home to be married and back to England again, now 
to Manchester University. At these universities, and 
later at the Cavendish Laboratory where he succeeded 
J. J. Thomson as director, Rutherford performed 
important experiments on radioactivity, the nuclear 
nature of the atom, and the structure of the nucleus. 
Rutherford introduced the concepts alpha," "beta" 
and gamma" rays, "protons," and "half-life." His 
contributions will be further discussed in Unit 6. For 
his scientific work, Rutherford was knighted and 
received a Nobel Prize. 



by which the atom should have acted on the projectile more like a 
cloud in which fine dust is suspended. Some years later, Rutherford 
wrote: 



... I had observed the scattering of a-particles. and Dr. 
Geiger in my laboratory had examined it in detail. He 
found, in thin pieces of heavy metal, that the scattering 
was usually small, of the order of one degree. One day 
Geiger came to me and said. "Don't you think that young 
Marsden, whom I am training in radioactive methods, 
ought to begin a small research?" Now I had thought 
that, too, so I said, "Why not let him see if any a-particles 
can be scattered through a large angle?"" I may tell you in 
confidence that I did not believe that they would be, since 
we knew that the a-particle was a very^ fast, massive 
particle, with a great deal of [kinetic] energy, and you 
could show that if the scattering was due to the accumu- 
lated effect of a number of small scatterings, the chance 
of an a-particle"s being scattered backward was very 
small. Then I remember two or three days later Geiger 
coming to me in great excitement and saying, "We have 



68 



The Rutherford-Bohr Model of the Atom 



been able to get some of the a-particles coming back- 
ward . . ." It was quite the most incredible event that 
has ever happened to me in my life. It was almost as 
incredible as if you fired a 15-inch shell at a piece of 
tissue paper and it came back and hit you. On considera- 
tion, I realized that this scattering backward must be the 
result of a single collision, and when I made calculations 
I saw that it was impossible to get anything of that order 
of magnitude unless you took a system in which the 
greater part of the mass of the atom was concentrated in 
a minute nucleus. It was then that I had the idea of an 
atom with a minute massive centre, carrying a charge. 




SG 19.6, 19.7 




Paths of two a particles A and A' ap- 
proaching a nucleus N. (Based on 
Rutherford, Philosophical Magazine. 
vol. 21 (1911), p. 669.) 



oc 



¥ 




Rutherford's scintillation apparatus 
was placed in an evacuated chamber 
so that tne a particles would not be 
slowed down by collisions with air 
molecules. 



These experiments and Rutherford's interpretation marked the 
origin of the modern concept of the nuclear atom. Let us look at 
the experiments more closely to see why Rutherford concluded that 
the atom must have its mass and positive charge concentrated in a 
tiny space at the center, thus forming a nucleus about which the 
electrons are clustered. 

A possible explanation of the observed scattering is that there 
exist in the foil concentrations of mass and charge — positively 
charged nuclei — much more dense than in Thomson's atoms. An a. 
particle heading directly toward one of them is stopped and turned 
back, as a ball would bounce back from a rock but not from a cloud 
of dust particles. The figure in the margin is based on one of 
Rutherford's diagrams in his paper of 1911, which may be said 
to have laid the foundation for the modern theory of atomic 
structure. It shows two positively charged a particles, A and A'. 
The a particle A is heading directly toward a massive nucleus N. 
If the nucleus has a positive electric charge, it will repel the 
positive oc particle. Because of the electrical repulsive force 
between the two, A is slowed to a stop at some distance r from N. 
and then moves directly back. A' is another a particle that is not 
headed directly toward the nucleus N; it is repelled by N along a 
path which calculation showed must be an hyperbola. The deflection 
of A' from its original path is indicated by the angle (/>. 

Rutherford considered the effects on the path of the a. particle 
due to the important variables — the a particle's speed, the foil 
thickness, and the quantity of charge Q on each nucleus. According 
to the model most of the a particles should be scattered through 
small angles, because the chance of approaching a very small 
nucleus nearly head-on is so small; but a noticeable number of a 
particles should be scattered through large angles. 

Geiger and Marsden undertook tests of these predictions with 
the apparatus shown schematically in the margin. The lead box B 
contains a radioactive substance (radon) which emits a particles. 
The particles emerging from the small hole in the box are deflected 
through various angles 4> in passing through the thin metal foil F. 
The number of particles deflected through each angle <i> is found 
by letting the particles strike a zinc sulftide screen S. Each a 
particle that strikes the screen produces a scintillation (a momen- 



Section 19.4 



69 



tary pinpoint of fluorescence). These scintillations can be observed 
and counted by looking through the microscope M; S and M can be 
moved together along the arc of a circle. In later experiments, the 
number of a particles at any angle </> was counted more conven- 
iently by replacing S and M by a counter invented by Geiger (see 
sketch in the margin). The Geiger counter, in its more recent 
versions, is now a standard laboratory item. 

Geiger and Marsden found that the number of a particles 
counted depended on the scattering angle, the speed of the particles, 
and on the thickness of the foil of scattering material, just as 
Rutherford had predicted. This bore out the model of the atom in 
which most of the mass and all positive charge are concentrated in 
a very small region at the center of the atom. 



Q7 Why are a particles scattered by atoms? Why is the angle 
of scattering mostly small but sometimes large? 

Q8 What was the basic diff'erence between the Rutherford 
and the Thomson models of the atom? 



19.4 Nuclear charge and size 

At the time Rutherford made his predictions about the effect of 
the speed of the a particle and the thickness of foil on the angle of 
scattering, there was no way to measure independently the 
nucleus charge Q which he had to assume. However, some of 
Rutherford's predictions were confirmed by scattering experiments 
and, as often happens when part of a theory is confirmed, it is 
reasonable to proceed temporarily as if the whole of that theory were 
justified. That is, pending further proof, one could assume that the 
value of Q needed to explain the observed scattering data was the 
correct value of Q for the actual nucleus. On this basis, from the 
scattering by different elements — among them carbon, aluminum 
and gold — the following nuclear charges were obtained: for carbon, 
Q = 6qp, for aluminum, Q = 13 or Mg^, and for gold, Q = 78 or IGq^. 
Similarly, tentative values were found for other elements. 

The magnitude of the positive charge of the nucleus was an 
important and welcome piece of information about the atom. If the 
nucleus has a positive charge of 6 q^, 13 to 14 q^, etc., the number 
of electrons surrounding the nucleus must be 6 for carbon, 13 or 14 
for aluminum, etc., since the atom as a whole is electrically neutral. 
This gave for the first time a good idea of just how many electrons 
an atom may have. But even more important, it was soon noticed 
that for each element the value found for the nuclear charge — in 
multiples of q^- was close to the atomic number Z, the place 
number of that element in the periodic table! While the results of 
experiments on the scattering of a particles were not yet precise 
enough to permit this conclusion to be made with certainty, the 
data indicated that each nucleus has a positive charge Q numer- 
ically equal to Zq^. 

The suggestion that the number of positive charges on the 




SG 19.8 



A Geiger counter (1928). It consists 
of a metal cylinder C containing a gas 
and a thin axial wire A that is insulated 
from the cylinder. A potential differ- 
ence slightly less than that needed 
to produce a discharge through the 
gas is maintained between the wire 
(anode A) and cylinder (cathode C). 
When an a particle enters through the 
thin mica window (W), it frees a few 
electrons from the gas molecules. 
The electrons are accelerated toward 
the anode, freeing more electrons 
along the way by collisions with gas 
molecules. The avalanche of electrons 
constitutes a sudden surge of current 
which may be amplified to produce a 
click in the loudspeaker (L) or to oper- 
ate a register (as in the Project Physics 
scaler, used in experiments in Unit 6). 



q, = numerical value of charge of 
one electron. 



70 



The Rutherford-Bohr Model of the Atom 






The central dot representing the 
nucleus in relation to the size of the 
atom as a whole is about 100 times 
too large. Popular diagrams of atoms 
often greatly exaggerate the relative 
size of the nucleus, (perhaps in order 
to suggest the greater mass). 



nucleus and also the number of electrons around the nucleus are 
equal to the atomic number Z made the picture of the nuclear atom 
at once much clearer and simpler. On this basis, the hydrogen 
atom (Z = 1) has one electron outside the nucleus; a helium atom 
(Z = 2) has in its neutral state two electrons outside the nucleus; 
a uranium atom (Z = 92) has 92 electrons. This simple scheme was 
made more plausible when additional experiments showed that it 
was possible to produce singly ionized hydrogen atoms, H^, and 
doubly ionized helium atoms, He^^, but not H^^ or He^^^ — evidently 
because a hydrogen atom has only one electron to lose, and a 
helium atom only two. Unexpectedly, the concept of the nuclear 
atom thus provided new insight into the periodic table of the 
elements: it suggested that the periodic table is really a listing of 
the elements according to the number of electrons around the 
nucleus, or according to the number of positive units of charge on 
the nucleus. 

These results made it possible to understand some of the dis- 
crepancies in Mendeleev's periodic table. For example, the elements 
tellurium and iodine had been put into positions Z = 52 and Z = 53 
on the basis of their chemical properties, contrary to the order of 
their atomic weights. Now that Z was seen to correspond to a 
fundamental fact about the nucleus, the reversed order of their 
atomic weights was understood to be a curious accident rather 
than a basic fault in the scheme. 

As an important additional result of these scattering experi- 
ments the size of the nucleus may be estimated. Suppose an a 
particle is moving directly toward a nucleus. Its kinetic energy on 
approach is transformed into electrical potential energy. It slows 
down and eventually stops. The distance of closest approach may 
be computed from the original kinetic energy of the a particle and 
the charges of a particle and nucleus. (See SG 19.8.) The value 
calculated for the closest approach is approximately 3 x 10 "'^m. If 
the a particle is not penetrating the nucleus, this distance must be 
at least as great as the sum of the radii of oc particle and nucleus; 
so the radius of the nucleus could not be larger than about 10"'*m, 
only about 1/1000 of the known radius of an atom. Thus if one 
considers its volume, which is proportional to the cube of the radius, 
it is clear that the atom is mostly empty, with the nucleus occupying 
only one billionth of the space! This in turn explains the ease with 
which a particles or electrons penetrate thousands of layers of 
atoms in metal foils or in gases, with only occasional large 
deflection backward. 

Successful as this model of the nuclear atom was in explaining 
scattering phenomena, it raised many new questions: What is the 
arrangement of electrons about the nucleus? What keeps the 
negative electron from falling into a positive nucleus by electrical 
attraction? Of what is the nucleus composed? What keeps it from 
exploding on account of the repulsion of its positive charges? 
Rutherford openly realized the problems raised by these questions, 
and the failure of his model to answer them. But he rightly said 
that one should not expect one model, made on the basis of one 



Section 19.5 71 

set of puzzling results which it handled well, also to handle all 

other puzzles. Additional assumptions were needed to complete the SG 19.9 

model — to find answers to the additional questions posed about the 

details of atomic structure. The remainder of this chapter will deal 

with the theory proposed by Niels Bohr, a young Danish physicist 

who joined Rutherford's group just as the nuclear model was being 

announced. 

Q9 What does the "atomic number" of an element refer to, 
according to the Rutherford model of the atom? 

Q10 What is the greatest positive charge that an ion of 
lithium (the next heaviest element after helium) could have? 



19.5 The Bohr theory: the postulates 

If an atom consists of a positively charged nucleus surrounded 
by a number of negatively charged electrons, what keeps the 
electrons from falling into the nucleus — from being pulled in by the 
electric force of attraction? One possible answer to this question 
is that an atom may be like a planetary system with the electrons 
revolving in orbits around the nucleus. Instead of the gravitational 
force, the electric attractive force between the nucleus and an 
electron would supply a centripetal force that would tend to keep 
the moving electron in orbit. 

Although this idea seems to start us on the road to a theory of 
atomic structure, a serious problem arises concerning the stability 
of a planetary atom. According to Maxwell's theory of electro- 
magnetism, a charged particle radiates energy when it is 
accelerated. Now. an electron moving in an orbit around a nucleus 
continually changes its velocity vector, always being accelerated by 
the centripetal electric force. The electron, therefore, should lose 
energy by emitting radiation. A detailed analysis of the motion of 
the electron shows that the electron should be drawn closer to the 
nucleus, somewhat as an artificial satellite that loses energy due 
to friction in the upper atmosphere spirals toward the earth. Within 
a very short time, the energy-radiating electron should actually 
be pulled into the nucleus. According to classical physics — 
mechanics and electromagnetism — a planetary atom would not be 
stable for more than a very small fraction of a second. 

The idea of a planetary atom was nevertheless sufficiently 
appealing that physicists continued to look for a theoi^y that would 
include a stable planetary structure and predict discrete line spectra 
for the elements. Niels Bohr, an unknown young Danish physicist 
who had just received his PhD degree, succeeded in constructing 
such a theory in 1912-1913. This theory, although it had to be 
modified later to make it applicable to many more phenomena, was 
widely recognized as a major victory, showing how to attack 
atomic problems by using quantum theory. In fact, even though it 
is now a comparatively naive way of thinking about the atom 
compared to the view given by more recent quantum-mechanical 



72 



The Rutherford-Bohr Model of the Atom 



Since Bohr incorporated Ruther- 
ford's idea of the nucleus, the model 
which Bohr's theory discusses is 
often called the Rutherford-Bohr 

model. 



E. state-. 



\ 



\ - - '- / 

\ 



eiriiSSiOn; 



/ 



\^3^^ 



]\^ 



-£ sf<j+e; 






y 






theories, Bohr's theory is a beautiful example of a successful 
physical model, measured by what it was designed to do. 

Bohr introduced two novel postulates designed specifically to 
account for the existence of stable electron orbits and of the discrete 
emission spectra. These postulates may be stated as follows. 

(1) Contrary to the expectations based on classical mechanics 
and electromagnetism, an atomic system can exist in any one of a 
number of states in which no emission of radiation takes place, 
even if the particles (electrons and nucleus) are in motion relative 
to each other. These states are called stationary states of the atom. 

(2) Any emission or absorption of radiation, either as visible 
light or other electromagnetic radiation, will correspond to a sudden, 
discontinuous transition between two such stationary states. The 
radiation emitted or absorbed in a transition has a frequency / 
determined by the relation hf— E, — E/, where h is Planck's constant 
and Ei and Ef are the energies of the atom in the initial and final 
stationary states, respectively. 

The quantum theory had begun with Planck's idea that atoms 
emit light only in definite amounts of energy; it was extended by 
Einstein's idea that light travels only as definite parcels of energy; 
and now it was extended further by Bohr's idea that atoms exist 
only in definite energy states. But Bohr also used the quantum 
concept in deciding which of all the conceivable stationary states 
of the atom were actually possible. An example of how Bohr did 
this is given in the next section. 

For simplicity we consider the hydrogen atom, with a single 
electron revolving around the nucleus. Following Bohr, we assume 
that the possible electron orbits are simply circular. The details of 
some additional assumptions and the calculation are worked out 
on page 73. Bohr's result for the possible orbit radii r„ was r„ = an^ 
where a is a constant {h^l4'jT'^mkqe) that can be calculated from 
known physical values, and n stands for any whole number, 1, 
2, 3 

Q1 1 What was the main evidence that an atom could exist 
only in certain energy states? 

Q12 What reason did Bohr give for the atom existing only in 
certain energy states? 



19.6 The size of the hydrogen atom 

This is a remarkable result: in the hydrogen atom, the allowed 
orbital radii of the electrons are whole multiples of a constant that 
we can at once evaluate. That is n^ takes on values of V, 2^ 3^, . . . , 
and all factors to the right of n'^ are quantities known previously by 
independent measurement! Calculating the value (h'^l4Tr-mkq^) gives 
us 5.3 X 10~"m. Hence we now know that according to Bohr's 
model the radii of stable electron orbits should be r„ = 5.3 x 10~"m 
X n\ That is, 5.3 x 10-"m when n = 1 (first allowed orbit), 4 x 5.3 = 
10~"m when n = 2 (second allowed orbit), 9 x 5.3 x 10~"m when 
n — 3, etc. In between these values, there are no allowed radii. In 



Bohr's Quantization Rule and the Size of Orbits 



The magnitude of the charge on the electron 
is Qf.; the charge on a nucleus is Zq,., and for 
hydrogen (Z = 1) is just q^. The electric force 
with which the hydrogen nucleus attracts its 
electron is therefore 



Fel 



QeQe 



where k is the coulomb constant, and r is the 
center-to-center distance. If the electron is in a 
stable circular orbit of radius r around the 
nucleus, moving at a constant speed v, then 
the centripetal force is equal to mv^/r. Since 
the centripetal force is the electric attraction, 
we can write 



mv' _ q' 



In the last equation, m, q^ and k are 
constants; r and v are variables, whose values 
are related by the equation. What are the 
possible values of \/ and r for stationary states 
of the atom? 

We can begin to get an answer if we write 
the last equation in slightly different form, by 
multiplying both sides by r^ and dividing both 
sides by v\ the result is 

mvr = — ^ 

V 

The quantity on the left side of this equa- 
tion, which is the product of the momentum of 
the electron and the radius of the orbit, can be 
used to characterize the stable orbits. According 
to classical mechanics, the radius of the orbit 
could have any value, so the quantity mvr could 
also have any value. But we have seen that 
classical physics seemed to deny that there 
could be any stable orbits in the hydrogen 
atom. Since Bohr's first postulate implies that 
certain stable orbits (and only those) are 
permitted, Bohr needed to find the rule that 
decides which stable orbits were possible. Here 
Bohr appears to have been largely guided by 
his intuition. He found that what was needed 
was the recognition that the quantity m\//' does 
not take on any arbitrary value, but only certain 



discrete values. These values are defined by the 
relation 



mvr 



2v 



where h is Planck's constant, and n is a posi- 
tive integer; that is, n = 1, 2, 3, 4, . . . (but not 
zero). When the possible values of the mvr are 
restricted in this way, the quantity mvr is said 
to be quantized. The integer n which appears 
in the formula, is called the quantum number. 
The main point is that each quantum number 
(n = 1 or 2 or 3 . . .) corresponds to one 
allowed, stable orbit of the electron. 

If we accept this rule, we can at once 
describe the "allowed" states of the atom, say 
in terms of the radii r of the possible orbits. 
We can combine the last expression above 
with the classical centripetal force relation as 
follows: the quantization rule is 

nh 





mi/r = — - 
2v 




nh 


so 


Inmv 


and 


,,_ n'h^ 



4v'-m-v^ 
From classical mechanics, we had 



mv _ 1^ q'e 



so 



mr 



Substituting this "classical" value for v- into the 
quantization expression for r- gives 



r- 



n'h' 



47^/77-1 

mr 



which simplifies to the expression for the 
allowed radii, r„: 

n'h' 



r = 



A-TT-kmq^ 



74 The Rutherford-Bohr Model of the Atom 

SG 19.10 short, we have found that the separate allowed electron orbits are 

spaced around the nucleus in a regular way, with the allowed radii 
quantized in a regular manner, as indicated in the marginal 
drawing. Emission and absorption of light should then be accom- 
panied by the transition of the electron from one allowed orbit to 
another. 

This is just the kind of result we had hoped for; it tells us 
which radii are possible, and where they lie. But so far, it has all 
been model building. Do the orbits in a real hydrogen atom actually 
correspond to this model? In his first paper of 1913, Bohr could 
give at least a partial yes as answer: It was long known that the 
normal "unexcited" hydrogen atom has a radius of about 5 x 10~" m. 
(That is, for example, the size of the atom obtained by interpreting 
measured characteristics of gases in the light of the kinetic theory.) 
This known value of 5 x 10~" m corresponds excellently to the 
prediction from the equation for the orbital radius r if n has the 
lower value, namely 1. For the first time there was now a way to 
understand the size of the neutral, unexcited hydrogen atom: for 
every atom the size corresponds to the size of the innermost allowed 
electron orbit, and that is fixed by nature as described by the 
quantization rule. 



Q13 Why do all unexcited hydrogen atoms have the same size? 
Q14 Why does the hydrogen atom have just the size it has? 



19.7 Other consequences of the Bohr model 

With his two postulates and his choise of the permitted 
stationary states, Bohr could calculate not only the radius of each 
permitted orbit, but also the total energy of the electron in each 
orbit; this energy is the energy of the stationary state. 

The results that Bohr obtained may be summarized in two 
simple formulas. As we saw, the radius of an orbit with quantum 
number n is given by the expression 



where r, is the radius of the first orbit (the orbit for n = 1) and 
has the value 5.3 x IQ-** cm or 5.3 x lO"" m. 

The energy (including both kinetic and electric potential 
energy) of the electron in the orbit with quantum number n can be 
computed from Bohr's postulate also (see SG 19.11). As we pointed 
out in Chapter 10, it makes no sense to assign an absolute value to 
potential energy — since only changes in energy have physical 
meaning we can pick any convenient zero level. For an electron 
orbiting in an electric field, the mathematics is particularly simple 

Note: Do not confuse this use of £ '^ ^^ ^^°°^^ ^^ ^ ^^^° ^^^^^ ^°^ ^"^^^8^ ^^^ ^*^^^ ^ = "' ^^^^ ^^' 

for energy with earlier use of Efor when the electron is infinitely far from the nucleus (and therefore 

electric field. free of it). If we consider the energy for any other state E„ to be 



Section 19.8 75 

the difference from this free state, we can write the possible 
energy states for the hydrogen atom as 

where Ej is the total energy of the atom when the electron is in the 
first orbit; Ei, the lowest energy possible for an electron in a 
hydrogen atom, is —13.6 eV (the negative value means only that the 
energy is 13.6 eV less than the free state value Ex). This is called 
the "ground" state. In that state, the electron is most tightly 
"bound" to the nucleus. The value of E,, the first "excited" state 
above the ground state, is 1/2^ x -13.6 eV = -3.4 eV, that is, only 
3.4 eV less than in the free state. 

According to the formula for r„, the first Bohr orbit has the 
smallest radius, with n = 1. Higher values of n correspond to 
orbits that have larger radii. Although the higher orbits are spaced 
further and further apart, the force field of the nucleus falls off 
rapidly, so the work required to move out to the next larger orbit 
actually becomes smaller and smaller; therefore also the jumps in 
energy from one level of allowed energy E to the next become small 
and smaller. 



19.8 The Bohr theory: the spectral series of hydrogen 

It is commonly agreed that the most spectacular success of « . .. . 

See the radius and energy diagrams 
Bohr's model was that it could be used to explain all emission (and ^^ -g^g jq 

absorption lines in the hydrogen spectrum. That is, Bohr could use 

his model to derive, and so to explain, the B aimer formula! By 

applying his second postulate, we know that the radiation emitted 

or absorbed in a transition in Bohr's atom should have a frequency 

/ determined by the relation 

hf = E,. - E, 

If Uf is the quantum number of the final state, and n, is the 
quantum number of the initial state, then according to the result 
for E„ we know that 

E^ = ^Ei and Ei^^—^E, 

The frequency of radiation emitted or absorbed when the atom goes 
from the initial state to the final state is therefore determined by 
the equation 

hf-^.-h or hf=E,{-\-\ 
n,- Uf- \7Vi n^f. 

To deal with wavelength A. (as in Balmer's original formula, p. 63) 
rather than frequency /, we use now the relation between fre- 
quency and wavelength given in Unit 3: the frequency is equal to 




Niels Bohr (1885-1962) was born in Copenhagen, 
Denmark and was educated there, receiving his 
doctor's degree in physics in 191 1. In 1912 he was 
at work in Rutherford's laboratory in Manchester, 
England, which was a center of research on radio- 
activity and atomic structure. There he developed 
his theory of atomic structure to explain chemical 
properties and atomic spectra. Bohr later played an 
important part in the development of quantum 
mechanics, in the advancement of nuclear physics, 
and in the study of the philosophical aspects of 
modern physics. In his later years he devoted much 
time to promoting plans for international coopera- 
tion and the peaceful uses of nuclear physics. 





Section 19.8 77 

the speed of the hght wave divided by its wavelength: /= c/X. If 
we substitute c/X for /in this equation, and then divide both sides 
by the constant he (Planck's constant times the speed of light), we 
obtain the equation 



i^£i/J L 

X he \n^i n^f. 



According to Bohr's model, then, this equation gives the wave- 
length X of the radiation that will be emitted or absorbed when the 
state of a hydrogen atom changes from one stationary state with 
quantum number n, to another with Uf. 

How does this prediction from Bohr's model compare with the 
empirical Balmer formula for the Balmer series? The Balmer 
formula was given on page 64: 

i=R (1-1 

We see at once that the equation for X of emitted (or absorbed) 
light derived from the Bohr model is exactly the same as B aimer's 
formula, if Rff = —EJhc and nf= 2. 

The Rydberg constant R^, long known from spectroscopic 
measurements to have the value of 1.097 x 10^m~S now could 
be compared with the value for —(EJhc). Remarkably, there SG 19.11 

was fine agreement. R^, which had previously been regarded as 
just an experimentally determined constant, was now shown 
not to be arbitrary or accidental, but to depend on the mass and 
charge of the electron, on Planck's constant, and on the speed 
of hght. 

More important, one now saw the meaning, in physical terms, 
of the old empirical formula for the Balmer series. All the lines in 
the Balmer series simply correspond to transitions from various 
initial states (various values of n,) to the same final state, the state 
for which nf = 2. 

When the Bohr theory was proposed, in 1913, emission lines in 
only the Balmer and Paschen series for hydrogen were known 
definitely. Balmer had suggested, and the Bohr model agreed, that 
additional series should exist. The experimental search for these 
series yielded the discovery of the Lyman series in the ultraviolet 
portion of the spectrum (1916), the Brackett series (1922), and the 
Pfund series (1924). In each series the measured frequencies of the 
lines were found to be those predicted by Bohr's theory. Similarly, 
the general formula that Balmer guessed might apply for all spec- 
tral lines of hydrogen is explained; lines of the Lyman series 
correspond to transitions from various initial states to the final 
state n^== 1, the lines of the Paschen series correspond to transitions 
from various initial states to the final state Uf = 3, etc. (see table SG 19.12, 19.13 

on page 65). The general scheme of possible transitions among the 



78 



The Rutherford-Bohr Model of the Atom 




n = 6 



Above: A schematic diagram of the 
possible transitions of an electron 
in the Bohr model of the hydrogen 
atom (first six orbits). 
At the right: Energy-level diagram for 
the hydrogen atom. Possible transi- 
tions between energy states are shown 
for the first six levels. The dotted arrow 
for each series indicates the series 
limit, a transition from the state where 
the electron is completely free (in- 
finitely far) from the nucleus. 



first six stable orbits is shown in the figure at the left. Thus 
the theory not only correlated currently known information 
about the spectrum of hydrogen, but also predicted 
correctly the wavelength of hitherto unknown 
series of lines in the spectrum. Moreover, it did 
so on a physically plausible model rather than, 
as Balmer's general formula had done, with 
out any physical reason. All in all, these 
were indeed triumphs that are worth cele- 
brating! 
The schematic diagram shown at the left 
is useful as an aid for the imagination, 
but it also has the danger of being too 
specific. For instance, it leads us to visual- 
ize the emission of radiation in terms of 
"jumps" of electrons between orbits. These 
are useful ideas to aid our thinking, but one 
must not forget that we cannot actually de- 
tect an electron moving in an orbit, nor can we 
watch an electron "jump" from one orbit to an- 
other. Hence a second way of presenting the results 
'"' of Bohr's theory is used which yields the same facts 
,.--^'' but does not commit us too closely to a picture of orbits. 
This scheme is shown in the figure below. It focuses attention 
not on orbits but on the corresponding possible energy states, which 

ENERGY 



Lyman 
series 



Balmer 
series 



n = 5 
n = 4 

n = 3 



n = 2 



t t 



I 



Paschen 

series 

1 

It 



Brackett 
series 



'ii 



Pfund 
series 

... X - 



\i 



iiit i 



0.0 

-0.87 X 10- 

-1.36 

-2.42 



-5.43 



n=i JjiiH 



■21.76 



Section 19.9 



79 



are all given by the formula E„ = 1/n^ x £,. In terms of this 
mathematical m.odel, the atom is normally unexcited, with an 
energy £, about -22 x 10~'^ joules (-13.6 eV). Absorption of energy 
can place the atoms in an excited state, with a correspondingly 
higher energy. The excited atom is then ready to emit light, with 
a consequent reduction in energy. The energy absorbed or emitted 
always shifts the total energy of the atom to one of the values 
specified by the formula for E„. We may thus, if we prefer, represent 
the hydrogen atom by means of the energy-level diagram. 

Q15 Balmer had predicted accurately the other spectral series 
of hydrogen thirty years before Bohr did. Why is Bohr's prediction 
considered more significant? 

Q16 How does Bohr's model explain line absorption spectra? 



19.9 Stationary states of atoms: the Franck-Hertz experiment 

The success of the Bohr theory in accounting for the spectrum 
of hydrogen leaves this question: can experiments show directly 
that atoms have only certain discrete energy states? In other words, 
apart from the success of the idea in explaining spectra, are there 
really gaps between the energies that an atom can have? A famous 
experiment in 1914, by the German physicists James Franck and 
Gustav Hertz, showed the existence of these discrete energy states. 

Franck and Hertz bombarded atoms with electrons (from an 
electron gun) and were able to measure the energy lost by electrons 
in collisions with atoms. They could also determine the energy 
gained by atoms in these collisions. In their first experiment, Franck 
and Hertz bombarded mercury vapor contained in a chamber at 
very low pressure. Their experimental procedure was equivalent to 
measuring the kinetic energy of electrons leaving the electron gun 
and the kinetic energy of electrons after they had passed through 
the mercury vapor. The only way electrons could lose energy was in 
collisions with mercury atoms. Franck and Hertz found that when 
the kinetic energy of the electrons leaving the electron gun was 
small, for example, up to several eV, the electrons after passage 
through the mercury vapor still had almost exactly the same energy 
as they had on leaving the gun. This result could be explained in 
the following way. A mercury atom is several hundred thousand 
times more massive than an electron. When it has low kinetic 
energy the electron just bounces off a mercury atom, much as a 
golf ball thrown at a bowling ball would bounce off. A collision of 
this kind is called an "elastic" collision. In an elastic collision, 
the mercury atom (bowling ball) takes up only an extremely small 
part of the kinetic energy of the electron (golf ball). The electron 
loses practically none of its kinetic energy. 

But when the kinetic energy of the bombarding electrons was 
raised to 5 electron-volts, there was a dramatic change in the 
experimental results. When an electron collided with a mercury 



'4.oeV 



4.o&f O 

BcSCTROfJ 




M6RCUR.y AfVH 



0.1 eV t^^j£f^i 



'BlecrOm 




HeUCOBJATDH 







/^eeoisy Aran 



The Nobel Prize 








Alfred Bernhard Nobel (1833-1896), a Swed- 
ish chemist, was the inventor of dynamite. 
As a result of his studies of explosives, 
Nobel found that when nitroglycerine (an 
extremely unstable chemical) was absorbed 
in an inert substance it could be used 
safely as an explosive. This combination 
is dynamite. He also invented other ex- 
plosives (blasting gelatin and ballistite) 
and detonators. Nobel was primarily inter- 
ested in the peaceful uses of explosives, 
such as mining, road building and tunnel 
blasting, and he amassed a large fortune 
from the manufacture of explosives for 
these applications. Nobel abhorred war and 
was conscience-stricken by the military 
uses to which his explosives were put. At 



his death, he left a fund of some $315 mil- 
lion to honor important accomplishments in 
science, literature and international under- 
standing. Prizes were established to be 
awarded each year to persons who have 
made notable contributions in the fields of 
physics, chemistry, medicine or physiology, 
literature or peace. (Since 1969 there has 
been a Nobel Memorial Prize in economics 
as well.) The first Nobel Prizes were awarded 
in 1901. Since then, men and women from 
about 30 countries have received prizes. 
At the award ceremonies the recipient re- 
ceives a medal and the prize money from the 
king of Sweden, and is expected to deliver 
a lecture on his work. The Nobel Prize is 
generally considered the most prestigious 
prize in science. 



I 



Nobel Prize winners in Physics. 



1901 Wilhelm Rontgen (Ger) — discovery of x-rays. 1938 

1902 H. A. Lorentz and P. Zeeman (Neth)-influence of 
magnetism on radiation. 

1903 A. H. Becquerel (Fr)- discovery of spontaneous radio- 1939 
activity. Pierre and Marie Curie (Fr) — work on rays 

first discovered by Becquerel. 1940 

1904 Lord Rayieigh (Gr Brit)-density of gases and dis- 1941 
covery of argon. 1942 

1905 Philipp Lenard (Ger) -work on cathode rays. 1943 

1906 J. J. Thomson (Gr Brit)-conduction of electricity 

by gases. 1944 

1907 Albert A. Michelson (US) — optical precision instru- 
ments and spectroscopic and metrological investi- 1945 
gations. 1946 

1908 Gabriel Lippmann (Fr)-color photography by 1947 
interference. 

1909 Guglielmo Marconi (Ital)-and Ferdinand Braum 

(Ger) — development of wireless telegraphy. 1948 

1910 Johannes van der Waals (Neth)-equation of state 
for gases and liquids. 

1911 Wilhelm Wien (Ger)-laws governing the radiation 1949 
of heat. 

1912 Nils Gustaf Dalen (Swed) -automatic gas regulators 1950 
for lighthouses and buoys. 

1913 Kamerlingh Onnes (Neth)-low temperature and 
production of liquid helium. 1951 

1914 Max von Laue (Ger) -diffraction of Rontgen rays 
by crystals. 

1915 W. H. and W. L. Bragg (Gr Brit)-analysis of crystal 1952 
structure by Rontgen rays. 

1916 No award. 1953 

1917 Charles Glover Barkla(GrBrit)-discovery of Rontgen 1954 
radiation of the elements. 

1918 Max Planck (Ger) — discovery of energy quanta. 

1919 Johannes Stark (Ger) -discovery of the Doppler 1955 
effect in canal rays and the splitting of spectral lines 

in electric fields. 

1920 Charles-Edouard Guillaume (Switz)- discovery of 1956 
anomalies in nickel steel alloys. 

1921 Albert Einstein (Ger)-for contributions to theoretical 
physics and especially for his discovery of the law 1957 
of the photoelectric effect. 

1922 Niels Bohr (Den) — atomic structure and radiation. 

1923 Robert Andrews Millikan (US)-elementary charge 1958 
of electricity and photoelectric effect. 

1924 Karl Siegbahn (Swed) -field of x-ray spectroscopy. 

1925 James Franck and Gustav Hertz (Ger) — laws govern- 1959 
ing the impact of an electron upon an atom. 

1926 Jean Baptiste Perrin (Fr)-discontinuous structure 1960 
of matter and especially for his discovery of sedi- 1961 
mentation equilibrium. 

1927 Arthur Compton (US) -discovery of effect named 
after him. C. T. R. Wilson (Gr Brit) - method of making 

paths of electrically charged particles visible by con- 1962 

densation of vapor. 

1928 Owen Williams Richardson (Gr Brit)-thermionic 1963 
phenomena and discovery of effect named after him. 

1929 Louis-Victor de Broglie (Fr)- discovery of wave 

nature of electrons. 1964 

1930 Sir Chandrasehara V. Raman (Ind)-scattering of 

light and effect named after him. 1965 

1931 No award. 

1932 Werner Heisenberg (Ger) — quantum mechanics lead- 
ing to discovery of allotropic forms of hydrogen. 1966 

1933 Erwin Schrodinger (Ger) and P. A. M. Dirac (Gr Brit)- 

new productive forms of atomic theory. 1967 

1934 No award. 

1935 James Chadwick (Gr Brit) — discovery of the neutron. 1968 

1936 Victor Franz Hess (Aus. — cosmic radiation. Carl David 
Anderson (US) — discovery of the positron. 

1937 Clinton J. Davisson (US) -and George P. Thomson 1969 
(Gr Brit) — experimental diffraction of electrons by 
crystals. 



Enrico Fermi (Ital) — new radioactive elements pro- 
duced by neutron irradiation and nuclear reactions 
by slow neutrons. 

Ernest O. Lawrence (US) -cyclotron and its use in 
regard to artificial radioactive elements. 
No award 
No award 
No award 

Otto Stern (Ger) -molecular ray method and magnetic 
moment of the proton. 

Isidor Isaac Rabi (US) -resonance method for mag- 
netic properties of atomic nuclei. 
Wolfgang Pauli (Aus) — exclusion or Pauli principle. 
P. W. Bridgman (US) — high pressure physics. 
Sir Edward V. Appleton (Gr Brit) — physics of the upper 
atmosphere and discovery of so-called Appleton 
layers. 

Patrick M. S. Blackett, (Gr Brit) -development of 
Wilson cloud chamber and discoveries in nuclear 
physics and cosmic rays. 

Hideki Yukawa (Japan) — prediction of mesons and 
theory of nuclear forces. 

Cecil Frank Powell (Gr Brit) — Photographic method of 
studying nuclear processes and discoveries regarding 
mesons. 

Sir John D. Cockcroft and Ernest T. S. Walton (Gr 
Brit) -transmutation of atomic nuclei by artificially 
accelerated atomic particles. 

Felix Bloch (Switz) and Edward M. Purcell (US)- 
nuclear magnetic precision measurements. 
Frits Zernike (Neth)- phase-contrast microscope. 
Max Born (Ger) -statistical interpretation of wave 
functions, and Walter Bothe (Ger)-coincidence 
method for nuclear reactions and cosmic rays. 
Willis E. Lamb (US) -fine structure of hydrogen spec- 
trum and Polykarp Kusch (US) -precision determina- 
tions of magnetic moment of electron. 
William Shockley, John Bardeen and Walter Houser 
Brattain (US) -researches on semiconductors and 
their discovery of the transistor effects. 
Chen Ning Yang and Tsung Dao Lee (Chin)-investi- 
gation of laws of parity, leading to discoveries regard- 
ing the elementary particles. 

Pavel A. Cerenkov, H'ya M. Frank and Igor E. Tamm 
(USSR) -discovery and interpretation of the Cerenkov 
effect. 

Emilio G. Segre and Owen Chamberlain (US)-dis- 
covery of the antiproton. 

Donald A. Giaser (US)-invention of bubble chamber. 
Robert Hofstadter (US) -electron scattering in atomic 
nuclei. Rudolf Ludwig Mossbauer (Ger) -resonance 
absorption of -y-radiation and discovery of effect 
which bears his name. 

Lev D. Landau (USSR)-theories for condensed mat- 
ter, especially liquid helium. 

Eugene P. Wigner (US)-theory of the atomic nucleus 
and elementary particles. Marie Goeppert-Mayer (US) 
and J. Hans D. Jensen (Ger) -nuclear shell structure. 
Charles Townes (US), Alexander Prokhorov and 
Nikolay Basov (USSR) -development of maser. 
S. Tomonaga (Japan), Julian Schwinger and Richard 
Feynman (US)-quantum electrodynamics and ele- 
mentary particles. 

Alfred Kastler (Fr)-new optical methods for studying 
properties of atom. 

Hans Bethe (US) -nuclear physics and theory of 
energy production in the sun. 

Louis W. Alvarez (American) for research in physics 
of sub atomic particles and techniques for detection 
of these particles. 

Murray Gell-Mann (American) for contributions and 
discoveries concerning the classification of elemen- 
tary particles and their interactions. 



82 



The Rutherford-Bohr Model of the Atom 



We now know two ways of "exciting" 
an atom: by absorption of a photon 
with just the right energy to make 
a transition from the lowest energy 
level to a higher one, or by doing 
the same thing by collision— with an 
electron from an electron gun, or by 
collision among agitated atoms (as 
in a heated enclosure or a discharge 
tube). 



SG 19.14, 19.15 



SG 19.16 



atom it lost almost exactly 4.9 eV of energy. And when the electron 
energy was increased to 6 eV, the electron still lost just 4.9 eV of 
energy in a collision with a mercury atom, being left with 1.1 eV of 
energy. These results indicated that a mercury atom cannot accept 
less than 4.9 eV of energy; and that when it is offered somewhat 
more, for example, 5 or 6 eV, it still can accept only 4.9 eV. The 
accepted amount of energy cannot go into kinetic energy of the 
mercury because of the relatively enormous mass of the atom as 
compared with that of an electron. Hence, Franck and Hertz con- 
cluded that the 4.9 eV of energy is added to the internal energy 
of the mercury atom — that the mercury atom has a stationary state 
with energy 4.9 eV greater than that of the lowest energy state, 
with no allowed energy level in between. 

What happens to this extra 4.9 eV of internal energy? According 
to the Bohr model of atoms, this amount of energy should be 
emitted in the form of electromagnetic radiation when the atom 
returns to its lowest state. Franck and Hertz looked for this radia- 
tion, and found it. They observed that the mercury vapor emitted 
light at a wavelength of 2535 A, a line known previously to exist 
in the emission spectrum of hot mercury vapor. The wavelength 
corresponds to a frequency / for which the photon's energy, hf, 
is just 4.9 eV (as you can calculate). This result showed that 
mercury atoms had indeed gained (and then radiated) 4.9 eV of 
energy in collisions with electrons. 

Later experiments showed that mercury atoms bombarded by 
electrons could also gain other, sharply defined amounts of energy, 
for example, 6.7 eV and 10.4 eV. In each case radiation was emitted 
that corresponded to known lines in the emission spectrum of 
mercury; in each case analogous results were obtained. The elec- 
trons always lost energy, and the atoms always gained energy, both 
in sharply defined amounts. Each type of atom studied was found to 
have discrete energy states. The amounts of energy gained by the 
atoms in collisions with electrons could always be correlated with 
known spectrum lines. The existence of discrete or stationary 
states of atoms predicted by the Bohr theory of atomic spectra was 
thus verified by direct experiment. This verification was considered 
to provide strong confirmation of the validity of the Bohr theory. 



Q17 How much kinetic energy will an electron have after a 
collision with a mercury atom if its kinetic energy before collision 
is (a) 4.0 eV? (b) 5.0 eV? (c) 7.0 eV? 



19.10 The periodic table of the elements 



In the Rutherford-Bohr model, atoms of the different elements 
differ in the charge and mass of their nuclei, and in the number 
and arrangement of the electrons about each nucleus. Bohr came 
to picture the electronic orbits as shown on the next page, though 
not as a series of concentric rings in one plane but as tracing out 



Section 19.10 



83 



patterns in three dimensions. For example, the orbits of the two 
electrons of helium in the normal state are indicated as circles in 
planes inclined at about 60° with respect to each other. For each 
circular orbit, elliptical ones with the nucleus at one focus are also 
possible, and with the same (or nearly the same) total energy as in 
the circular orbit. 

Bohr found a way of using his model to understand better the 
periodic table of the elements. In fact, it was the periodic table 

rather than the explanation of B aimer spectra that was Bohr's 
primary concern when he began his study. He suggested that the 
chemical and physical properties of an element depend on how the 
electrons are arranged around the nucleus. He also indicated how 
this might come about. He regarded the electrons in an atom as 
grouped together in layers or shells around the nucleus. Each shell 
can contain not more than a certain number of electrons. The 
chemical properties are related to how nearly full or empty a shell 
is. For example, full shells are associated with chemical stabiUty, 
and in the inert gases the electron shells are completely filled. 

To see how the Bohr model of atoms helps to understand 
chemical properties we may begin with the observation that the 
elements hydrogen (Z = 1) and hthium (Z = 3) are somewhat alike 
chemically. Both have valences of 1. Both enter into compounds of 
analogous types, for example hydrogen chloride, HCl, and hthium 
chloride. LiCl. Furthermore there are some similarities in their 
spectra. All this suggests that the lithium atom resembles the 
hydrogen atom in some important respects. Bohr conjectured that 
two of the three electrons of the lithium atom are relatively close 
to the nucleus, in orbits resembling those of the helium atom, while 
the third is in a circular or elliptical orbit outside the inner system. 
Since this inner system consists of a nucleus of charge (+) Sq^ and 
two electrons each of the charge (— ) <?«,, its net charge is (+) Qg. Thus 
the lithium atom may be roughly pictured as having a central core 
of charge (+) gp, around which one electron revolves, somewhat as 
for a hydrogen atom. The analogous physical structure, then, is the 
reason for the analogous chemical behavior. 

Helium (Z = 2) is a chemically inert element, belonging to the 
family of noble gases. So far no one has been able to form com- 
pounds from it. These properties indicated that the helium atom is 
highly stable, having both of its electrons closely bound to the 
nucleus. It seemed sensible to regard both electrons as moving in 
the same innermost shell around the nucleus when the atom is 
unexcited. Moreover, because the helium atom is so stable and 
chemically inert, we may reasonably assume that this shell cannot 
accommodate more than two electrons. This shell is called the 
K-shell. The single electron of hydrogen is also said to be in the 
K-shell when the atom is unexcited. For lithium two electrons are 
in the K-shell. filling it to capacity, and the third electron starts a 
new one, called the L-shell. This single outlying and loosely bound 
electron is the reason for the strong chemical affinity of lithium for 
oxygen, chlorine, and many other elements. 



The sketches below are based on dia- 
grams Bohr used in his university 
lectures. 




i^^KO^BU Cfl^ 




ye.uioMCi=2>^ 




L/ry-ioM C'i^S'y 




/VfipVc'H'/C) 




5op\UH (2 - ll') 




At^$e*/(^Z'^lg) 



84 



The Rutherford-Bohr Model of the Atom 



These two pages will be easier to 
follow if you refer to the table of the 
elements and the periodic table in 
Chapter 17 page 23. 



Shell Number of electrons in 

name filled shell 



2 

8 

18 



Sodium (Z = 11) is the next element in the periodic table that 
has chemical properties similar to those of hydrogen and lithium, 
and this suggests that the sodium atom also is hydrogen-like in 
having a central core about which one electron revolves. More- 
over, just as lithium follows helium in the periodic table, so does 
sodium follow another noble gas, neon (Z = 10). For the neon atom, 
we may assume that two of its 10 electrons are in the first (K) shell, 
and that the remaining 8 electrons are in the second (L) shell. 
Because of the chemical inertness and stability of neon, these 8 
electrons may be expected to fill the L-shell to capacity. For sodium, 
then, the eleventh electron must be in a third shell, which is called 
the M-shell. Passing on to potassium (Z = 19), the next alkah metal 
in the periodic table, we again have the picture of an inner core 
and a single electron outside it. The core consists of a nucleus with 
charge (+) 19q^ and with 2, 8, and 8 electrons occupying the K-. L-. 
and M-shells, respectively. The 19th electron revolves around the 
core in a fourth shell, called the N-shell. The atom of the noble 
gas argon, with Z = 18, just before potassium in the periodic table, 
again represents a distribution of electrons in a tight and stable 
pattern, with 2 in the K-, 8 in the L-, and 8 in the M-shell. 

These qualitative considerations have led us to a consistent 
picture of electrons distributed in groups, or shells, around the 
nucleus. The arrangement of electrons in the noble gases can be 
taken to be particularly stable, and each time we encounter a new 
alkali metal in Group I of the periodic table, a new shell is started; 
there is a single electron around a core which resembles the pattern 
for the preceding noble gas. We may expect that this outlying 
electron will easily come loose by the action of neighboring atoms, 
and this corresponds with the facts. The elements lithium, sodium 
and potassium belong to the group of alkali metals. In compounds 
or in solution (as in electrolysis) they may be considered to be in the 
form of ions such as Li+, Na* and K^, each lacking one electron and 
hence having one positive net charge (+) q^. In the neutral atoms 
of these elements, the outer electron is relatively free to move about. 
This property has been used as the basis of a theory of electrical 
conductivity. According to this theory, a good conductor has many 
"free" electrons which can form a current under appropriate 
conditions. A poor conductor has relatively few "free" electrons. 
The alkali metals are all good conductors. Elements whose electron 
shells are filled are very poor conductors; they have no "free" 
electrons. 

Turning now to Group II of the periodic table, we would expect 
those elements that follow immediately after the alkali metals to 
have atoms with two outlying electrons. For example, beryllium 
(Z = 4) should have 2 electrons in the K-shell. thus filhng it. and 2 
in the L-shell. If the atoms of all these elements have two outlying 
electrons, they should be chemically similar, as indeed they are. 
Thus, calcium and magnesium, which belong to this group, should 
easily form ions such as Ca^^ and Mg^^, each with a positive net 
charge of (+) 2(j2. and this is also found to be tioie. 



Section 19.10 85 

As a final example, consider those elements that immediately 
precede the noble gases in the periodic table. For example, fluorine 
atoms (Z = 9) should have 2 electrons filHng the K-shell but only 7 
electrons in the L-shell, which is one less than enough to fill it. If 
a fluorine atom should capture an additional electron, it should 
become an ion F" with one negative net charge. The L-shell would 
then be filled, as it is for neutral neon (Z = 10), and thus we would 
expect the F" ion to be relatively stable. This prediction is in accord 
with observation. Indeed, all the elements immediately preceding 
the inert gases in the periodic table tend to form stable singly- 
charged negative ions in solution. In the solid state, we would 
expect these elements to be lacking in free electrons, and all of 
them are in fact poor conductors of electricity. 

Altogether there are seven main shells, K, L, M, . . . Q, and 
further analysis shows that all but the first are divided into sub- 
shells. The second (L) shell consists of two subshells, the third (M) 
shell consists of three subshells, and so on. The first subshell in any 
shell can always hold up to 2 electrons, the second up to 6, the third 
up to 10, the fourth up to 14, and so on. For all the elements up to 
and including argon (Z = 18), the buildup of electrons proceeds 
quite simply. Thus the argon atom has 2 electrons in the K-shell, 
8 in the L-shell, then 2 in the first M-subshell and 6 in the second 
M-subshell. But the first subshell of the N-shell is lower in energy 
than the third subshell of the M-shell. Since atoms are most likely 
to be in the lowest energy state available, the N-shell will begin to 
fill before the M-shell is completed. Therefore, after argon, there 
may be electrons in an outer shell before an inner one is filled. 




SG 19.17, 19.18 



Relative energy levels of electron 
states in atoms. Each circle represents 
a state which can be occupied by 2 
electrons. 



86 



The Rutherford-Bohr Model of the Atom 



Period 
II 



This complicates the scheme somewhat but still allows it to be con- 
sistent. The arrangement of the electrons in any unexcited atom is 
always the one that provides greatest stability for the whole atom. 
And according to this model, chemical phenomena generally involve 
only the outermost electrons of the atoms. 

Bohr carried through a complete analysis along these lines and, 
in 1921, proposed the form of the periodic table shown below. The 
periodicity results from the completion of subshells, which is 
complicated even beyond the shell overlap in the figure on page 85 
by the interaction of electrons in the same subshell. This still 
useful table was the result of physical theory and offered a funda- 
mental physical basis for understanding chemistry — for example, 
how the structure of the periodic table follows from the shell 
structure of atoms. This was another triumph of the Bohr theory. 

Period 
VII 

87 -- 

88 Ra 

89 Ac 

90 Th 
Period Period /// 59 Pr 91 Pa 

IV V /// 60 Nd 92 U 




Bohr's periodic table of the elements (1921). For example some of the names 
and symbols have been changed. Masurium (43) is now called Technetium 
(43), and Niton (86) is Radon (86). The rectangles indicate the filling of sub- 
shells of a higher shell. 




Q18 Why do the next heavier elements after the noble gases 
easily become positively charged? 

Q19 Why are there only 2 elements in Period I. 8 in Period II, 
8 in Period III, etc? 



19.11 The inadequacy of the Bohr theory, and the state of atomic 
theory in the early 1920's 



As we are quite prepared to find, every model, every theory has 
limits. In spite of the successes achieved with the Bohr theory 
in the years between 1913 and 1924, problems arose for which the 



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88 



The Rutherford-Bohr Model of the Atom 



In March 1913, Bohr wrote to Ruther- 
ford enclosing a draft of his first 
paper on the quantum theory of 
atomic constitution. On March 20, 
1913, Rutherford replied in a letter, 
the first part of which we quote, 
"Dear Dr. Bohr: 

I have received your paper and 
read it with great interest, but I want 
to look it over again carefully when 
I have more leisure. Your ideas as 
to the mode of origin of spectra in 
hydrogen are very ingenious and 
seem to work out well; but the mix- 
ture of Planck's ideas with the old 
mechanics makes it very difficult 
to form a physical idea of what is 
the basis of it. There appears to me 
one grave difficulty in your hypoth- 
esis, which I have no doubt you fully 
realize, namely, how does an elec- 
tron decide what frequency it is 
going to vibrate at when it passes 
from one stationary state to the 
other. It seems to me that you would 
have to assume that the electron 
knows before hand where it is going 
to stop. . . 



theory proved inadequate. Bohr's theory accounted excellently for 
the spectra of atoms with a single electron in the outermost shell, 
but serious discrepancies between theory and experiment appeared 
in the spectra of atoms with two electrons or more in the outermost 
shell. It was also found experimentally that when a sample of an 
element is placed in an electric or magnetic field, its emission 
spectrum shows additional lines. For example, in a magnetic field 
each line is split into several lines. The Bohr theory could not 
account in a quantitative way for the observed splitting. Further, 
the theory supplied no method for predicting the relative brightness 
of spectral lines. These relative intensities depend on the probabili- 
ties with which atoms in a sample undergo transitions among the 
stationary states. Physicists wanted to be able to calculate the 
probability of a transition from one stationary state to another. They 
could not make such calculations with the Bohr theory. 

By the early 1920's it had become clear that the Bohr theory, 
despite its great successes, was deficient beyond certain limits. 
It was understood that to get a theory that would be successful in 
solving more problems, Bohr's theory would have to be revised, or 
replaced by a new one. But the successes of Bohr's theory showed 
that a better theory of atomic structure would still have to account 
also for the existence of stationary states — discrete atomic energy 
levels — and would, therefore, have to be based on quantum 
concepts. 

Besides the inability to predict certain properties of atoms at all, 
the Bohr theory had two additional shortcomings: it predicted some 
results that were not in accord with experiment (such as the 
spectra of elements with two or three electrons in the outermost 
electron shells); and it predicted others that could not be tested in 
any known way (such as the details of electron orbits). Although 
orbits were easy to draw on paper, they could not be observed 
directly, nor could they be related to any observable properties of 
atoms. Planetary theory has very different imphcations when 
applied to a real planet moving in an orbit around the sun. and 
when applied to an electron in an atom. The precise position of a 
planet is important, especially if we want to do experiments such 
as photographing an eclipse, or a portion of the surface of Mars 
from a satellite. But the moment-to-moment position of an electron 
in an orbit has no such meaning because it has no relation to any 
experiment physicists have been able to devise. It thus became 
evident that, in using the Bohr theory, physicists could be led to ask 
some questions which could not be answered experimentally. 

In the early 1920's, physicists — above all. Bohr himself— began 
to work seriously on the revision of the basic ideas of the theory. 
One fact that stood out was that the theory started with a mixture 
of classical and quantum ideas. An atom was assumed to act in 
accordance with the laws of classical physics up to the point where 
these laws did not work; then the quantum ideas were introduced. 
The picture of the atom that emerged from this inconsistent mixture 
was a combination of ideas from classical physics and concepts for 



Section 19.11 



89 



which there was no place in classical physics. The orbits of the 
electrons were determined by the classical, Newtonian laws of 
motion. But of the many possible orbits, only a small portion were 
regarded as possible, and these were selected by rules that contra- 
dicted classical mechanics. Or again, the frequency calculated for 
the orbital revolution of electrons was quite different from the 
frequency of light emitted or absorbed when the electron moved 
from or to this orbit. Or again, the decision that n could never be 
zero was purely arbitrary, just to prevent the model from collapsing 
by letting the electron fall on the nucleus. It became evident that 
a better theory of atomic structure would have to be built on a more 
consistent foundation in quantum concepts. 

In retrospect, the contribution of the Bohr theory may be sum- 
marized as follows. It provided some excellent answers to earlier 
questions raised about atomic structure in Chapters 17 and 18. 
Although the theory turned out to be inadequate it drew attention to 
how quantum concepts can be used. It indicated the path that a 
new theory would have to take. A new theory would have to supply 
the right answers that the Bohr theory gave, and would also have to 
supply the right answers for the problems the Bohr theory could 
not solve. And without doubt one of the most intriguing aspects of 
Bohr's work was the proof that physical and chemical properties of 
matter can be traced back to the fundamental role of integers — 
(quantum numbers such as n = 1, 2, 3 . . .). As Bohr said, "The 
solution of one of the boldest dreams of natural science is to build 
up an understanding of the regularities of nature upon the con- 
sideration of pure number." We catch here an echo of the hope of 
Pythagoras and Plato, of Kepler and GaUleo. 

Since the 1920's, a successful theory of atomic structure has 
been developed and has been generally accepted by physicists. It is 
part of "quantum mechanics," so called because it is built directly 
on quantum concepts; it goes now far beyond understanding atomic 
structure, and in fact is the basis of our modern conception of 
events on a submicroscopic scale. Some aspects will be discussed in 
the next chapter. Significantly, Bohr himself was again a leading 
contributor. 



Remember, for example, (in Unit 1) 
how proudly Galileo pointed out, 
when announcing that all falling 
bodies are equally and constantly 
accelerated: "So far as I know, 
no one has yet pointed out that 
the distances traversed, during 
equal intervals of time, by a body 
falling from rest, stand to one 
another in the same ratio as the 
odd numbers beginning with unity 
[namely 1:3:5:7: . . .]." 



SG 19.19-19.23 



Q20 The Bohr model of atoms is widely given in science 
books. What is wrong with it? What is good about it? 



STUDY GUIDE 



19.1 The Project Physics materials particularly 
appropriate for Chapter 19 include: 

Experiment 

Spectroscopy 

Activities 

Scientists on stamps 

Measuring ionization, a quantum effect 

"Black box" atoms 

Reader Article 

The Teacher and the Bohr Theory of the Atom 

Film Loop 

Rutherford Scattering 

Transparencies 

Alpha Scattering 

Energy Levels — Bohr Theory 

19.2 (a) Suggest experiments to show which of 

the Fraunhofer lines in the spectrum of 
sunlight are due to absorption in the 
sun's atmosphere rather than to absorp- 
tion by gases in the earth's atmosphere. 

(b) How might one decide from spectro- 
scopic observations whether the moon 
and the planets shine by their own light 
or by reflected light from the sun? 

19.3 Theoretically, how many series of lines are 
there in the emission spectrum of hydrogen? In 
all these series, how many lines are in the visible 
region? 

19.4 The Rydberg constant for hydrogen, JR„, has 
the value 1.097 x lOVm. Calculate the wave- 
lengths of the lines in the Balmer series 
corresponding to n = 8, n = 10, n = 12. Compare 
the values you get with the wavelengths listed 

in the table on p. 63. Do you see any trend in the 
values? 



19.6 In what ways do Thomson's and Ruther- 
ford's atomic models agree? In what ways do 
they disagree? 

19.7 In 1903, the German physicist Philipp 
Lenard (1864-1947) proposed an atomic model 
diff'erent from those of Thomson and Rutherford. 
He observed that, since cathode-ray particles 
can penetrate matter, most of the atomic volume 
must off'er no obstacle to their penetration. In 
Lenard's model there were no electrons and no 
positive charges separate from the electrons. His 
atom was made up of particles called dynamides, 
each of which was an electric doublet possessing 
mass. (An electric doublet is a combination of a 
positive charge and a negative charge very close 
together.) All the dynamides were supposed to be 
identical, and an atom contained as many of 
them as were needed to make up its mass. They 
were distributed throughout the volume of the 
atom, but their radius was so small compared 
with that of the atom that most of the atom was 
empty. 

(a) In what ways does Lenard's model agree 
with those of Thomson and Rutherford? In 
what ways does it disagree with those 
models? 

(b) Why would you not expect a particles to be 
scattered through large angles if Lenard's 
model were valid? 

(c) In view of the scattering of a particles that 
is observed, is Lenard's model valid? 

19.8 Determine a plausible upper limit for the 
eff'ective size of a gold atom from the following 
facts and hypotheses: 

i. A beam of a-particles of known velocity v = 
2 X 10' m/sec is scattered from a gold foil in a 
manner explicable only if the a particles were 
repelled by nuclear charges that exert a Coulomb's 
law repulsion on the a particles. 



19.5 (a) As indicated in the figure on p. 63 the 

lines in one of hydrogen's spectral series 
are bunched very closely at one end. 
Does the formula 



A in 



suggest that such bunching will occur? 

(b) The "series limit" corresponds to the 
last possible line(s) of the series. What 
value should be taken for n, in the 
above equation to compute the wave- 
length of the series limit? 

(c) Compute the series limit for the Lyman, 
Balmer, or Paschen series of hydrogen. 

(d) Consider a photon with a wavelength 
corresponding to the series limit of the 
Lyman series. What energy could it 
carry? Express the answer in joules and 
in electron volts (1 eV = 1.6 x lO"'* J). 



ii. Some of these a particles come straight back 
after scattering. They therefore approached the 
nuclei up to a distance r from the nucleus' center, 
where the initicd kinetic energy jTn„vJ has been 
completely changed to the potential energy of 
the system. 

iii. The potential energy of a system made up 
of an a particle of charge 2q^ at a distance r 
from a nucleus of charge Zq^ is given by the 
product of the "potential" (Zqjr) set up by the 
nucleus at distance r, and the charge (2^^) of 
the a particle. 

iv. The distance r can now be computed, since 
we know Va, rUa (7 x 10~" kg. from other evidences 
to be discussed in Unit 6). Z for gold atoms (see 
periodic table), q^ (see Section 14.5). 

V. The nuclear radius must be equal to or less 
than r. Thus we have a plausible upper limit 
for the size of this nucleus. 



90 



19.9 We generally suppose that the atom and the 
nucleus are each spherical, that^the diameter of 
the atom is of the order of 1 A (Angstrom unit = 
10"'" m) and that the diameter of the nucleus is 
of the order of 10"'- cm. 



the hydrogen atom for each of the first 4 allowed 
orbits (n = 1, 2, 3, 4). 

vi. As a final point, show that the quantity —EJhc 
has the same value as the constant R^, as 
claimed in Sec. 19.8. 



(a) What are the evidences that these are 
reasonable suppositions? 

(b) What is the ratio of the diameter of the 
nucleus to that of the atom? 

19.10 The nucleus of the hydrogen atom is 
thought to have a radius of about 1.5 x 10"'^ cm. 
If the atom were magnified so that the nucleus is 
0.1 mm across (the size of a grain of dust), how 
far away from it would the electron be in the 
Bohr orbit closest to it? 

19.11 Show that the total energy of a neutral 
hydrogen atom made up of a positively charged 
nucleus and an electron is given by 

n^ ' 

where E, is the energy when the electron is in the 
first orbit (n = 1), and where the value of 
E, = —13.6 electron-volts. (You may consult other 
texts, for example Foundation of Modern Physical 
Science by Holton and Roller, sections 34.4 and 
34.7.) Program and hints: 

i. The total energy E of the system is the kinetic 
and potential energy' KE + PE of the electron in 
its orbit. Since mv-jr = k q/lr'^ (see p. 73), 
KE = imi;- can be quickly calculated. 

ii. The electrical potential energy PE of a charged 
point object (electron) is simply given by the 
electrical potential V of the region in which it 
finds itself, times its own charge. The value of 
V set up by the (positive) nucleus at 
distance r is given by Kqjr and the charge on the 
electron (including sign, for once!) is — q^. Hence 
PE = —kq^glr. The meaning of the negative sign 
is simply that PE is taken to be zero if the elec- 
tron is infinitely distant; the system radiates 
energy as the electron is placed closer to the 
nucleus, or conversely that energy must be sup- 
phed to move the electron away from the nucleus. 

iii. Now you can show that the total energy E is 



E = KE + PE = -k 



2r 



iv. Using the equation derived on p. 73, namely 

n'^h^ 
r = -7—; —, show that 



47r^Treg^ 



E = 



^_k^2nhnq^_ 1 



n^h^ 



£, 



where E^ = k^2TT^niq/lh^. 



The numerical value for this can be computed by 
using the known values (in consistent units) 
for k, m, q^ and h. 

V. Find the numerical value of the energy of 



19.12 Using the Bohr theory, how would you 
account for the existence of the dark lines in 
the absorption spectrum of hydrogen? 

19.13 A group of hydrogen atoms is excited (by 
collision, or by absorption of a photon of proper 
frequency), and they all are in the stationary state 
for which n = 5. Refer to the figure in the margin 
on p. 78 and list all possible lines emitted by this 
sample of hydrogen gas. 

19.14 Make an energy level diagram to represent 
the results of the Franck-Hertz experiment. 

19.15 Many substances emit visible radiation 
when illuminated with ultraviolet hght; this 
phenomenon is an example of fluorescence. 
Stokes, a British physicist of the nineteenth 
century, found that in fluorescence the wave- 
length of the emitted light usually was the same 
or longer than the illuminating light. How would 
you account for this phenomenon on the basis of 
the Bohr theory? 

19.16 In Query 31 of his Opticks, Newton wrote: 

All these things being consider'd, it 
seems probable to me that God in the 
beginning formed matter in solid, massy, 
hard, impenetrable, moveable particles, of 
such sizes and figures, and with such 
other properties, and in such proportion to 
the end for which he formed them; and 
that these primitive particles being sohds, 
are incomparably harder than any porous 
bodies compounded of them, even so very 
hard, as never to wear or break in pieces; 
no ordinary power being able to divide 
what God himself made one in first the 
creation. While the particles continue 
entire, they may compose bodies of one 
and the same nature texture and in all 
ages: But should they wear away, or break 
in pieces, the nature of things depending 
on them would be changed. Water and 
earth, composed of old worn particles and 
fragments of particles, would not be of the 
same nature and texture now, with water 
and earth composed of entire particles in 
the beginning. And therefore that nature 
may be lasting, the changes of corporeal 
things are to be placed only in the various 
separations and new associations and 
motions of these permanent particles; 
compound bodies being apt to break, not 
in the midst of solid particles, but where 
those particles are laid together, and only 
touch in a few points. 

Compare what Newton says here about atoms with 

91 



(a) the views attributed to Leucippus and 
Democritus concerning atoms (see the 
Prologue to this unit); 

(b) Dalton's assumptions about atoms (see the 
end of the prologue to this unit); 

(c) the Rutherford-Bohr model of the atom 

19-17 Use the chart on p. 85 to explain why 
atoms of potassium (Z = 19) have electrons in 
the N shell even though the M shell is not filled. 

19.18 Use the chart on p. 85 to predict the 
atomic number of the text inert gas after argon. 
That is, imagine filling the electron levels with 
pairs of electrons until you reach an apparently 
stable, or complete, pattern. Do the same for the 
next inert gas following. 

19.19 Make up a glossary, with definitions, of 
terms which appeared for the first time in this 
chapter. 

19.20 The philosopher John Locke (1632-1704) 
proposed a science of human nature which was 
strongly influenced by Newton's physics. In 
Locke's atomistic view, elementary ideas ("atoms") 
are produced by elementary sensory experiences 
and then drift, collide and interact in the mind. 
Thus the association of ideas was but a special 
case of the universal interactions of particles. 

Does such an approach to the sulaject of 
human nature seem reasonable to you? What 
argument for and against this sort of theory can 
you think of? 

19.21 In a recently published textbook of physics, 
the following statement is made: 

Arbitrary though Bohr's new postulate 
may seem, it was just one more step in 
the process by which the apparently con- 
tinuous macroscopic world was being 



analyzed in terms of a discontinuous, 
quantized, microscopic world. Although 
the Greeks had speculated about quan- 
tized matter (atoms), it remained for the 
chemists and physicists of the nineteenth 
century to give them reality. In 1900 
Planck found it necessary to quantize the 
energy of electromagnetic waves. Also, in 
the early 1900's a series of experiments 
culminating in Millikan's oil-drop experi- 
ment conclusively showed that electric 
charge was quantized. To this hst of 
quantized entities. Bohr added angular 
momentum (mvr). 

(a) What other properties or things in physics 
can you think of that are "quantized?" 

(b) What properties or things can you think of 
outside physics that might be said to be 
"quantized?"" 

19.22 Write an essay on the successes and 
failures of the Bohr model. Can it be called a good 
model? A simple model? A beautiful model? 

19.23 In 1903 a philosopher wrote: 

The propounders of the atomic view of 
electricity disagree with theories which 
would restrict the method of science to the 
use of only such quantities and data as 
can be actually seen and directly mea- 
sured, and which condemn the introduc- 
tion of such useful conceptions as the 
atom and the electron, which cannot be 
directly seen and can only be measured by 
indirect processes. 

On the basis of the information now available 
to you, with which view do you agree: the view of 
those who think in terms of atoins and electrons, 
or the view that we must use only such things as 
can be actually seen and measured? 



92 




This construction is meant to represent the arrangement of mutually 
attracting sodium and chlorine ions in a crystal of common salt. Notice 
that the outermost electrons of the sodium atoms have been lost to the 
chlorine atoms, leaving positively charged sodium ions with completed 
K and L shells, and negatively charged chlorine ions with completed K, 
L and M shells. 



20.1 Some results of relativity theory 95 

20.2 Particle-like behavior of radiation 99 

20.3 Wave-like behavior of particles 101 

20.4 Mathematical vs visualizable atoms 104 

20.5 The uncertainty principle 108 

20.6 Probability interpretation 111 



The diffraction pattern on the left was made by a beam of x rays passing through 
thin aluminum foil. The diffraction pattern on the right was made by a beam of 
electrons passing through the same foil. 




CHAPTER TWENTY 



Some Ideas from Modern 
Physical Theories 



20.1 Some results of relativity theory 

Progress in atomic and nuclear physics has been based on two 
great advances in physical thought: quantum theory and relativity. 
In so short a space as a single chapter we cannot even begin to give SG 20.1 
a coherent account of the actual development of physical and 
mathematical ideas in these fields. All we can do is offer you some 
idea of what kind of problems led to the development, suggest 
some of the unexpected conclusions, prepare for material in later 
chapters, and — very important!— introduce you to the beautiful 
ideas on relativity theory and quantum mechanics — offered in 
articles in Reader 5. 

In Chapters 18 and 19 we saw how quantum theory entered 
into atomic physics. To follow its further development into quantum 
mechanics, we need to learn some of the results of the relativity 
theory. These results will also be essential to our treatment of 
nuclear physics in Unit 6. We shall, therefore, devote this section 
to a brief discussion of one essential result of the theory of relativity 
introduced by Einstein in 1905 — the same year in which he 
published the theory of the photoelectric effect. 

In Unit 1 we discussed the basic idea of relativity — that certain 
aspects of physical events appear the same from different frames 
of reference, even if the reference frames are moving with respect 
to one another. We said there that mass, acceleration, and force 
seemed to be such invariant quantities, and Newton's laws relating 
them were equally good in all reference frames. 

By 1905 it had become clear that this is true enough for all 
ordinary cases of motion, but not if the bodies involved move with 
respect to the observer at a speed more than a few percent of that 
of light. Einstein considered whether the same relativity principle 
could be extended to include not only the mechanics of rapidly 
moving bodies, but also the description of electromagnetic waves. 
He found this could be done by replacing Newton's definitions of 
length and time by others that produce a more consistent physics. 

95 



96 



Some Ideas From Modern Physical Theories 



Topics in relativity theory are 
developed further in Reader 5. 
See the articles: 
"The Clock Paradox" 
"Mr. Tompkins and Simultaneity" 
"Mathematics and Relativity" 
"Parable of the Surveyors ' 
"Outside and Inside the Elevator" 
"Space Travel: Problems of Physics 
and Engineering" 



one that resulted in a new viewpoint. The viewpoint is the most 
interesting part of Einstein's thinking, and parts of it are discussed 
in articles in Reader 5 and Reader 6; but here we will deal with 
high-speed phenomena from an essentially Newtonian viewpoint, 
in terms of corrections required to make Newtonian mechanics a 
better fit to a new range of phenomena. 

For bodies moving at speeds which are small compared to the 
speed of light, measurements predicted by relativity theory are only 
negligibly different from measurements predicted by Newtonian 
mechanics. This must be true because we know that Newton's laws 
account very well for the motion of the bodies with which we are 
familiar in ordinary life. The differences between relativistic 
mechanics and Newtonian mechanics become noticeable in 
experiments involving high-speed particles. 

We saw in Sec. 18.2 that J. J. Thomson devised a method for 
determining the speed v and the ratio of charge to mass qjm for 
electrons. Not long after the discovery of the electron by Thomson, 
it was found that the value of Qp/m seemed to vary with the speed 
of the electrons. Between 1900 and 1910, several physicists found 
that electrons have the value ^p/m = 1.76 x 10" coul/kg only for 
speeds that are very small compared to the speed of light; the ratio 
became smaller as electrons were given greater speeds. The relativity 
theory offered an explanation for these results: the electron charge 
is invariant — it does not depend on the speed of the electrons; but 
the mass of an electron, as an observer in a laboratory would 
measure it, should vary with speed, increasing according to the 
formula: 



The Relativistic Increase of 
Mass with Speed 

v/c m/m,, v/c m/m„ 



0.0 


1.000 


0.95 


3.203 


0.01 


1.000 


0.98 


5.025 


0.10 


1.005 


0.99 


7.089 


0.50 


1.155 


0.998 


15.82 


0.75 


1.538 


0.999 


22.37 


0.80 


1.667 


0.9999 


70.72 



0.90 



2.294 



0.99999 



223.6 



VI - y-'lc' 
In this formula, v is the speed the electron has relative to the 
observer, c is the speed of light in a vacuum, and m„ is the rest 
mass — the electron's mass measured by an observer when an 
electron is at rest with respect to the observer; m is the mass of 
an electron measured while it moves with speed v relative to the 
observer. We may call m the relativistic mass. It is the mass 
determined, for example, by means of J. J. Thomsons method. 

The ratio of relativistic mass to rest mass, mlm^. which is equal 
to 1/Vl - v-lc'\ is listed in the table in the margin for values of vie 
which approach 1. The value of mlm^^ becomes very large as v 
approaches c. 

The formula for the relativistic mass, which was derived by 
Einstein from fundamental ideas of space and time, has been tested 
experimentally; some of the results, for electrons with speeds so 
high that the value of v reaches about 0.8 c, are shown as points on 
the graph on the next page. At z; = 0.8 c the relativistic mass m is 
about 1.7 times the rest mass m„. The curve shows the theoretical 
variation of m as the value of v increases, and the dots and crosses 
are results from two different experiments. The agreement of 
experiment and theory is excellent. The increase in mass with 
speed fully accounts for the shrinking of the ratio qjm with speed, 
which was mentioned earlier. 



Section 20.1 



97 




Variation of relativistic mass with 
speed (expressed as a fraction of 
the speed of light). 



The formula for variation of mass with speed is vahd for all 
moving bodies, not just for electrons and other atoinic particles. But 
larger bodies, such as those with which we are familiar in everyday 
life, we observe at speeds so small compared to that of light that 
the value of vie is very small. The value of v^lc' in the denominator 
is then extremely small, and the values of m and m^ are so nearly 
the same that we cannot tell the difference. In other words, the 
relativistic increase in mass can be detected in practice only for 
particles of atomic or sub-atomic size, those that can be given 
speeds higher than a small fraction of c. 

The effects discussed so far are mainly of historical interest 
because they helped to convince physicists (eventually) of the 
correctness of relativity theory. Experiments done more recently 
provide more striking evidence of the inadequacy of Newtonian 
physics for particles with very high speeds. Electrons can be given 
very high energies by accelerating them in a vacuum by means of 
a high voltage V. Since the electron charge q^ is known, the energy 
increase, q^v, is known, the rest mass m,, of an electron is also 
known (see Sec. 18.3), and the speed v can be measured by timing 
the travel over a known distance. It is, therefore, possible to 
compare the values of the energy supplied, q^V, with the expression 
for kinetic energy in classical mechanics, Ttriov''^. When experiments 
of this kind are done, it is found that when the electrons have 
speeds that are small compared to the speed of light, TTnoi^"' = ^pV. 
We used this relation in Sec. 18.5 in discussing the photoelectric 



SG 20.2-20.4 



98 



Some Ideas From Modern Physical Theories 



SPtBD Sfi/A/?ei> 



i 


, 


2c'* 


y CLASSICAL 




/ 

/ 

/ 

/ 
. _^ 

£. ( . , ■( 1 > t »>■ 



I o-i luf. OS o-i, 
fCinBTic fvEftjy (MeV) 



Unit 6 deals further with acceler- 
ators, and the operation of the CEA 
apparatus is also the subject of a 
Project Physics film Synchrotron. 



effect. We could do so quite correctly because photoelectrons do, 
indeed, have small speeds, and m and mo have nearly the same 
value. But when the speed of the electron becomes large, so that 
vie is no longer a small fraction, it is found that the quantity Tmoi^^ 
does not increase in proportion to q^V; this discrepancy increases as 
QgV increases. The increase in kinetic energy still is equal to the 
amount of work done by the electrical field, q^V, but the mass is no 
longer mo and so kinetic energy can't be measured by j'^o^^- The 
value of v^, instead of steadily increasing with energy supplied, 
approaches a limiting value: c^. 

In the Cambridge Electron Accelerator (CEA) operated in 
Cambridge, Massachusetts, by Harvard University and the 
Massachusetts Institute of Technology, electrons are accelerated 
to an energy which is equivalent to what they would gain in being 
accelerated by a potential difference of 6 x 10^ volts; it is an 
enormous energy for electrons. The speed attained by the electrons 
is 0.999999996 c; at this speed the relativistic mass m (both by 
calculation and by experiment) is over 10,000 times greater than 
the rest mass mo! 

Another way of saying mass increases with speed is this: any 
increase in kinetic energy is consistently accompanied by an 
increase in mass. If the kinetic energy measured from a frame of 
reference is KE, the increase in mass Am (above the rest mass) 
measured in that frame is proportional to KE: 



Am ^ KE 



To increase the mass of a body 
by 1 gram, it would have to be given 
a kinetic energy of 10" joules (about 
6 million mile-tons). 



The rest energy m„c- includes the 
potential energy, if there is any. 
Thus a compressed spring has a 
somewhat larger rest mass and 
rest energy than the same spring 
when relaxed. 



But it takes a great deal of kinetic energy to give a measurable 
increase in mass; the proportionality constant is very small — in 
fact, Einstein showed it would be 1/c-, where c is the speed of light 
in a vacuum: 



Am = 



KE 



Thus the total mass tti of a body is its rest mass mo plus KEIc-: 



m 



KE 
c- 



Einstein proposed that the "mass equivalent" of kinetic energy 
is only a special case, and that there is in general a precise 
equivalence between mass and energy. Thus one might expect that 
the rest mass mo also would correspond to an equivalent amount of 
"rest energy" Eo: mo = EqIc^. That is, 

Eo^KE 
C' c^ 



m 



If we use the symbol E for the total energy of a body, E = Eo + KE, 
we could then write 

E 

m = — 

This is just that Einstein concluded in 1905: "The mass of a body is 
a measure of its energy content." We can write this in a more 



Section 20.2 99 

familiar form, as what is probably the most famous equation in 
physics: 

£ — -YYiQ-i Do not confuse E with symbol for 

electric field. 
The last four equations all represent the same idea — that mass and 
energy are different expressions for the same characteristic of a 
system. It is not appropriate to think of mass being "converted" to SG 20.5, 20.6 

energy or vice versa. Rather, a body with a measured mass m has 
an energy E equal to mc'-; and vice versa — a body of total energy E 
has a mass equal to £/c-. 

The implications of this equivalence are exciting. First, two of 
the great conservation laws have become alternative statements 
of a single law: in any system whose total mass is conserved, the 
total energy will be conserved also. Second, the idea arises that 
some of the rest energy might be transformed into a more familiar 
form of energy. Since the energy equivalent of mass is so great, a 
very small reduction in rest mass would be accompanied by the 
release of a tremendous amount of energy, for example, kinetic 
energy or electromagnetic radiation. 

In Chapters 23 and 24, we shall see how such changes come 
about experimentally, and see additional experimental evidence 
which supports this relationship. 

Q1 What happens to the measurable mass of a particle as its 
kinetic energy is increased? 

Q2 What happens to the speed of a particle as its kinetic 
energy is increased? 

20.2 Particle-like behavior of radiation 

We shall now make use of one of these relations in the further 
study of light quanta and of their interaction with atoms. Study of 
the photoelectric effect taught us that a light quantum has energy 
hf, where h is Planck's constant and /is the frequency of the light. 
This concept also applies to x rays which, like visible light, are 
electromagnetic radiation, but of higher frequency than visible 
light. The photoelectric effect, however, did not tell us anything 
about the momentum of a quantum. We may raise the question: if 
a light quantum has energy, does it also have momentum? 

The magnitude of the momentum ^ of a body is defined as the SG 20.7 

product of its mass m and speed v: p — mv. If we replace m with 
its energy equivalent £/c^ we can write 

Note that the last equation is an expression for the momentum in 
which there is no explicit reference to mass. If we now speculate 
that this same equation might define the momentum of a photon of 
energy E, v would be replaced by the speed of light c and we would 
get 

^Ec^E 
^ c^~ c 



100 



Some Ideas From Modern Physical Theories 



SG 20.8 



X-RA/BCAH 




Foil 




Arthur H. Compton (1892-1962) was 
born in Wooster, Ohio and graduated 
from the College of Wooster. After re- 
ceiving his doctor's degree in physics 
from Princeton University in 1916, he 
taught physics and then worked in in- 
dustry. In 1919-1920 he did research 
under Rutherford at the Cavendish 
Laboratory of the University of Cam- 
bridge. In 1923, while studying the 
scattering of x rays, he discovered 
and interpreted the changes in the 
wavelengths of x rays when the rays 
are scattered. He received the Nobel 
Prize in 1927 for this work. 



Now, E^hf for a light quantum, and if we substitute this expres- 
sion for E in p = Ejc, we would get the momentum of a light 
quantum: 

Or, using the wave relation that the speed equals the frequency 
times the wavelength, c =fK we could express the momentum as 

h 

Does it make sense to define the momentum of a photon in this 
way? It does, if the definition is of help in understanding experi- 
mental results. The first example of the successful use of the 
definition was in the analysis of an effect discovered by Arthur H. 
Compton which we will now consider. 

According to classical electromagnetic theory, when a beam of 
light (or X rays) strikes the atoms in a target (such as a thin sheet 
of metal), the light will be scattered in various directions, but its 
frequency will not be changed. The absorption of light of a certain 
frequency by an atom may be followed by re-emission of light 
of another frequency; but, if the light wave is simple scattered, 
then according to classical theory there should be no change in 
frequency. 

According to quantum theory, however, light is made up of 
photons. Compton reasoned that if photons have momentum in 
accord with the argument for relativity theory, then in a collision 
between a photon and an atom the law of conservation of momen- 
tum should apply. According to this law (see Chapter 9), when a 
body of small mass collides with a massive object at rest, it simply 
bounces back or glances off with little loss in speed — that is, with 
very little change in energy. But if the masses of the two colliding 
objects are not very much different, a significant amount of energy 
can be transferred in the collision. Compton calculated how much 
energy a photon should lose in a collision with an atom, if the 
momentum of the photon is hflc. He concluded that the change 
in energy is too small to observe if a photon simply bounces off an 
entire atom. If, however, a photon strikes an electron, which has 
a small mass, the photon should transfer a significant amount of 
energy to the electron. 

In experiments up to 1923, no difference has been observed 
between the frequencies of the incident and scattered light (or 
X rays) when electromagnetic radiation was scattei'ed by matter. In 
1923 Compton was able to show that when a beam of x rays is 
scattered, the scattered beam consists of two parts: one part has the 
same frequency as the incident x rays; the other part has slightly 
lower frequency. The reduction in frequency of some of the 
scattered x rays is called the Compton effect. The scattered x rays 
of unchanged frequency have been scattered by whole atoms, 
whereas the component of x rays with changed frequency indicates 
a transfer of energy from some photons to electrons, in accordance 
with the laws of conservation of momentum and energy. The 



Section 20.3 



101 



observed change in frequency is just what would be predicted if 
the photons were acting hke particle-hke projectiles having 
momentum p = hflc. 

Furthermore, the electrons which were struck by the photons 
could also be detected, because they were knocked out of the target. 
Compton found that the momentum of these electrons was related 
to their direction in just the way that would be expected if they 
had been struck by particles with momentum equal to hflc. 

Compton's experiment showed that a photon can be regarded as 
a particle with a definite momentum as well as energy; it also 
showed that collisions between photons and electrons obey the laws 
of conservation of momentum and energy. 

Photons are not like ordinary particles — if only because they 
do not exist at speeds other than that of light. (There can be no 
resting photons, and therefore no rest mass for photons.) But in 
other ways, as in their scattering behavior, photons act much like 
particles of matter, having momentum as well as energy; and they 
also act like waves, having frequency and wavelength. In other 
words, the behavior of electromagnetic radiation is in some experi- 
ments similar to what we are used to thinking of as particle 
behavior, and in other experiments is similar to what we are used 
to thinking of as wave behavior. This behavior is often referred to 
as the wave-particle dualism of radiation. The question, "Is a 
photon a wave or a particle?" can only be answered: it can act 
like either, depending on what we are doing with it. (This fascinating 
topic is elaborated in several of the Reader 5 articles.) 

Q3 How does the momentum of a photon depend on the 
frequency of the light? 

Q4 What is the Compton effect, and what did it prove? 



aA/l/lAr^ • 


f 


"' / 




/.• 




o 




(b) \v 


¥ 


^ /1^ 


(c) %.P 



SG 20.9 



SG 20.10 



20.3 Wave-like behavior of particles 

In 1923, the French physicist Louis de Broglie suggested that 
the wave-particle dualism which applies to radiation might also 
apply to electrons and other atomic particles. Perhaps, he said, the 
wave-particle dualism is a fundamental property of all quantum 
processes, and what we have always thought of as material particles 
can, in some circumstances, act like waves. He sought an expres- 
sion for the wavelength that might be associated with wave-hke 
behavior of an electron, and he found one by means of a simple 
argument. 

The momentum of a photon of wavelength X is p = h/X. De 
Broglie suggested that this relation, derived for photons, would 
also apply to electrons with the momentum p = mv. He therefore 
boldly suggested that the wavelength of an electron is: 

mv 
where m is the mass of the electron and v its speed. 

What does it mean to say that an electron has a wavelength 
equal to Planck's constant divided by its momentum? If this 



The "de Broglie wavelength" of a 
material particle does not refer to 
anything having to do with light, 
but to some new wave property 
associated with the motion of 
matter itself. 



102 



Some Ideas From Modern Physical Theories 




Diffraction pattern produced by di- 
recting a beam of electrons through 
polycrystalline aluminum. With a 
similar pattern, G. P. Thomson dem- 
onstrated the wave properties of 
electrons— 28 years after their par- 
ticle properties were first demon- 
strated by J. J. Thomson, his father. 



statement is to have any physical meaning, it must be possible to 
test it by some kind of experiment. Some wave property of the 
electron must be measured. The first such property to be measured 
was diffraction. 

The relationship X = himv implies that the wavelengths 
associated with electrons will be very short, even for fairly slow 
electrons; an electron accelerated across a potential difference of 
only lOOV would have a wavelength of only 10"'" meter. So small 
a wavelength would not give noticeable diffraction effects on 
encountering any object of appreciable size — even microscopically 
small size (say, 10"^ meter). 

By 1920 it was known that crystals have a regular lattice 
structure; the distance between rows or planes of atoms in a crystal 
is about lO"'" m. After de Broglie proposed his hypothesis that 
electrons have wave properties, several physicists suggested that 
the existence of electron waves might be shown by using crystals as 
diffraction gratings. Experiments begun in 1923 by C. J. Davisson 
and L. H. Germer in the United States, yielded diffraction patterns 
similar to those obtained for x rays (see Sec. 18.6) as illustrated in 
the two drawings at the left below. The experiment showed two 
things: first that electrons do have wave properties — one may say 
that an electron moves along the path taken by the de Broglie wave 
that is associated with the electron. Also, it showed that their 
wavelengths are correctly given by de Broglie's relation, X = hImv. 
These results were confirmed in 1927 by G. P. Thomson, who directed 
an electron beam through thin gold foil to produce a pattern like the 
one in the margin, similar to diffraction patterns produced by 
light beams going through thin slices of materials. By 1930. diffrac- 
tion from crystals had been used to demonstrate the wave-like 
behavior of helium atoms and hydrogen molecules, as illustrated 
in the drawing on page 103. 



The de Broqiie wavelength: examples. 


A body of mass 1 kg moves with 
a speed of 1 m/sec. What is its 
de Broglie wavelength? 


An electron of mass 9.1 x IQ-^' kg 
moves with a speed of 2 x io^ m/sec. 
What is its de Broglie wavelength? 


mv 


x = A 

mv 


rt = 6.6 X 10 •'' joulesec 


/7 = 6.6 X 10-^' joulesec 


mv = 1 kg- m/sec 


mv= 1.82 X 10"-' kg m/sec 


6.6 X 10--" joule.sec 
1 kgm/sec 


6.6 X iQ--'^ joulesec 
1.82 X 10--' kg m/sec 


so 


so 


X = 6.6x 10 -'^ m 


\ = 3.6 X 10"'" m 


The de Broglie wavelength is many 
orders of magnitude smaller than an 
atom, and so is much too small to be 
detected— there are, for example, no 
slits or obstacles small enough to 
show diffraction effects. We would 
expect to detect no wave aspects in 
the motion of this body. 


The de Broglie wavelength is of 
atomic dimensions; for example, 
it is of the same order of magnitude 
as the distances between atoms in 
a crystal. So we expect to see wave 
aspects in the interaction of elec- 
trons with crystals. 



Section 20.3 



103 




(a) 







(b) 



oerecnsK. 



O 



X 



■■\-.f,' ■ 



Vat£TXH. 




a. One way to demonstrate the wave 
behavior of x rays is to direct a beam 
at the surface of a crystal. The reflec- 
tions from different planes of atoms 
in the crystal interfere to produce 
reflected beams at angles other than 
the ordinary angle of reflection. 



b. A very similar effect can be demon- 
strated for a beam of electrons. The 
electrons must be accelerated to an 
energy that corresponds to a de 
Broglie wavelength of about 10"'" m 
(which requires an accelerating volt- 
age of only about 100 volts). 



c. Like any other beam of particles, 
a beam of molecules directed at a 
crystal will show a similar diffraction 
pattern. The diagram above shows 
how a beam of hydrogen molecules 
(Ho) can be formed by slits at the 
opening of a heated chamber; the 
average energy of the molecules is 
controlled by adjusting the tempera- 
ture of the oven. The graph, repro- 
duced from Zeitschrift fur Physik, 
1930, shows results obtained by I. 
Estermann and O. Stern in Germany. 
The detector reading is plotted against 
the deviation to either side of the 
angle of ordinary reflection. 



zso'/f 



Li 



DireMer StrohlSSOcm. 



I I I 



-S 



zo' ^o" '5' W zo' 

Diffraction pattern for Ha molecules 
glancing off a crystal of lithium 
fluoride. 



According to de Broglie's hypothesis, which has been confirmed 
by all experiments, wave-particle dualism is a general property not 
only of radiation but also of matter. It is now customary to use the 
word "particle" to refer to electrons and photons while recognizing 
that they both have properties of waves as well as of particles (and, 
of course, that there are important differences between them). 

De Broglie's relation, A. = h/mv, has an interesting yet simple 
application which makes more reasonable Bohr's postulate that the 
quantity mvr (the angular momentum) of the electron in the 
hydrogen atom can only have certain values. Bohr assumed that 
mvr can have only the values: 

h 
mvr — n r— where n = 1, 2, 3, . . . 
2n 

Now, suppose that an electron wave is somehow spread over an 
orbit of radius r — that, in some sense, it "occupies" an orbit of 
radius r. We may ask if standing waves can be set up as indicated, 
for example, in the sketch in the margin. The condition for such 
standing waves is that the circumference of the orbit is equal in 
length to a whole number of wavelengths, that is, to nX. The 
mathematical expression for this condition of "fit" is: 



SG 20.11-20.13 

Only certain wavelengths will "fit" 
around a circle. 



-it": 




27rr = nX 



104 Some Ideas From Modern Physical Theories 

If we now replace X by himv according to de Broglie's relation 
we get 

o ^ 
zTtr = n 

mv 

h 
or mvr = n -^r— 

277 

But, this is just Bohr's quantization condition! The de BrogUe 
relation for electron waves — and the idea that the electron is in 
SG 20.14 orbits that allow a standing wave — allows us to derive the quantiza- 
tion that Bohr had to assume. 

The result obtained indicates that we may picture the electron 
in the hydrogen atom in two ways: either as a particle moving in 
Either way is incomplete by itself. an orbit with a certain quantized value of mvr, or as a standing 

de Broglie-type wave occupying a certain region around the nucleus. 



Q5 Where did de Broghe get the relation X = hImv for electrons? 
Q6 Why were crystals used to get diffraction patterns of 
electrons? 

20.4 Mathematical vs. visualizable atoms 

The proof that "things" (electrons, atoms, molecules) which had 
been regarded as particles also show properties of waves has 
served as the basis for the currently accepted theory of atomic 
structure. This theory, quantum mechanics, was introduced in 
1925; its foundations were developed with great rapidity during 
the next few years, primarily by Heisenberg, Born, Schrddinger, 
Bohr, and Dirac. Initially the theory appeared in two different 
mathematical forms, proposed independently by Heisenberg and 
Schrodinger. A few years later, these two forms were shown by 
Dirac to be equivalent, different ways of expressing the same 
relationships. The form of the theory that is closer to the ideas of 
de Broglie. discussed in the last section, was that of Schrodinger. 
It is often referred to as "wave mechanics". 

One of the fundamental requirements for a physical theory is 
that it predict the path taken by a particle when it interacts with 
other particles. It is possible, as we have already indicated for light, 
to write an equation describing the behavior of waves that will 
imply the path of the waves — the "rays." 

Schrodinger sought to express the dual wave and particle nature 
of matter mathematically. Maxwell had formulated the electro- 
magnetic theory of light in terms of a wave equation, and physicists 
were familiar with this theory and its applications. Schrodinger 
reasoned that the de Broglie waves associated with electrons would 
resemble the classical waves of light, including also that there be 
a wave equation that holds for matter waves just as there is a wave 
equation for electromagnetic waves. We cannot discuss this 
mathematical part of wave mechanics even adequately without 
using an advanced part of mathematics, but the physical ideas 



Section 20.4 



105 



involved require only a little mathematics and are essential to an 
understanding of modern physics. So, in the rest of this chapter, 
we shall discuss some of the physical ideas of the theory to try to 
make them seem plausible; and we shall consider some of the 
results of the theory and some of the implications of these results. 
But again our aim is not (and cannot honestly be in the available 
time and space) a full presentation. We want only to prepare for the 
use of specific results, and for reading in Reader 5 and Reader 6. 

Schrbdinger was successful in deriving an equation for the 
waves presumed to "guide" the motion of electrons. This equation, 
which has been named after him. defines the wave properties of 
electrons and also predicts particle-hke behavior. The Schrbdinger 
equation for an electron bound in an atom has a solution only 
when a constant in the equation has the whole-number values 1, 
2, 3. ... It turns out that these numbers correspond to different 
energies, so the Schrodinger equation predicts that only certain 
electron energies are possible in an atom. In the hydrogen atom, for 
example, the single electron can only be in those states for which 
the energy of the electron has the values: 

_ 2TT-mqe* 

with n having only whole number values. But these values of the 
energies are what are found experimentally — and are just the ones 
given by the Bohr theory! In Schrodinger's theory, this result follows 
directly from the mathematical formulation of the wave and 
particle nature of the electron. The existence of these stationary 
states has not been assumed, and no assumptions have been made 
about orbits. The new theory yields all the results of the Bohr theory 
without having any of the inconsistent hypotheses of the earlier 
theory. The new theory also accounts for the experimental informa- 
tion for which the Bohr theory failed to account, such as the prob- 
ability of an electron changing from one energy state to another. 

On the other hand, quantum mechanics does not supply a 
physical model or visualizable picture of what is going on in the 
world of the atom. The planetary model of the atom has had to be 
given up, and has not been replaced by another simple picture. 
There is now a highly successful mathematical model, but no easily 
visualized physical model. The concepts used to build quantum 
mechanics are more abstract than those of the Bohr theory; it is 
hard to get an intuitive feeling for atomic structure without 
training in the field. But the mathematical theory of quantum 
mechanics is much more powerful than the Bohr theory, in 
predicting and explaining phenomena, and many problems that were 
previously unsolvable have been solved with quantum mechanics. 
Physicists have learned that the world of atoms, electrons, and 
photons cannot be thought of in the same mechanical terms as the 
world of everyday experience. The world of atoms has presented us 
with some fascinating concepts which will be discussed in the next 
two sections; what has been lost in easy visualizability is amply 
made up for by the increased range of fundamental understanding. 



Topics in quantum physics are 

developed further in Reader 5. 

See the articles: 

"Ideas and Theories" 

"The New Landscape of Science" 

"The Evolution of the Physicist's 

Picture of Nature" 
"Dirac and Born" 
"I am the Whole World: Erwin 

Schrbdinger" 
"The Fundamental Idea of Wave 

Mechanics" 
"The Sea-Captain's Box" 



Visualizability is an unnecessary 
luxury when it is bought at the cost 
of clarity. For the same reason we 
learned to do without visualizability 
in many other fields. For example, 
we no longer think of the action of 
an ether to explain light propaga- 
tion. (Nor do we demand to see 
pieces of silver or gold or barter 
goods when we accept a check as 
payment.) 




p. A. M. Dirac (1902-), an English physicist, was one 
of the developers of modern quantum mechanics. 
In 1932, at the age of 30, Dirac was appointed 
Lucasian Professor of Mathematics at Cambridge 
University, the post held by Newrton. 



Max Born (1882-1969) was born in Germany, but left that 
country for England in 1933 when Hitler and the Nazis gained 
control. Born was largely responsible for introducing the 
statistical interpretation of wave mechanics. 





Prince Louis Victor de Broglie (1892-) comes 
of a noble French family. His ancestors 
served the French kings as far back as the 
time of Louis XIV. He was educated at the 
Sorbonne in Paris, and proposed the idea of 
wave properties of electrons in his PhD 
thesis. 




Erwin Schrodinger (1887-1961) was born in 
Austria. He developed wave mechanics in 
1926, fled from Germany in 1933 when Hitler 
and the Nazis came to power. From 1940 to 
1956, when he retired, he was professor of 
physics at the Dublin Institute for Advanced 
Studies. 



Werner Heisenberg (1 901 -). a german physicist, was one of the developers 
of modern quantum mechanics (at the age of 23). He first stated the un- 
certainty principle, and after the discovery of the neutron in 1932, pro- 
posed the proton-neutron theory of nuclear structure. 




108 Some Ideas From Modern Physical Theories 

Q7 The set of energy states of hydrogen could be derived from 
Bohr's postulate that mvr = nhl2TT. In what respect was the 
derivation from Schrodinger's equation better? 

Q8 Quantum (or wave) mechanics has had great success. 
What is its drawback for those trained on physical models? 

20.5 The uncertainty principle 

Up to this point we have always talked as if we could measure 
any physical property as accurately as we pleased; to reach any 
desired degree of accuracy we would have only to design a 
sufficiently precise instrument. Wave mechanics showed, however, 
that even in thought experiments with ideal instruments there are 
limitations on the accuracy with which measurements can be made. 

Think how you would go about measuring the positions and 
velocity of a car that moves slowly along a driveway. We can mark 
the position of the front end of the car at a given instant by making 
a scratch on the ground; at the same time, we start a stop-watch. 
Then we can run to the end of the driveway, and at the instant that 
the front end of the car reaches another mark placed on the ground 
we stop the watch. We then measure the distance between the 
marks and get the average speed of the car by dividing the 
measured distance traversed by the measured time elapsed. Since 
we know the direction of the car's motion, we know the average 
velocity. Thus we know that at the moment the car reached the 
second mark it was at a certain distance from its starting point 
and had traveled at a certain average velocity. By the process of 
going to smaller and smaller intervals we could also get the 
instantaneous velocity at any point along its path. 

How did we get the needed information? We located the position 
of the car by sunlight bounced off the front end into our eyes; that 
permitted us to see when the car reached a certain mark on the 
ground. To get the average speed we had to locate the front end 
twice. 

But suppose that we had decided to use reflected radio waves 
instead of light of visible wavelength. At 1000 kilocycles per second, 
\ = f = ^ TlO "'^sec gQQ ^ ^ typical value for radio signals, the wavelength is 300 meters. 



f 10'7sec 



With radiation of this wavelength, which is very much greater than 
the dimensions of the car, it is impossible to locate the car with 
any accuracy. The wave would reflect from the car ("scatter" is a 
more appropriate term) in all directions, just as it would sweep 
around any man-sized device we used to detect the wave direction. 
The wavelength has to be comparable with or smaller than the 
dimensions of the object before the object can be located well. 
Radar uses wavelengths from about 0.1 cm to about 3 cm; so a 
radar apparatus could have been used instead of sunlight, but 
would leave uncertainties as large as several centimeters in the two 
measurements of position. With visible light whose wavelength is 
less than 10" m, we could design instruments that would locate the 
position of the car to an accuracy of a few thousandths of a millimeter. 



Section 20.5 



109 



The extreme smallness of the atomic scale is indicated by these pictures made 
with techniques that are near the very limits of magnification-about 10,000,000 
times in these reproductions. 




!li^'L 






^-^'.i'v,' 




Pattern produced by electron beam scattered 
from a section of a single gold crystal. The 
entire section of crystal shown is only 100A 
across-smaller than the shortest wavelength 
of ultraviolet light that could be used in a light 
microscope. The finest detail that can be re- 
solved with this "electron microscope" is just 
under 2A, so the layers of gold atoms (spaced 
slightly more than 2A) show as a checked pat- 
tern; individual atoms are beyond the resolving 
power. 



Let us now turn from car and driveway, and think of an electron 
moving across an evacuated tube. We shall try to measure the 
position and speed of the electron. But some changes have to be 
made in the method of measurement. The electron is so small that 
we cannot locate its position by using visible light: the wavelength 
of visible light, small as it is, is still at least 10* times greater 
than the diameter of an atom. 

To locate an electron within a region the size of an atom (about 
10~*° m across) we must use a light beam whose wavelength is 
comparable to the size of the atom, preferably smaller. Now a 
photon of such a short wavelength k (and high frequency/) has 
very great momentum (h/X) and energy (hf); and, from our study 
of the Compton effect, we know that the photon will give the 
electron a strong kick when it is scattered by the electron. As a 
result, the velocity of the electron will be greatly changed, into a 
new and unknown direction. (This is a new problem, one we did 
not even think about when speaking about measuring the position 
of the car!) Hence, when we receive the scattered photon we can 
deduce from its direction where the electron had been — and so we 
have "located" the electron. But in the process we have altered the 
velocity of the electron (in both magnitude and direction). 




Pattern produced by charged par- 
ticles repelled from the tip of a micro- 
scopically thin tungsten crystal. The 
entire section shown is only about 
100A across. The finest detail that can 
be revealed by this "field-ion micro- 
scope" is about 1A, but the bright 
spots indicate the locations of atoms 
along edges of the crystal, and should 
not be thought of as pictures of the 
atoms. 



SG 20.15 



110 



Some Ideas From Modern Physical Theories 



SG 20.16-20.18 



To say this more directly: the more accurately we locate the electron 
(by using photons of shorter wavelength) the less accurately we can 
know its velocity. We could try to disturb the electron less by using 
less energetic photons. But because light exists in quanta of energy 
hf, a lower-enevgy photon will have a longer wavelength — and 
therefore would give us greater uncertainty in the electron's position! 

To summarize: we are unable to measure both the position 
and velocity of an electron to unlimited accuracy. This conclusion 
is expressed in the uncertainty principle, and was first stated by 
Werner Heisenberg. The uncertainty principle can be expressed 
quantitatively in a simple formula, derived from Schrbdinger's 
wave equation for the motion of particles. If Ax is the uncertainty 
in position, and Ap is the uncertainty in momentum, then the 
product of the two uncertainties must be equal to, or greater than, 
Planck's constant divided by 27r: 

AjcAp ^ — 

The same reasoning (and equation) holds for the experiment on 
the car, but the limitation is of no practical consequence with such 
a massive object. (See the worked-out example below.) It is only on 
the atomic scale that the limitation becomes evident and important. 



The chief use made of the un- 
certainty principle is in general 
arguments in atomic theory rather 
than in particular numerical 
problems. We do not really need 
to know exactly where an electron 
is, but we sometimes want to know 
if it could be in some region of 
space. 



The uncertainty principle: examples 



A large mass. 
Consider a car, with a mass of 
1000 kg, moving with a speed of 
about 1 m/sec. Suppose that in this 
experiment the inherent uncertainty 
Ai' in the measured speed is 0.1 m/sec 
(10% of the speed). What is the un- 
certainty in the position of the car? 



A small mass. 
Consider an electron, with a 
mass of 9.1 X 10"^' kg, moving with 
a speed of about 2 x lO*' m/sec. 
Suppose that the uncertainty Ai/ in 
the speed is 0.2 x 10*^ m/sec (10% of 
the speed). What is the uncertainty in 
the position of the electron? 



AxAp > 



273- 



AxAp 



277 



Ap = mAv = 100 kgm/sec 
h = 6.63 X 10"''* joulesec 



Ap = mlv = 1 .82 X 10~" kgm/sec 
h = 6.63 X 10"'^ joule/sec 



Ax = 
Ax 



6.63 
6.28 



lO'^-* joulesec 



10- kgm/sec 
1 X io-''« m. 



Ax 



6.63 



10'^^ joule/sec 



6.28 1.82 X 10-" kgm/sec 

Ax >5x 10-'" m. 

The uncertainty in position is of 
the order of atomic dimensions, and 
is significant in atomic problems. 
It is impossible to specify where 
an electron is in an atom. 



This uncertainty in position— many 
of orders smaller than the size of 
atoms— is much too small to be 
observable. In this case we can 
determine the position of the body 
with as high an accuracy as we 
would ever need. 

The reason for the difference between these two results is that 
Planck's constant h is very small; so small that the uncertainty 
principle becomes important only on the atomic scale. Ordinary 
objects behave as if, in the equations used here, h is effectively 
equal to zero. 



Section 20.6 



111 



Q9 If photons used in finding the velocity of an electron 
disturb the electron too much, why cannot the observation be 
improved by using less energetic photons? 

Q10 If the wavelength of light used to locate a particle is too 
long, why cannot the location be found more precisely by using 
light of shorter wavelength? 



To explore further the implications of dualism we need to 
review some ideas of probability. Even in situations in which no 
single event can be predicted with certainty, it may still be possible 
to make predictions of the statistical probabilities of certain events. 
On a holiday weekend during which perhaps 25 million cars are on 
the road, the statisticians report a high probability that about 600 
people will be killed in accidents. It is not known which cars in 
which of the 50 states will be the ones involved in the accidents, 
but on the basis of past experience the average behavior is still 
quite accurately predictable. 

It is in this way that physicists think about the behavior of 
photons and material particles. As we have seen, there are 
fundamental limitations on our ability to describe the behavior 
of an individual particle. But the laws of physics often enable us 
to describe the behavior of large collections of particles with good 
accuracy. The solutions of Schrodinger's wave equations for the 
behavior of waves associated with particles give us the probabilities 
for finding the particles at a given place at a given time. 

To see how probability fits into the picture, consider the 
situation of a star being photographed through a telescope. As you 
have already seen (for example on the page on Diffraction and Detail 
in Chapter 13), the image of a point source is not a precise point 
but is a diffraction pattern — a central spot with a series of 
progressively fainter circular rings. 

The image of a star on the photographic film in the telescope 
would be a similar pattern. Imagine now that we wished to 
photograph a very faint star. If the energy in light rays were not 
quantized, but spread continuously over ever-expanding wave 
fronts, we would expect that the image of a very faint star would 
be exactly the same as that of a much brighter star — except that 
the intensity of light would be less over the whole pattern. However, 
the energy of light is quantized — it exists in separate quanta, 
"photons," of definite energy. When a photon strikes a photographic 
emulsion, it produces a chemical change in the film at a single 
location -not all over the image area. If the star is very remote, 
only a few photons per second may arrive at the film. The effect on 
the film after a very short period of exposure would not be at all 
like the diffraction pattern in drawing C in the margin, but 
something like the scatter in A. As the exposure continued, the 
effect on the film would begin to look like B. Eventually, a pattern 
like C would be produced, just like the image produced by a bright 
star with a much shorter exposure. 



These sketches represent greatly en- 
larged images of a distant star on a 
photographic plate. 






112 



Some Ideas From Modern Physical Theories 



As we have already discussed in 
connection with l<inetic theory and 
disorder, it is easy to predict the 
average behavior of very large 
numbers of particles, even though 
nothing at all is known about the 
behavior of any single one of them. 



If there are tremendous numbers of quanta, then then' overall 
distribution will be very well described by the distribution of wave 
intensity. For small numbers of quanta, the wave intensity will not 
be very useful for predicting where they will go. We expect them to 
go mostly to the "high-intensity" parts of the image but we cannot 
predict exactly where. These facts fit together beautifully if we 
consider the wave intensity at a location to indicate the probability 
of the photon going there! 

A similar connection can be made for de Broglie waves and 
particles of matter. Rather than considering an analogous example, 
such as a diffraction pattern formed by an electron beam, we can 
consider a bound electron wave — a wave confined to a region of 
space by the electric attraction of a positive nucleus and a negative 
electron. For example, the de Broglie wave associated with an 
electron is spread out all over an atom — but we need not think of 
the electron as spread out. It is quite useful to think of the electron 
as a particle moving around the nucleus, and the wave amplitude 
at some location represents the probability of the electron being 
there. 

According to modern quantum theory, the hydrogen atom does 
not consist of a localized negative particle moving around a nucleus 
as in the Bohr model. Indeed, the theory does not provide any picture 
of the hydrogen atom. A description of the probability distribution 
is the closest thing that the theory provides to a picture. The proba- 
bility distribution for the lowest energy state of the hydrogen atom 
is represented in the drawing at the left below, where whiter 
shading at a point indicates greater probability. The probability 
distribution for a higher energy state, still for a single electron, is 
represented in the drawing at the right. 

Quantum theory is, however, not really concerned with the 
position of any individual electron in any individual atom. Instead, 
the theory gives a mathematical representation that can be used to 
predict interaction with particles, fields, and radiation. For example, 
it can be used to calculate the probability that hydrogen will emit 
light of a particular wavelength; the intensity and wavelength of 
light emitted by a large number of hydrogen atoms can then be 
compared with these calculations. Comparisons such as these have 
shown that the theory agrees with experiment. 





Section 20.6 



113 



To understand atomic physics, we deal with the average 
behavior of many atomic particles; the laws governing this average 
behavior turn out to be those of wave mechanics. The waves, it 
seems, are waves that measure probability. The information about 
the probability (that a particle will have some position at a given 
time) travels through space in waves. These waves can interfere 
with each other in exactly the same way that water waves do. So, 
for example, if we think of a beam of electrons passing through 
two slits, we consider the electrons to be waves and compute the 
interference patterns which determine the directions in which there 
are high wave amplitudes (high probability of electrons going 
there). Then, as long as there are no more slits or other interactions 
of the waves with matter, we can return to our description in terms 
of particles and say that the electrons are likely to (and on the 
average will) end up going in such and such directions with such 
and such speeds. 

The success of wave mechanics emphasized the importance of 
the dual wave-and-particle nature of radiation and matter. But it is 
natural to ask how a particle can be thought of as "really" having 
wave properties. The answer is that matter, particularly on the 
scale of the atom, does not have to be thought of as being either 
"really" particles or "really" waves. Our ideas of waves and of 
particles are taken from the world of visible things and just do not 
apply on the atomic scale. 

When we try to describe something that no one has ever seen or 
can ever see directly, it would be surprising if the concepts of the 
visible world could be used unchanged. It appeared natural before 
1925 to try to talk about the transfer of energy in either wave terms 
or particle terms, because that was all physicists needed or knew 
at the time. Almost no one was prepared to find that both wave and 
particle descriptions could apply to light and to matter. But as long 
as our imagination and language has only these two ideas — waves 
and particles — to stumble along on, this dualism cannot be wished 
away; it is the best way to handle experimental results. 

Max Born, one of the founders of quantum mechanics, has 
written : 



The ultimate origin of the difficulty lies in the fact (or 
philosophical principle) that we are compelled to use the 
words of common language when we wish to describe a 
phenomenon, not by logical or mathematical analysis, but 
by a picture appealing to the imagination. Common 
language has grown by everyday experience and can 
never surpass these limits. Classical physics has restricted 
itself to the use of concepts of this kind; by analyzing 
visible motions it has developed two ways of representing 
them by elementary processes: moving particles and 
waves. There is no other way of giving a pictorial descrip- 
tion of motions — we have to apply it even in the region of 
atomic processes, where classical physics breaks down. 



See "Dirac and Born" in Reader 5. 



Despite the successes of the idea that the wave represents the 



114 



Some Ideas From Modern Physical Theories 



probability of finding its associated particle in some specific condi- 
SG 20.23 tion of motion, many scientists found it hard to accept the idea 

that men cannot know exactly what any one particle is doing. The 
most prominent of such disbelievers was Einstein. In a letter to 
Born written in 1926, he remarked: 

The quantum mechanics is very imposing. But an inner 
voice tells me that it is still not the final truth. The theory 
yields much, but it hardly brings us nearer to the secret 
of the Old One. In any case, I am convinced that He does 
not play dice. 



"Deterministic" means here that if 
all the conditions of an isolated 
system are known and the laws 
describing interaction are known, 
then it is possible to predict 
precisely what happens next, without 
any need for probability ideas. 



SG 20.19-20.23 



Thus, Einstein, while agreeing with the usefulness and success 
of wave mechanics so interpreted, refused to accept probability- 
based laws as the final level of explanation in physics; in the 
remark about not believing that God played dice — an expression he 
used many times later — he expressed his faith that there are more 
basic, deterministic laws yet to be found. Yet despite the refusal of 
Einstein (and some others) to accept the probability laws in 
mechanics, neither he nor other physicists have yet succeeded in 
replacing Born's probability interpretation of quantum mechanics. 

Scientists agree that quantum mechanics works; its gives the 
right answers to many questions in physics, it unifies ideas and 
occurrences that were once unconnected, and it has been wonder- 
fully productive of new experiments and new concepts. On the 
other hand, there is still vigorous argument about its basic 
significance. It yields probability functions, not precise trajectories. 
Some scientists see in this aspect of the theory an important 
revelation about the nature of the world; for other scientists this 
same fact indicates that quantum theory is incomplete. Some in 
this second group are trying to develop a more basic, non-statistical 
theory for which the present quantum theory is only a limiting case. 
As in other fields of physics, the greatest discoveries here may be 
those yet to be made. 

Q11 In wave terms, the bright lines of a diffraction pattern are 
regions where there is a high field intensity produced by constructive 
interference. What is the probability interpretation of quantum 
mechanics for the bright lines of a diffraction pattern? 

Q12 If quantum mechanics can predict only probabilities for 
the behavior of any one particle, how can it predict many 
phenomena, for example, half-lives and diffraction patterns, with 
great certainty? 




"Sea and Sky", by M. C. Escher 




Models of the Atom 

EPILOGUE In this unit we have traced the concept of the atom from 
the early ideas of the Greeks to the quantum mechanics now generally 
accepted by physicists. The search for the atom started with the 
qualitative assumptions of Leucippus and Democritus who thought 
that their atoms offered a rational explanation of the behavior of 
matter. For many centuries most natural philosophers thought that 
other explanations, not involving atoms, were more reasonable. 
Atomism was pushed aside and received only occasional consideration 
until the seventeenth century. With the growth of the mechanical 
philosophy of nature in the seventeenth and eighteenth centuries, 
particles (corpuscles) became important. Atomism was reexamined, 
mostly in connection with physical properties of matter. Galileo, Boyle, 
Newton and others speculated on the role of particles for explaining the 
expansion and contraction of gases. Chemists speculated about atoms 
in connection with chemical change. Finally, Dalton began the modern 
development of atomic theory, introducing a quantitative conception 
that had been lacking — the relative atomic mass. 

Chemists, in the nineteenth century, found that they could correlate 
the results of many chemical experiments in terms of atoms and 
molecules. They also found that there are relations between the 
properties of different chemical elements. Quantitative information 
about atomic masses provided a framework for the system organizing 
these relations — the periodic table of Mendeleev. During the nineteenth 
century, physicists developed the kinetic theory of gases. This theory- 
based on the assumption of very small corpuscles, or particles, or 



Epilogue 



117 



molecules, or whatever else they might be called — helped strengthen 
the position of the atomists. Other work of nineteenth-century physicists 
helped pave the way to the study of the structure of atoms-through 
the study of the spectra of the elements and of the conduction of 
electricity in gases, the discovery of cathode rays, electrons, and 
X rays. 

Nineteenth-century chemistry and physics converged, at the 
beginning of the twentieth century, on the problem of atomic structure. 
It became clear that the uncuttable, infinitely hard atom was too simple 
a model: that the atom itself is made up of smaller particles. And so the 
search for a model with structure began. Of the early models, that of 
Thomson gave way to Rutherford's nuclear atom, with its small, heavy, 
positively charged nucleus, surrounded somehow by negative charges. 
Then came the atom of Bohr, with its electrons thought to be moving in 
orbits like planets in a miniature solar system. The Bohr theory had 
many successes and linked chemistry and spectra to the physics of 
atomic structure. But beyond that, it could not advance substantially 
without giving up an easily grasped picture of the atom. The tool 
needed is the mathematical model, not pictures. Quantum mechanics 
enables us to calculate how atoms behave; it helps us understand the 
physical and chemical properties of the elements. But at the most basic 
level, nature still has secrets. 

The next stage in our story. Unit 6, is the nucleus at the center of 
the atom. Is the nucleus made up of smaller components? Does it have 
laws of physics all its own? 



o®©o® 

© (D © (D) © 
OO©©© 

©®©®o 






20.1 The Project Physics materials particularly 
appropriate for Chapter 20 include: 



and show that KE = jnioV^ is a good 
approximation for familiar objects. 



Activities 

Standing waves on a band-saw blade 
Turntable oscillator patterns resembling 

de Broglie waves 
Standing waves in a wire ring 

Reader Articles 

The Clock Paradox 

Ideas and Theories 

Mr. Tompkins and Simultaneity 

Mathematics and Relativity 

Parable of the Surveyors 

Outside and Inside the Elevator 

Einstein and Some Civilized Discontents 

The New Landscape of Science 

The Evolution of the Physicist's Picture 

of Nature 
Dirac and Born 

I am the Whole World: Erwin Schrodinger 
The Fundamental Idea of Wave Mechanics 
The Sea-Captain's Box 
Space Travel: Problems of Physics and 

Engineering 
Looking for a New Law 

20.2 How fast would you have to move to 
increase your mass by 1%? 

20.3 The centripetal force on a mass moving 
with relativistic speed v around a circular orbit of 
radius R is F = mv^lR, where m is the relativistic 
mass. Electrons moving at a speed 0.60 c are to 
be deflected in a circle of radius 1.0 m: what 
must be the magnitude of the force applied? 

(mo = 9.1 X lO-»' kg.) 

20.4 The formulas (p = ruoV, KE = jtnov'^) used in 
Newtonian physics are convenient approxima- 
tions to the m ore gener al relativistic formulas. 
The factor 1/Vl - v^lc'^ can be expressed as an 
infinite series of steadily decreasing terms by 
using a binomial series expansion. When this is 
done we find that 



1 



V 



1-^ 



V' t;" v" 

= 1 + 1/2 ^ -f 3/8 -^ + 5/16 ^ + 
c^ c* c® 



35/128-^ 

c* 



20.5 According to relativity theory, changing 
the energy of a system by AE also changes the 
mass of the system by Am = A£/c-. Something 
like 10^ joules per kilogram of substance are 
commonly released as heat energy in chemical 
reactions. 

(a) Why then aren't mass changes detected in 
chemical reactions? 

(b) Calculate the mass change associated with 
a change of energy of 10^ joules. 

20.6 The speed of the earth in its orbit is about 
18 miles/sec (3 x 10^ m/sec). Its "rest" mass is 
6.0 X 102" kg 

(a) What is the kinetic energy of the earth in 
its orbit? 

(b) What is the mass equivalent of that kinetic 
energy? 

(c) By what percentage is the earth's "rest" 
mass increased at orbital speed? 

(d) Refer back to Unit 2 to recall how the mass 
of the earth is found; was it the rest mass 
or the mass at orbital speed? 

20.7 In relativistic mechanics the formula 
^= mi/^ st ill holds, but the mass m is given by 
m = mo/Vi - v'^lc~. The rest mass of an electron 
is 9.1 X lO-'" kg. 

(a) What is its momentum when it is moving 
down the axis of a linear accelerator from 
left to right at a speed of 0.4 c with 
respect to the accelerator tube? 

(b) What would Newton have calculated for 
the momentum of the electron? 

(c) By how much would the relativistic momen- 
tum increase if the speed of the electron 
were doubled? 

(d) What would Newton have calculated its 
change in momentum to be? 

20.8 Calculate the momentum of a photon of 
wavelength 4000A. How fast would an electron 
have to move in order to have the same 
momentum? 



(a) Show, by simple substitution, that when — 

is less than 0.1, the values of the terms 
drop off so rapidly that only the first few 
terms need be considered. 

(b) We rarely observe familiar objects moving 
faster than about 3,000 m/sec; the speed of 
light is 3 X 10" m/sec, so the value of v/c 
for familiar objects is rarely greater than 
about 10 •'*. What error do we suffer by using 
only the first two terms of the series? 

(c) Substitute the first two terms of the series 
into the relativistic expression 



20.9 Construct a diagram showing the change 
that occurs in the frequency of a photon as a 
result of its collision with an electron. 

20.10 What explanation would you offer for the 
fact that the wave aspect of light was shown to 
be valid before the particle aspect was demon- 
strated? 

20.11 The electrons which produced the diffrac- 
tion photograph on p. 102 had de Broglie 
wavelengths of 10""* meter. To what speed must 
they have been accelerated? (Assume that the 



118 



speed is small compared to c, so that the electron 
mass is about 10"^" kg.) 

20.12 A bilhard ball of mass 0.2 kilograms 
moves with a speed of 1 meter per second. What 
is its de Broghe wavelength? 

20.13 Show that the de Broglie wavelength of a 
classical particle of mass m and kinetic energy 
KE is given by 

h 



V2Tn(K£) 

What happens when the mass is very small and 
the speed is very great? 

20.14 A particle confined in a box cannot have 
a kinetic energy less than a certain amount; this 
least amount corresponds to the longest de Broghe 
wavelength which produces standing waves in 
the box; that is, the box size is one-half wave- 
length. For each of the following situations find 
the longest de Broglie wavelength that would fit 
in the box: then use p = hi K to find the momen- 
tum p, and use p = mv to find the speed v. 

(a) a dust particle (about lO-^* kg) in a display 
case (about 1 m across). 

(b) an argon atom (6.6 x 10"-'* kg) in a hght 
bulb (about 10~* m across). 

(c) a protein molecule (about 10"-- kg) in a 
bacterium (about 10"® m across). 



(d) an electron (about 10"^' 
(about 10"'" m across). 



kg) in an atom 



20.15 Suppose that the only way you could obtain 
information about the world was by throwing 
rubber balls at the objects around you and 
measuring their speeds and directions of rebound. 
What kind of objects would you be unable to 
learn about? 

20.16 A bullet can be considered as a particle 
having dimensions approximately 1 centimeter. 
It has a mass of about 10 grams and a speed of 
about 3x10^ centimeters per second. Suppose 
we can measure its speed to an accuracy of 

±1 cm/sec. What is the corresponding uncertainty 
in its position according to Heisenberg's 
principle? 

20.17 Show that if Planck's constant were equal 
to zero, quantum effects would disappear and 
even atomic particles would behave according 

to Newtonian physics. What effect would this 
have on the properties of light? 

20.18 Some writers have claimed that the un- 
certainty principle proves that there is free will. 
Do you think this extrapolation from atomic 
phenomena to the world of animate beings is 
justified? 

20.19 A physicist has written 



It is enough that quantum mechanics predicts 
the average value of observable quantities 
correctly. It is not really essential that the 
mathematical symbols and processes corre- 
spond to some intelligible physical picture of 
the atomic world. 

Do you regard such a statement as acceptable? 

Give reasons. 

20.20 In Chapters 19 and 20 we have seen that 

it is impossible to avoid the wave-particle duahsm 
of light and matter. Bohr has coined the word 
complementarity for the situation in which two 
opposite views seem valid, and the correct choice 
depends only on which aspect of a phenomenon 
one chooses to consider. Can you think of situa- 
tions in other fields (outside of atomic physics) 
to which this idea might apply? 

20.21 In Units 1 through 4 we discussed the 
behavior of large-scale "classical particles" (for 
example, tennis balls) and "classical waves" 
(for example, sound waves), that is, of particles 
and waves that in most cases can be described 
without any use of ideas such as the quantum of 
energy or the de Broghe matter-wave. Does this 
mean that there is one sort of physics ("classical 
physics") for the phenomena of the large-scale 
world and quite a different physics ("quantum 
physics") for the phenomena of the atomic world? 
Or does it mean that quantum physics really 
applies to all phenomena but is not distinguish- 
able from classical physics when applied to large- 
scale particles and waves? What arguments or 
examples would you use to defend your answer? 

20.22 If there are laws that describe precisely 
the behavior of atoms, it can be inferred that the 
future is completely determined by the present 
(and the present was determined in the ancient 
past). This idea of complete determinism^ was 
uncomfortable to many philosophers during the 
centuries following the great success of 
Newtonian mechanics. The great French physi- 
cist Pierre Laplace (1748-1827) wrote. 

Given for one instant an intelligence which 
could comprehend all the forces by which 
nature is animated and the respective 
situation of the beings who compose it — an 
intelhgence sufficiently vast to submit these 
data to analysis — it would embrace in the 
same formula the movements of the greatest 
bodies of the universe and those of the 
hghtest atom; for it, nothing would be un- 
certain and the future, as the past, would be 
present to its eyes [A Philosophical Essay on 
Probabilities.] 

Is this statement consistent with modem 

physical theory? 

20.23 (The later statistical view of kinetic theory 
may have emphasized the difficulty of actually 
predicting the future, but did not weaken the 
idea of an underlying chain of cause and effect.) 

(a) What implications do you see in relativity 
theorv for the idea of determinism? 



119 



STUDY G 



(b) What implications do you see for determinism 
in quantum theory? 

20.24 Those ancient Greeks who beUeved in 
natural law were also troubled by the idea of 
determinism. How do the Greek ideas expressed 
in the following passage from Lucretius' On the 
Nature of Things (about 80 B.C.) compare with 
modern physics ideas? 
If cause forever follows after cause 
In infinite, undeviating sequence 
And a new motion always has to come 
Out of an old one, by fixed law; if atoms 



Do not, by swerving, cause new moves which 

break 

The laws of fate; if cause forever follows, 

In infinite sequence, cause — where would we 

get 

This free will that we have, wrested from fate . . . 

What keeps the mind from having inside itself 

Some such compulsiveness in all its doings. 

What keeps it from being matter's absolute 

slave? 

The answer is that our free-will derives 

From just that ever-so-slight atomic swerve 

At no fixed time, at no fixed place whatever. 



120 



» 



I 



Kenneth Ford, University of California, Irvine 
Robert Gardner, Harvard University 
Fred Geis, Jr., Harvard University 
Nicholas J. Georgis, Staples High School, 

Westport, Conn. 
H. Richard Gerfin, Somers Middle School, 

Somers, N.Y. 
Owen Gingerich, Smithsonian Astrophysical 

Observatory, Cambridge, Mass. 
Stanley Goldberg, Antioch College, Yellow Springs, 

Ohio 
Leon Goutevenier, Paul D. Schreiber High School, 

Port Washington, N.Y. 
Albert Gregory, Harvard University 
Julie A. Goetze, Weeks Jr. High School, Newton, 

Mass. 
Robert D. Haas, Clairemont High School, San 
Diego, Calif. 

Walter G. Hagenbuch, Plymouth- Whitemarsh 

Senior High School, Plymouth Meeting, Pa. 

John Harris, National Physical Laboratory of 

Israel, Jerusalem 
Jay Hauben, Harvard University 
Peter Heller, Brandeis University, Waltham, Mass. 
Robert K. Henrich, Kennewick High School, 

Washington 
Ervin H. HofFart, Raytheon Education Co., Boston 
Banesh Hoffmann, Queens College, Flushing, N.Y. 
Elisha R. Huggins, Dartmouth College, Hanover, 

N.H. 
Lloyd Ingraham, Grant High School, Portland, 

Ore. 
John Jared, John Rennie High School, Pointe 

Claire, Quebec 
Harald Jensen, Lake Forest College, 111. 
John C. Johnson, Worcester Polytechnic Institute, 

Mass. 
Kenneth J. Jones, Harvard University 
LeRoy Kallemeyn, Benson High School, Omaha, 

Neb. 
Irving Kaplan, Massachusetts Institute of 

Technology, Cambridge 
Benjamin Karp, South Philadelphia High School, 

Pa. 
Robert Katz, Kansas State University, Manhattan, 

Kans. 
Harry H. Kemp, Logan High School, Utah 
Ashok Khosla, Harvard University 
John Kemeny, National Film Board of Canada, 

Montreal 
Merritt E. Kimball, Capuchino High School, San 

Bruno, Calif. 
Walter D. Knight, University of California, 

Berkeley 
Donald Kreuter, Brooklyn Technical High School, 

N.Y. 
Karol A. Kunysz, Laguna Beach High School, 

Calif. 
Douglas M. Lapp, Harvard University 
Leo Lavatelli, University of Illinois, Urbana 



122 



Joan Laws, American Academy of Arts and 

Sciences. Boston 
Alfred Leitner, Michigan State University, East 

Lansing 
Robert B. Lillich. Solon High School. Ohio 
James Lindblad, Lowell High School, Whittier 

Calif. 
Noel C. Little, Bowdoin College, Brunswick, Me. 
Arthur L. Loeb, Ledgemont Laboratory, Lexington, 

Mass. 
Richard T. Mara. Gettysburg College, Pa. 
Robert H. Maybury, UNESCO, Paris 
John McClain, University of Beirut, Lebanon 
E. Wesley McNair, W. Charlotte High School. 

Charlotte, N.C. 
William K. Mehlbach, Wheat Ridge High School, 

Colo. 
Priya N. Mehta. Harvard University 
Glen Mervyn, West Vancouver Secondary School, 

B.C., Canada 
Franklin Miller, Jr.. Kenyon College, Gambler 

Ohio 
Jack C. Miller, Pomona College, Claremont. Calif. 
Kent D. Miller, Claremont High School, Calif. 
James A. Minstrell, Mercer Island High School, 

Washington 
James F. Moore, Canton High School, Mass. 
Robert H. Mosteller, Princeton High School, 

Cincinnati, Ohio 
William Naison, Jamaica High School. N.Y. 
Henry Nelson, Berkeley High School, Calif. 
Joseph D. Novak, Purdue University, Lafayette 

Ind. 
Thorir Olafsson, Menntaskolinn Ad, Laugarvatni, 

Iceland 
Jay Orear, Cornell University, Ithaca, N.Y. 
Paul O'Toole. Dorchester High School, Mass. 
Costas Papaliolios, Harvard University 
Jacques Parent, National Film Board of Canada. 

Montreal 
Father Thomas Pisors, C.S.U., Griffin High 

School, Springfield, 111. 
Eugene A. Platten, San Diego High School, Calif. 
L. Eugene Poorman, University High School, 

Bloomington, Ind. 
Gloria Poulos, Harvard University 
Herbert Priestley, Knox College, Galesburg, 111. 
Edward M. Purcell, Harvard University 
Gerald M. Rees, Ann Arbor High School, Mich. 
James M. Reid. J. W. Sexton High School, 

Lansing, Mich. 
Robert Resnick, Rensselaer Polytechnic Institute, 

Troy, NY. 
Paul I. Richards, Technical Operations, Inc., 

Burlington, Mass. 
John Rigden, Eastern Nazarene College, Quincy, 

Mass. 
Thomas J. Ritzinger, Rice Lake High School, Wise. 
Nickerson Rogers, The Loomis School, Windsor, 
Conn. 

(Continued on page 167) 



I 




The Project Physics Course 




Models of the Atom 






Contents 



HANDBOOK SECTION 



Chapter 17 The Chemical Basis of Atomic Theory 

Experiment 

40. Electrolysis 126 

Activities 

Dalton's Puzzle 129 
Electrolysis of Water 129 
Periodic Table 129 
Single-electrode Plating 131 
Activities from Scientific American 1 31 

Film Loop 

Film Loop 46 : Production of Sodium by Electrolysis 1 32 

Chapter 18 Electrons and Quanta 

Experiments 

41. The Charge-to-mass Ratio for an Electron 133 

42. TheMeasurementof Elementary Charge 136 

43. The Photoelectric Effect 139 

Activities 

Writings By or About Einstein 143 
Measuring Q/M for the Electron 143 
Cathode Rays in a Crookes Tube 1 43 
X-rays from a Crookes Tube 143 
Lighting an Electric Lamp with a Match 1 43 

Film Loop 

Film Loop 47: Thomson Model of the Atom 145 

Chapter 19 The Rutherford-Bohr Model of the Atom 

Experiment 

44. Spectroscopy 146 

Activities 

Scientists on Stamps 149 

Measuring Ionization, a Quantum Effect 148 

Modeling Atoms with Magnets 150 

"Black Box" Atoms 151 

Another Simulation of the Rutherford Atom 1 52 

Film Loop 

Film Loop 48 : Rutherford Scattering 153 

Chapter 20 Some Ideas from Modern Physical Theories 

Activities 

Standing Waves on a Band-saw Blade 154 

Turntable Oscillator Patterns Resembling de Broglie Waves 154 

Standing Waves in a Wire Ring 154 



17 



Chapter I f The Chemical Basis of Atomic Theory 



EXPERIMENT 40 ELECTROLYSIS 

Volta and Davy discovered that electric cur- 
rents created chemical changes never observed 
before. As you have already learned, these 
scientists were the first to use electricity to 
break down apparently stable compounds and 
to isolate certain chemical elements. 

Later Faraday and other experimenters 
compared the amount of electric charge used 
with the amount of chemical products formed 
in such electrochemical reactions. Their mea- 
surements fell into a regular pattern that 
hinted at some underlying link between elec- 
tricity and matter. 

In this experiment you will use an electric 
current just as they did to decompose a com- 
pound. By comparing the charge used with the 
mass of one of the products, you can compute 
the mass and volume of a single atom of the 
product. 

Theory Behind the Experiment 

A beaker of copper sulfate (CUSO4) solution in 
water is supported under one arm of a balance 
(Fig. 17-1). A negatively charged copper elec- 
trode is supported in the solution by the bal- 



ance arm so that you can measure its mass 
without removing it from the solution. A sec- 
ond, positively charged copper electrode fits 
around the inside wall of the beaker. The 
beaker, its solution and the positive electrode 
are not supported by the balance arm. 

If you have studied chemistry, you proba- 
bly know that in solution the copper sulfate 
comes apart into separate charged particles, 
called ions, of copper (Cu++) and sulfate (S04=), 
which move about freely in the solution. 

When a voltage is applied across the cop- 
per electrodes, the electric field causes the 
S04= ions to drift to the positive electrode (or 
anode) and the Cu++ ions to drift to the nega- 
tive electrode (or cathode). At the cathode the 
Cu++ particles acquire enough negative charge 
to form neutral copper atoms which deposit 
on the cathode and add to its weight. The mo- 
tion of charged particles toward the electrodes 
is a continuation of the electric current in the 
wires and the rate of transfer of charge (cou- 
lombs per second) is equal to it in magnitude. 
The electric current is provided by a power sup- 
ply that converts 100- volt alternating current 
into low-voltage direct current. The current 




Fig. 17-1 



Experiment 40 



127 



is set by a variable control on the power supply 
(or by an external rheostat) and measured by 
an ammeter in series with the electrolytic cell 
as shown in Fig. 17-1. 

With the help of a watch to measure the 
time the current flows, you can compute the 
electric charge that passed through the cell. 
By definition, the current I is the rate of trans- 
fer or charge: I = AQ/At. It follows that the 
charge transferred is the product of the cur- 
rent and the time. 



AQ = I X At 

coulombs 
(coulombs = 



sec 



X sec) 



Since the amount of charge carried by a 
single electron is known (qe = 1.6 x 10"*^ cou- 
lombs), the number of electrons transferred, 
Ne, is 



If n electrons are needed to neutralize each 
copper ion, then the number of copper atoms 
deposited, N^u, is 



N =^ 
n 



'Cu 



If the mass of each copper atom is rric^, then 
the total mass of copper deposited, M^u, is 

Mcu = ^curricu 

Thus, if you measure I, At and Mf.„, and you 
know q^ and n, you can calculate a value for 
nicu, the mass of a single copper atom! 

Setup and Procedure 

Either an equal-arm or a triple-beam balance 
can be used for this experiment. First arrange 
the cell and the balance as shown in Fig. 17-1. 
The cathode cylinder must be supported far 
enough above the bottom of the beaker so that 
the balance arm can move up and down freely 
when the cell is full of the copper sulfate 
solution. 

Next connect the circuit as illustrated in 



the figure. Note that the electrical connection 
from the negative terminal of the power supply 
to the cathode is made through the balance 
beam. The knife-edge and its seat must be by- 
passed by a short piece of thin flexible wire, 
as shown in Fig. 17-1 for equal-arm balances, 
or in Fig. 17-2 for triple-beam balances. The 
positive terminal of the power supply is con- 
nected directly to the anode in any convenient 
manner. 




Fig. 17-2 This cutaway view shows how to by-pass the 
knife-edge of a typical balance. The structure of other 
balances may differ. 



Before any measurements are made, op- 
erate the cell long enough (10 or 15 minutes) to 
form a preliminary deposit on the cathode— 
unless this has already been done. In any case, 
run the current long enough to set it at the 
value recommended by your teacher, probably 
about 5 amperes. 

When all is ready, adjust the balance and 
record its reading. Pass the current for the 
length of time recommended by your teacher. 
Measure and record the current I and the time 
interval At during which the current passes. 
Check the ammeter occasionally and, if neces- 
sary, adjust the control in order to keep the 
current set at its original value. 

At the end of the run, record the new read- 
ing of the balance, and find by subtraction the 
increase in mass of the cathode. 



128 



Experiment 40 



Calculating Mass and Volume of an Atom 

Since the cathode is buoyed up by a Uquid, the 
masses you have measured are not the true 
masses. Because of the buoyant force exerted 
by the Uquid, the mass of the cathode and its 
increase in mass will both appear to be less 
than they would be in air. To find the true mass 
increase, you must divide the observed mass 
increase by the factor (1 - DglD,.), where Dg is 
the density of the solution and D^. is the density 
of the copper. 

Your teacher will give you the values of 
these two densities if you cannot find values 
for them yourself. He will also explain how the 
correction factor is derived. The important 
thing for you to understand here is why a cor- 
rection factor is necessary. 
Ql How much positive or negative charge 
was transferred to the cathode? 



In the solution this positive charge is car- 
ried from anode to cathode by doubly charged 
copper ions, Cu++. At the cathode the copper 
ions are neutralized by electrons and neutral 
copper atoms are deposited: Cu^+ + 2e"Cu. 
Q2 How many electrons were required to 
neutralize the total charge transferred? (Each 
electron carries -1.6 x 10"'" coulombs.) 
Q3 How many electrons (single negative 
charge) were required to neutralize each cop- 
per ion? 

Q4 How many copper atoms were deposited? 
Q5 What is the mass of each copper atom? 
Q6 The mass of a penny is about 3 grams. If 
it were made of copper only, how many atoms 
would it contain? (In fact modern pennies con- 
tain zinc as well as copper.) 
Q7 The volume of a penny is about 0.3 cm^ 
How much volume does each atom occupy? 



ACTIVITIES 



129 



DALTON'S PUZZLE 

Once Dalton had his theory to work with, the 
job of figuring out relative atomic masses and 
empirical formulas boiled down to nothing 
more than working through a series of puzzles. 
Here is a very similar kind of puzzle with 
which you can challenge your classmates. 

Choose three sets of objects, each having a 
different mass. Large ball bearing with masses 
of about 70, 160, and 200 grams work well. Let 
the smallest one represent an atom of hydro- 
gen, the middle-sized one an atom of nitrogen, 
and the large one an atom of oxygen. 

From these "atoms" construct various 
"molecules." For example, NHg could be repre- 
sented by three small objects and one middle- 
sized one, N2O by two middle-sized ones and 
one large, and so forth. 

Conceal one molecule of your collection in 
each one of a series of covered Styrofoam cups 
(or other hght-weight, opaque containers). 
Mark on each container the symbols (but not 
the formula!) of the elements contained in the 
compound. Dalton would have obtained this 
information by quahtative analysis. 

Give the covered cups to other students. 
Instruct them to measure the "molecular" 
mass of each compound and to deduce the rela- 
tive atomic masses and empirical formulas 
from the set of masses, making Dalton's as- 
sumption of simplicity. If the objects you have 
used for "atoms" are so hght that the mass of 
the styrofoam cups must be taken into account, 
you can either supply this information as part 
of the data or leave it as a comphcation in the 
problem. 

If the assumption of simphcity is relaxed, 
what other atomic masses and molecular 
formulas would be consistent with the data? 

ELECTROLYSIS OF WATER 

The fact that electricity can decompose water 
was an amazing and exciting discovery, yet 
the process is one that you can easily demon- 
strate with materials at your disposal. Fig. 
17-3 provides all the necessary information. 
Set up an electrolysis apparatus and demon- 
strate the process for your classmates. 

In Fig. 17-3 it looks as if about twice as 




Fig. 17-3 



many bubbles were coming from one electrode 
as from the other. Which electrode is it? Does 
this happen in your apparatus? Would you 
expect it to happen? 

How would you collect the two gases that 
bubble off the electrodes? How could you 
prove their identity? 

If water is really just these two gases "put 
together" chemically, you should be able to 
put the gases together again and get back the 
water with which you started. Using your 
knowledge of physics, predict what must then 
happen to all the electrical energy you sent 
flowing through the water to separate it. 

PERIODIC TABLE 

You may have seen one or two forms of the 
periodic table in your classroom, but many 
others have been devised to emphasize var- 
ious relationships among the elements. Some, 
such as the ones shown on the next page, are 
more visually interesting than others. Check 
various sources in your library and prepare an 
exhibit of the various types. An especially good 
lead is the article, "Ups and Down of the Per- 
iodic Table" in Chemistry, July 1966, which 
shows many different forms of the table, in- 
cluding those in Fig. 17-4. 

It is also interesting to arrange the ele- 
ments in order of discovery on a Unear time 
chart. Periods of intense activity caused by 
breakthroughs in methods of extended work by 
a certain group of investigators show up in 
groups of names. A simple way to do this is to 
use a typewriter, letting each Une represent 
one year (from 1600 on). All the elements then 
fit on six normal typing pages which can be 



130 Activities 




(c) 




Three two-dimensional spiral forms, (a) Janet. 1928. (b) Kipp, 1942. (c) Sibaiua, 1941. 



Activities 



131 



fastened together for mounting on a wall. A 
list of discovery dates for all elements appears 
at the end of Chapter 21 in the Text. 

SINGLE-ELECTRODE PLATING 

A student asked if copper would plate out from 
a solution of copper sulfate if only a negative 
electrode were placed in the solution. It was 
tried and no copper was observed even when 
the electrode was connected to the negative 
terminal of a high voltage source for five 
minutes. Another student suggested that only 
a very small (invisible) amount of copper was 
deposited since copper ions should be attracted 
to a negative electrode. 

A more precise test was devised. A nickel- 
sulfate solution was made containing several 
microcuries of radioactive nickel (no radio- 
copper was available). A single carbon elec- 
trode was immersed in the solution, and con- 
nected to the negative terminal of the high 
voltage source again for five minutes. The 
electrode was removed, dried, and tested with 
a Geiger counter. The rod was slightly radio- 
active. A control test was run using identical 
test conditions, except that no electrical con- 
nection was made to the electrode. The control 
showed more radioactivity. 

Repeat these experiments and see if the 
effect is true generally. What explanation 
would you give for these effects? (Adapted 



from Ideas for Science Investigations, N. S.- 
T. A. 1966). 

ACTIVITIES FROM SCIENTIFIC AMERICAN 

The following articles from the "Amateur 
Scientist" section of Scientific American re- 
late to Unit 5. They range widely in difficulty. 
Accelerator, electron, Jan. 1959, p. 138. 
Beta ray spectrometer, Sept. 1958, p. 197. 
Carbon 14 dating, Feb. 1957, p. 159. 
Cloud chamber, diffusion, Sept. 1952, p. 179. 
Cloud chamber, plumber's friend, Dec. 1956, 
p. 169. 

Cloud chamber, Wilson, Apr. 1956, p. 156. 
Cloud chamber, with magnet, June 1959, 
p. 173. 

Cyclotron, Sept. 1953, p. 154. 
Gas discharge tubes, how to make, Feb, 1958, 
p. 112. 

Geiger counter, how to make. May 1960, p. 189. 
Isotope experiments. May 1960, p. 189. 
Magnetic resonance spectrometer, Apr. 1959, 
p. 171. 

Scintillation counter, Mar. 1953, p. 104. 
Spectrograph, astronomical, Sept. 1956, p. 259. 
Spectrograph, Bunsen's, June 1955, p. 122. 
Spinthariscope, Mar. 1953, p. 104. 
SpectroheUograph, how to make, Apr. 1958, 
p. 126. 

Subatomic particle scattering, simulating, 
Aug. 1965, p. 102. 



FILM LOOP 



FILM LOOP 46: PRODUCTION OF SODIUM 
BY ELECTROLYSIS 

In 1807, Humphry Davy produced metallic 
sodium by electrolysis of molten lye — sodium 
hydroxide. 

In the film, sodium hydroxide (NaOH) is 
placed in an iron crucible and heated until it 
melts, at a temperature of 318°C. A rectifier 
connected to a power transformer supphes a 
steady current through the Uquid NaOH 
through iron rods inserted in the melt. Sodium 
ions are positive and are therefore attracted 
to the negative electrode; there they pick up 
electrons and become metalHc sodium, as in- 
dicated symbohcally in this reaction: 

Na+ + e- = Na. 



The sodium accumulates in a thin, shiny layer 
floating on the surface of the molten sodium 
hydroxide. 

Sodium is a dangerous material which 
combines explosively with water. The experi- 
menter in the film scoops out a little of the 
metal and places it in water. (Fig. 17-5.) En- 
ergy is released rapidly, as you can see from 
the violence of the reaction. Some of the so- 
dium is vaporized and the hot vapor emits the 
yellow hght characteristic of the spectrum of 
sodium. The same yellow emission is easily 
seen if common salt, sodium chloride, or some 
other sodium compound, is sprinkled into an 
open flame. 




Fig. 17-5 



Chapter 



18 



Electrons and Quanta 



EXPERIMENT 41 THE CHARGE-TO-MASS 
RATIO FOR AN ELECTRON 

In this experiment you make measurements on 
cathode rays. A set of similar experiments by 
J. J. Thomson convinced physicists that these 
rays are not waves but streams of identical 
charged particles, each with the same ratio of 
charge to mass. If you did experiment 38 in 
Unit 4, "Electron-Beam Tube," you have al- 
ready worked with cathode rays and have seen 
how they can be deflected by electric and 
magnetic fields. 

Thomson's use of this deflection is des- 
cribed on page 36 of the Unit 5 Text. Read 
that section of the text before beginning this 
experiment. 



radius R by a uniform magnetic field B, the 
centripetal force rm/IR on each electron is 
supplied by the magnetic force Bq^v. Therefore 



R 



Bq,v, 



or, rearranging to get v by itself, 

m 

The electrons in the beam are accelerated 
by a voltage V which gives them a kinetic 
energy 



mv^ 



Theory of the experiment 

The basic plan of the experiment is to measure 
the bending of the electron beam by a known 
magnetic field. From these measurements and 
a knowledge of the voltage accelerating the 
electrons, you can calculate the electron 
charge-to-mass ratio. The reasoning behind 
the calculation is illustrated in Fig. 18-1. The 
algebraic steps are described below. 



yqe- 



If you replace v in this equation by the expres- 
sion for V in the preceding equation, you get 



m _ (BqeR 



or, after simpHfying, 



yqe 




m 



2V 

Bm^ 



Fig. 18-1 The combination of two relationships, for 
centripetal and kinetic energy, with algebraic steps that 
eliminate velocity, v, lead to an equation for the charge- 
to-mass ratio of an electron. 



When the beam of electrons (each of mass 
m and charge <je) is bent into a circular arc of 



You can measure with your apparatus all 
the quantities on the right-hand side of this 
expression, so you can use it to calculate the 
charge-to-mass ratio for an electron. 

Preparing the apparatus 

You will need a tube that gives a beam at least 
5 cm long. If you kept the tube you made in 
Experiment 38, you may be able to use that. 
If your class didn't have success with this 
experiment, it may mean that your vacuum 
pump is not working well enough, in which 
case you will have to use another method. 



134 



Experiment 41 



In this experiment you need to be able to 
adjust the strength of the magnetic field until 
the magnetic force on the charges just bal- 
ances the force due to the electric field. To 
enable you to change the magnetic field, you 
will use a pair of coils instead of permanent 
magnets. A current in a pair of coils, which 
are separated by a distance equal to the coil 
radius, produces a nearly uniform magnetic 
field in the central region between the coils. 
You can vary the magnetic field by changing 
the current in the coils. 

Into a cardboard tube about 3" in diameter 
and 3" long cut a slot I4" wide. (Fig. 18-2.) 
Your electron-beam tube should fit into this 
slot as shown in the photograph of the com- 
pleted set-up. (Fig. 18-4.) Current in the pair 
of coils will create a magnetic field at right 
angles to the axis of the cathode rays. 

Now wind the coils, one on each side of the 
slot, using a single length of insulated copper 
wire (magnet wire). Wind about 20 turns of 
wire for each of the two coils, one coil on each 
side of the slot, leaving 10" of wire free at both 
ends of the coil. Don't cut the wire off the reel 
until you have found how much you will need. 
Make the coils as neat as you can and keep 
them close to the slot. Wind both coils in the 
same sense (for example, make both clock- 
wise). 

When you have made your set of coils, you 
must "calibrate" it; that is, you must find out 
what magnetic field strength B corresponds 
to what values of current I in the coils. To do 





Fig. 18-2 



Fig. 18-3 



this, you can use the current balance, as you 
did in Experiment 36. Use the shortest of the 
balance "loops" so that it will fit inside the 
coils as shown in Fig. 18-3. 

Connect the two leads from your coils to 
a power supply capable of giving up to 5 amps 
direct current. There must be a varable con- 
trol on the power supply (or a rheostat in the 
circuit) to control the current; and an ammeter 
to measure it. 

Measure the force F for a current / in the 
loop. To calculate the magnetic field due to 
the current in the coils, use the relationship 
F = BU where i is the length of short section of 
the loop. Do this for several different values of 
current in the coil and plot a calibration graph 
of magnetic field B against coil current I. 

Set up your electron-beam tube as in Ex- 
periment 38. Reread the instructions for oper- 
ating the tube. 

Connect a shorting wire between the pins 
for the deflecting plates. This will insure that 
the two plates are at the same electric poten- 
tial, so the electric field between them will be 
zero. Pump the tube out and adjust the fila- 
ment current until you have an easily visible 
beam. Since there is no field between the 
plates, the electron beam should go straight 
up the center of the tube between the two 
plates. (If it does not, it is probably because 
the filament and the hole in the anode are not 
properly aligned.) 

Turn down the filament current and switch 
off the power supply. Now, without releasing 



Experiment 41 



135 




Fig. 18-4 The magnetic field is parallel to the axis of 
the coils; the electric and magnetic fields are perpen- 
dicular to each other and to the electron beam. 

the vacuum, mount the coils around the tube 
as shown in Fig. 18-4. 

Connect the coils as before to the power 
supply. Connect a voltmeter across the power 
supply terminals that provide the accelerating 
voltage V. 

Your apparatus is now complete. 

Performing the experiment 

Turn on the beam, and make sure it is travel- 
hng in a straight line. The electric field re- 
mains off throughout the experiment, and the 
deflecting plates should still be connected 
together. 

Turn on and slowly increase the current in 
the coils until the magnetic field is strong 
enough to deflect the electron beam noticeably. 

Record the current I in the coils. 

Using the cahbration graph, find the mag- 
netic field B. 

Record the accelerating voltage V between 
the filament and the anode plate. 

Finally you need to measure R, the radius 
of the arc into which the beam is bent by the 
magnetic field. The deflected beam is sUghtly 
fan-shaped because some electrons are slowed 
by collisions with air molecules and are bent 
into a curve of smaller R. You need to know the 
largest value of R (the "outside" edge of the 
curved beam), which is the path of electrons 
that have made no collisions. You won't be 
able to measure R directly, but you can find 







heary herft tn1b 
I Circuhor arc 



tane-fi 



! peATperfCdCLihr 



f? 



.X 



d 



\ 



\ 



\ 



f?-x. 



Fig. 18-5 



it from measurements that are easy to make. 
(Fig. 18-5.) 

You can measure x and d. It follows from 
Pythagoras' theorem that R^ = d^ + (R — xf, 



so R = 



d^ + x^ 
2x ' 



Ql What is your calculation of R on the basis 
of your measurements? 

Now that you have values for V, B and R, 
you can use the formula qelm= 2VIB^R'^ to cal- 
culate your value for the charge-to-mass ratio 
for an electron. 

Q2 What is your value for Qelm, the charge- 
to-mass ratio for an electron? 



136 



EXPERIMENT 42 THE MEASUREMENT OF 
ELEMENTARY CHARGE 

In this experiment, you will investigate the 
charge of the electron, a fundamental physical 
constant in electricity, electromagnetism, and 
nuclear physics. This experiment is substan- 
tially the same as Millikan's famous oil-drop 
experiment, described on page 39 of the Unit 5 
Text. The following instructions assume that 
you have read that description. Like Milhkan, 
you are going to measure very small electric 
charges to see if there is a limit to how small 
an electric charge can be. Try to answer the 
following three questions before you begin to 
do the experiment in the lab. 
Ql What is the electric field between two 
parallel plates separated by a distance d me- 
ters, if the potential difference between them 
is V volts? 

Q2 What is the electric force on a particle 
carrying a charge of q coulombs in an electric 
field of E volts/meter? 

Q3 What is the gravitational force on a par- 
ticle of mass m in the earth's gravitational 
field? 

Background 

Electric charges are measured by measuring 
the forces they experience and produce. The 
extremely small charges that you are seeking 
require that you measure extremely small 
forces. Objects on which such small forces 
can have a visible effect must also in turn be 
very small. 

Millikan used the electrically charged 
droplets produced in a fine spray of oil. The 
varying size of the droplets comphcated his 
measurements. Fortunately you can now use 
suitable objects whose sizes are accurately 
known. You use tiny latex spheres (about 
10"^ cm diatmeter), which are almost identical 
in size in any given sample. In fact, these 
spheres, shown magnified (about 5000 x) in 
Fig. 18-6, are used as a convenient way to find 
the magnifying power of electron microscopes. 
The spheres can be bought in a water suspen- 
sion, with their diameter recorded on the 
bottle. When the suspension is sprayed into the 
air, the water quickly evaporates and leaves 




Fig. 18-6 Electron micrograph of latex spheres 1.1 x 
lO'^cm, silhouetted against diffracting grating of 28,800 
lines/inch. What magnification does this represent? 

a cloud of these particles, which have become 
charged by friction during the spraying. In 
the space between the plates of the Millikan 
apparatus they appear through the 50-power 
microscope as bright points of hght against 
a dark background. 

You will find that an electric field between 
the plates can pull some of the particles up- 
ward against the force of gravity, so you will 
know that they are charged electrically. 

In your experiment, you adjust the voltage 
producing the electric field until a particle 
hangs motionless. On a balanced particle 
carrying a charge q, the upward electric force 
Eq and the downward gravitational force mUg 
are equal, so 

mUg = Eq . 

The field E = VId, where V is the voltage 
between the plates (the voltmeter reading) 
and d is the separation of the plates. Hence 



q = 



mOgd 
V 



Notice that mUgd is a constant for all 
measurements and need be found only once. 
Each value of q will be this constant mUgd 
times 1/V as the equation above shows. That 
is, the value of q for a particle is proportional 
to 1/V: the greater the voltage required to bal- 
ance the weight of the particle, the smaller 
the charge of the particle must be. 



Experiment 42 



137 




Fig. 18-7 A typical set of apparatus. Details may vary 
considerably. 



Using the apparatus 

If the apparatus is not already in operating 
condition, consult your teacher. Study Figs. 
18-7 and 18-8 until you can identify the various 
parts. Then switch on the hght source and 
look through the microscope. You should see 
a series of Unes in clear focus against a uni- 
form gray background. 




to chamber 



to vo Hmtttr f^\ \\' 







Confrc 



Fig. 18-8 A typical arrangement of connections to the 
high-voltage reversing switch. 

The lens of the hght source may fog up as 
the heat from the lamp drives moisture out of 



the hght-source tube. If this happens, remove 
the lens and wipe it on a clean tissue. Wait 
for the tube to warm up thoroughly before 
replacing the lens. 

Squeeze the bottle of latex suspension two 
or three times until five or ten particles drift 
into view. You will see them as tiny bright 
spots of hght. You may have to adjust the focus 
slightly to see a specific particle clearly. No- 
tice how the particle appears to move upward. 
The view is inverted by the microscope— the 
particles are actually falhng in the earth's 
gravitational field. 

Now switch on the high voltage across the 
plates by turning the switch up or down. No- 
tice the effect on the particles of varying the 
electric field by means of the voltage-control 
knob. 

Notice the effect when you reverse the 
electric field by reversing the switch position. 
(When the switch is in its mid-position, there 
is zero field between the plates.) 
Q4 Do all the particles move in the same 
direction when the field is on? 
Q5 How do you explain this? 
Q6 Some particles move much more rapidly 
in the field than others. Do the rapidly moving 
particles have larger or smaller charges than 
the slowly moving particles? 

Sometimes a few particles chng together, 
making a clump that is easy to see — the clump 
falls more rapidly than single particles when 
the electric field is off. Do not try to use these 
for measuring q. 

Try to balance a particle by adjusting the 
field until the particle hangs motionless. Ob- 
serve it carefully to make sure it isn't slowly 
drifting up or down. The smaller the charge, 
the greater the electric field must be to hold 
up the particle. 

Taking data 

It is not worth working at voltages much below 
50 volts. Only highly charged particles can be 
balanced in these small fields, and you are 
interested in obtaining the smallest charge 
possible. 

Set the potential difference between the 
plates to about 75 volts. Reverse the field a 



138 



Experiment 42 



few times so that the more quickly moving 
particles (those with greater charge) are swept 
out of the field of view. Any particles that re- 
main have low charges. If no particles remain, 
squeeze in some more and look again for some 
with small charge. 

When you have isolated one of these par- 
ticles carrying a low charge, adjust the voltage 
carefully until the particle hangs motionless. 
Observe it for some time to make sure that it 
isn't moving up or down very slowly, and that 
the adjustment of voltage is as precise as pos- 
sible. (Because of uneven bombardment by 
air molecules, there will be some shght, un- 
even drift of the particles.) 

Read the voltmeter. Then estimate the pre- 
cision of the voltage setting by seeing how Ht- 
tle the voltage needs to be changed to cause the 
particle to start moving just perceptibly. This 
small change in voltage is the greatest amount 
by which your setting of the balancing voltage 
can be uncertain. 

When you have balanced a particle, make 
sure that the voltage setting is as precise as 
you can make it before you go on to another 
particle. The most useful range to work in is 
75-150 volts, but try to find particles that can 
be brought to rest in the 200-250 volt range 
too, if the meter can be used in that range. Re- 
member that the higher the balancing field 
the smaller the charge on the particle. 

In this kind of an experiment, it is helpful 
to have large amounts of data. This usually 
makes it easier to spot trends and to distin- 
guish main effects from the background scat- 
tering of data. Thus you may wish to contribute 
your findings to a class data pool. Before doing 
that, however, arrange your values of V in a 
vertical column of increasing magnitude. 
Q7 Do the numbers seem to clump together 
in groups, or do they spread out more or less 
evenly from the lowest to the highest values? 

Now combine your data with that collected 
by your classmates. This can conveniently 
be done by placing your values of V on a class 
histogram. When the histogram is complete, 
the results can easily be transferred to a trans- 
parent sheet for use on an overhead projector. 
Alternatively, you may wish to take a Polaroid 



photograph of the completed histogram for 

inclusion in your laboratory notebook. 

Q8 Does your histogram suggest that all 

values of q are possible and that electric 

charge is therefore endlessly divisible, or the 

converse? 

If you would like to make a more complete 
quantitative analysis of the class results, cal- 
culate an average value for each of the high- 
est three or four clumps of V values in the class 
histogram. Next change those to values of 1/V 
and hst them in order. Since q is proportional 
to 1/V, these values represent the magnitude 
of the charges on the particles. 

To obtain actual values for the charges, 
the 1/V's must be multipUed by mttgd. The sepa- 
ration d of the two plates, typically about 5.0 
mm, or 5.0 x 10~^m, is given in the specifica- 
tion sheets provided by the manufacturer. 
You should check this. 

The mass m of the spheres is worked out 
from a knowledge of their volume and the 
densitiy D of the material they are made from. 

Mass = volume x density, or 

The sphere diameter (careful: 2) has been 
previously measured and is given on the supply 
bottle. The density D is 1077 kg/m' (found by 
measuring a large batch of latex before it is 
made into Httle spheres). 

Q9 What is the spacing between the observed 
average values of 1/V and what is the differ- 
ence in charge that corresponds to this differ- 
ence in 1/V? 

QIO What is the smallest value of 1/V that 
you obtained? What is the corresponding value 
of q? 

Qll Do your experimental results support 
the idea that electric charge is quantized? 
If so, what is your value for the quantum of 
charge? 

Q12 If you have already measured qplm in 
Experiment 39, compute the mass of an elec- 
tron. Even if your value differs the accepted 
value by a factor of 10. perhaps you will agree 
that its measurement is a considerable intel- 
lectual triumph. 



139 



EXPERIMENT 43 THE PHOTOELECTRIC 
EFFECT 

In this experiment you will make observations 
on the effect of light on a metal surface; then 
you will compare the appropriateness of the 
wave model and the particle model of hght for 
explaining what you observe. 

Before doing the experiment, read text 
Sec. 18.4 (Unit 5) on the photoelectric effect. 

How the apparatus works 

Light that you shine through the window of the 
phototube falls on a half-cylinder of metal 
called the emitter. The hght drives electrons 
from the emitter surface. 

Along the axis of the emitter (the center 
of the tube) is a wire called the collector. When 
the collector is made a few volta positive with 
respect to the emitter, practically all the 
emitted electrons are drawn to it, and will 
return to the emitter through an external wire. 
Even if the collector is made sUghtly negative, 
some electrons will reach it and there will be 
a measurable current in the external circuit. 




de'f'cc+ov- 



However much the details may differ, any equipment for 
the photoelectric effect experiment will consist of these 
basic parts. 

The small current can be ampHfied several 
thousand times and detected in any of several 
different ways. One way is to use a small loud- 
speaker in which the ampUfied photoelectric 
current causes an audible hum; another is to 
use a cathode ray oscilloscope. The following 
description assumes that the output current 
is read on a microammeter (Fig. 18-9). 

The voltage control knob on the phototube 
unit allows you to vary the voltage between 
emitter and collector. In its full counter- 
clockwise position, the voltage is zero. As you 
turn the knob clockwise the "photocurrent" 
decreases. You are making the collector more 




detector 



ier~ 



\/t3t /a^>»^ 



Fig. 18-9 



140 



Experiment 43 



and more negative and fewer and fewer elec- 
trons get to it. Finally the photocurrent ceases 
altogether — all the electrons are turned back 
before reaching the collector. The voltage 
between emitter and collector that just stops 
all the electrons is called the "stopping volt- 
age." The value of this voltage indicates the 
maximum kinetic energy with which the elec- 
trons leave the emitter. To find the value of 
the stopping voltage precisely you will have to 
be able to determine precisely when the photo- 
current is reduced to zero. Because there is 
some drift of the amphfier output, the current 
indicated on the meter will drift around the 
zero point even when the actual current re- 
mains exactly zero. Therefore you will have to 
adjust the amphfier offset occasionally to be 
sure the zero level is really zero. An alternative 
is to ignore the precise reading of the current 
meter and adjust the collector voltage until 
turning the light off and on causes no detect- 
able change in the current. Turn up the nega- 
tive collector voltage until blocking the hght 
from the tube (with black paper) has no effect 
on the meter reading— the exact location of 
the meter pointer isn't important. 

The position of the voltage control knob at 
the current cutoff gives you a rough measure 
of stopping voltage. To measure it more pre- 
cisely, connect a voltmeter as shown in Fig. 
18-10. 

In the experiment you will measure the 
stopping voltages as hght of different fre- 
quencies falls on the phototube. Good colored 
filters will allow light of only a certain range of 
frequencies to pass through. You can use a 
hand spectroscope to find the highest fre- 
quency line passed by each filter. The filters 
select frequencies from the mercury spectrum 
emitted by an intense mercury lamp. Useful 
frequencies of the mercury spectrum are: 



Yellow 


5.2 X lO'Vsec 


Green 


5.5 X lO'^/sec 


Blue 


6.9 X lO'^/sec 


Violet 


7.3 X lO'^/sec 


(Ultraviolet) 


8.2 X lO'Vsec 



DOING THE EXPERIMENT 

Part I 

The first part of the experiment is qualitative. 
To see if there is time delay between hght fall- 
ing on the emitter and the emission of photo- 
electrons, cover the phototube and then quickly 
remove the cover. Adjust the hght source and 
filters to give the smallest photocurrent that 
you can conveniently notice on the meter. 
Ql Can you detect any time delay between 
the moment that hght hits the phototube and 
the moment that motion of the microamme- 
ter pointer (or a hum in the loudspeaker or 
deflection of the oscilloscope trace) signals 
the passage of photoelectrons through the 
phototube? 

To see if the current in the phototube de- 
pends on the intensity of incident hght, vary 
the distance of the hght source. 
Q2 Does the number of photoelectrons emit- 
ted from the sensitive surface vary with hght 
intensity— that is, does the output current of 
the amphfier vary with the intensity of the 
hght? 

To find out whether the kinetic energy of 
the photoelectrons depends on the intensity of 
the incident light, measure the stopping volt- 
age with different intensities of hght falhng 
on the phototube. 

Q3 Does the kinetic energy of the photoelec- 
trons depend on intensity— iha.t is, does the 
stopping voltage change? 

Finally, determine how the kinetic energy 
of photoelectrons depends on the frequency of 
incident light. You will remember (Text Sec. 
18.5) that the maximum kinetic energy of the 
photoelectrons is V^,gi,q^, where V,,op is the stop- 
ping voltage and q^ = 1.60 x 10"'^ coulombs, 
the charge on an electron. Measure the stop- 
ping voltage with various filters over the 
window. 

Q4 How does the stopping voltage and hence 
the kinetic energy change as the light is 
changed from red through blue or ultraviolet 
(no filters)? 

Part II 

In the second part of the. experiment you will 



Experiment 43 



141 



make more precise measurements of stopping 
voltage. To do this, adjust the voltage control 
knob to the cutoff (stopping voltage) position 
and then measure V with a voltmeter (Fig. 
18-10.) Connect the voltmeter only after the 
cutoff adjustment is made so that the volt- 
meter leads will not pick up any ac voltage 
induced from other conducting wires in the 
room. 




to 
Vo/t meter 



Fig. 18-10 

Measure the stopping voltage V^,gp for three 
or four different hght frequencies, and plot 
the data on a graph. Along the vertical axis, 
plot electron energy V^ig^q^. When the stopping 
voltage V is in volts, and q^ is in coulombs, 
Vqg will be energy, in joules. 

Along the horizontal axis plot frequency 
of hght/. 

Interpretation of Results 

As suggested in the opening paragraph, you 
can compare the wave model of light and the 
particle model in this experiment. Consider, 
then, how these models explain your obser- 
vations. 

Q5 If the hght striking your phototube acts 
as waves — 

a) Can you explain why the stopping voltage 
should depend on the frequency of hght? 

b) Would you expect the stopping voltage to 
depend on the intensity of the light? Why? 

c) Would you expect a delay between the time 



that hght first strikes the emitter and the emis- 
sion of photoelectrons? Why? 
Q6 If the light is acting as a stream of par- 
ticles, what would be the answer to questions 
a, b and c above? 

If you drew the graph suggested in the Part 
II of the experiment, you should now be pre- 
pared to interpret the graph. It is interesting to 
recall that Einstein predicted its form in 1905, 
and by experiments similar to yours, Milhkan 
verified Einstein's prediction in 1916. 

Einstein's photoelectric equation (Text 
Sec. 18.5) describes the energy of the most 
energetic photoelectrons (the last ones to be 
stopped as the voltage is increased), as 



A 9 



= hf-W. 

This equation has the form 

y = kx - c. 

In this equation -c is a constant, the value 
of y at the point where the straight hne cuts 
the vertical axis; and k is another constant, 
namely the slope of the line. (See Fig. 18-11.) 
Therefore, the slope of a graph oiVgig^q^ against 
/ should be h. 

Q7 What is the value of the slope of your 
graph? How well does this value compare with 




Fig. 18-11 



142 



Experiment 43 



the value of Planck's constant, h = 6.6 x 10 ^* 
joule-sec? (See Fig. 18-12). 







hf-w 



Fig. 18-12 

With the equipment you used, the slope is 
unlikely to agree with the accepted value of h 
(6.6 X 10"'^^ joule-sec) more closely than an 
order of magnitude. Perhaps you can give a 



few reasons why your agreement cannot be 
more approximate. 

Q8 The lowest frequency at which any elec- 
trons are emitted from the cathode surface is 
called the threshold frequency, /o- At this 
frequency imTy^^j. = and h/o = W, where W 
is the "work function." Your experimentally 
obtained value of W is not likely to be the same 
as that found for very clean cathode surfaces, 
more carefully filtered light, etc. The impor- 
tant thing to notice here is that there is a value 
of W, indicating that there is a minimum en- 
ergy needed to release photoelectrons from the 
emitter. 

Q9 Einstein's equation was derived from the 
assumption of a particle (photon) model of 
light. If your results do not fully agree with 
Einstein's equation, does this mean that your 
experiment supports the wave theory? 



I 



ACTIVITIES 



WRITINGS BY OR ABOUT EINSTEIN 

In addition to his scientific works. Einstein 
wrote many perceptive essays on other areas 
of life which are easy to read, and are still very 
current. The chapter titles from Out of My 
Later Years (Philosophical Library, N.Y. 1950) 
indicate the scope of these essays: Convictions 
and Beliefs; Science; Pubhc Affairs; Science 
and Life; Personahties; My People. This book 
includes his writings from 1934 to 1950. The 
World As I See It includes material from 1922 
to 1934. Albert Einstein: Philosopher-Scien- 
tist, Vol. I. (Harper Torchbook, 1959) contains 
Einstein's autobiographical notes, left-hand 
pages in German and right hand pages in En- 
ghsh, and essays by twelve physicist contem- 
poraries of Einstein about various aspects of 
his work. See also the three articles, "Ein- 
stein," "Outside and Inside the Elevator," and 
"Einstein and Some Civilized Discontents" in 
Reader 5. 



MEASURING q/m FOR THE ELECTRON 

With the help of a "tuning eye" tube such as 
you may have seen in radio sets, you can mea- 
sure the charge-to-mass ratio of the electron 
in a way that is very close to J. J. Thomson's 
original method. 

Complete instructions appear in the PSSC 
Physics Laboratory Guide, Second Edition, 
D. C. Heath Company, Experiment IV-12, 
"The Mass of the Electron," pp. 79-81. 



CATHODE RAYS IN A CROOKES TUBE 

A Crookes tube having a metal barrier inside 
it for demonstrating that cathode rays travel 
in straight hnes may be available in your class- 
room. In use, the tube is excited by a Tesla coil 
or induction coil. 

Use a Crookes tube to demonstrate to the 
class the deflection of cathode rays in mag- 
netic fields. To show how a magnet focuses 
cathode rays, bring one pole of a strong bar 
magnet toward the shadow of the cross-shaped 
obstacle near the end of the tube. Watch what 
happens to the shadow as the magnet gets 
closer and closer to it. What happens when you 



switch the poles of the magnet? What do you 
think would happen if you had a stronger 
magnet? 

Can you demonstrate deflection by an elec- 
tric field? Try using static charges as in Ex- 
periment 34, "Electric Forces I," to create a 
deflecting field. Then if you have an electro- 
static generator, such as a small Van de GraafF 
or a Wimshurst machine, try deflecting the 
rays using parallel plates connected to the 
generator. 



X RAYS FROM A CROOKES TUBE 

To demonstrate that x rays penetrate materials 
that stop visible Ught, place a sheet of 4" x 5" 
3000-ASA-speed Polaroid Land film, still in 
its protective paper jacket, in contact with the 
end of the Crookes' tube. (A film pack cannot 
be used, but any other photographic film in a 
Ught-tight paper envelope could be substi- 
tuted.) Support the film on books or the table so 
that it doesn't move during the exposure. Fig. 
18-13 was a 1-minute exposure using a hand- 
held Tesla coil to excite the Crookes tube. 




18-13 



LIGHTING AN ELECTRIC LAMP 
WITH A MATCH 

Here is a trick with which you can challenge 
your friends. It illustrates one of the many 
amusing and useful apphcations of the photo- 



144 



Activities 



electric effect in real life. You will need the 
phototube from Experiment 42, "The Photo- 
electric Effect," together with the Project 
Physics Amplifier and Power Supply. You will 
also need a 1 2"V dry cell or power supply and 
a 6V light source such as the one used in the 
MilHkan Apparatus. (If you use this light 
source, remove the lens and cardboard tube 
and use only the 6V lamp.) Mount the lamp on 
the Photoelectric Effect apparatus and connect 
it to the 0-5V, 5 amps variable output on the 
power supply. Adjust the output to maximum. 
Set the transistor switch input switch to 
switch. 

Connect the Photoelectric Effect appa- 
ratus to the Amplifier as shown in Fig. 18-14. 
Notice that the polarity of the 1.5V cell is re- 
versed and that the output of the Amphfier 
is connected to the transistor switch input. 

Advance the gain control of the amphfier 
to maximum, then adjust the offset control in 
a positive direction until the filament of the 
6V lamp ceases to glow. Ignite a match near 
the apparatus (the wooden type works the best) 
and bring it quickly to the window of the photo- 
tube while the phosphor of the match is still 
glowing brightly. The phosphor flare of the 
match head will be bright enough to cause suf- 
ficient photocurrent to operate the transistor 
switch which turns the bulb on. Once the bulb 
is lit, it keeps the photocell activated by its 
own hght; you can remove the match and the 
bulb will stay lit. 

When you are demonstrating this effect, 
tell your audience that the bulb is really a 
candle and that it shouldn't surprise them that 
you can light it with a match. And of course 
one way to put out a candle is to moisten your 
fingers and pinch out the wick. When your 
fingers pass between the bulb and the photo- 




! Amp/if I'er 



J 



ft>wev Supply 



inpui 



j O Ch O'S cmp 



f ? rr 



/.5V l_.__ 



^.^ 4V bulb 

If 3^ phoTo-fucK-^ 
Fig. 18-14 



-- J 



cell, the bulb turns off, although the filament 
may glow a httle, just as the wick of a freshly 
snuffed candle does. You can also make a 
"candle-snuffer" from a httle cone of any 
reasonable opaque material and use this in- 
stead of your fingers. Or you can "blow out" 
the bulb: It will go out obediently if you take 
care to remove it from in front of the photocell 
as you blow it out. 



FILM LOOP 



FILM LOOP 47 THOMSON MODEL 
OF THE ATOM 

Before the development of the Bohr theory, 
a popular model for atomic structure was the 
"raisin pudding" model of J. J. Thomson. Ac- 
cording to this model, the atom was supposed 
to be a uniform sphere of positive charge in 
which were embedded small negative "cor- 
puscles" (electrons). Under certain conditions 
the electrons could be detached and observed 
separately, as in Thomson's historic experi- 
ment to measure the charge/mass ratio. 

The Thomson model did not satisfactorily 
explain the stabiUty of the electrons and es- 
pecially their arrangement in "rings," as sug- 
gested by the periodic table of the elements. 
In 1904 Thomson performed experiments 
which to him showed the possibility of a ring 
structure within the broad outline of the raisin- 
pudding model. Thomson also made mathe- 
matical calculations of the various arrange- 
ments of electrons in his model. 

In the Thomson model of the atom, the 
cloud of positive charge created an electric 
field directed along radii, strongest at the sur- 
face of the sphere of charge and decreasing to 
zero at the center. You are famihar with a 
gravitational example of such a field. The 
earth's downward gravitational field is strong- 
est at the surface and it decreases uniformly 
toward the center of the earth. 

For his model-of-a-model Thomson used 
still another type of field — a magnetic field 
caused by a strong electromagnet above a tub 
of water. Along the water surface the field is 
"radial," as shown by the pattern of iron fihngs 
sprinkled on the glass bottom of the tub. Thom- 
son used vertical magnetized steel needles to 
represent the electrons; these were stuck 
through corks and floated on the surface of 
the water. The needles were oriented with Hke 
poles pointing upward; their mutual repulsion 
tended to cause the magnets to spread apart. 
The outward repulsion was counteracted by 
the radial magnetic field directed inward to- 
ward the center. When the floating magnets 
were placed in the tub of water, they came to 



equiUbrium configurations under the combined 
action of all the forces. Thomson saw in this 
experiment a partial verification of his calcula- 
tion of how electrons (raisins) might come to 
equilibrium in a spherical blob of positive 
fluid. 

In the film the floating magnets are 3.8 cm 
long, supported by ping pong balls (Fig. 18-15). 
Equihbrium configurations are shown for var- 
ious numbers of balls, from 1 to 12. Perhaps 
you can interpret the patterns in terms of 
rings, as did Thomson. 




Fig. 18-15 

Thomson was unable to make an exact 
correlation with the facts of chemistry. For 
example, he knew that the eleventh electron 
is easily removed (corresponding to sodium, 
the eleventh atom of the periodic table), yet 
his floating magnet model failed to show this. 
Instead, the patterns for 10, 11 and 12 floating 
magnets are rather similar. 

Thomson's work with this apparatus illus- 
trates how physical theories may be tested 
with the aid of analogies. He was disappointed 
by the failure of the model to account for the 
details of atomic structure. A few years later 
the Rutherford model of a nuclear atom made 
the Thomson model obsolete, but in its day the 
Thomson model received some support from 
experiments such as those shown in the film. 



Chapter 



19 



The Rutherford-Bohr Model of the Atom 



EXPERIMENT 44 SPECTROSCOPY 

In text Chapter 19 you learn of the immense 
importance of spectra to our understanding of 
nature. You are about to observe the spectra 
of a variety of Ught sources to see for yourself 
how spectra differ from each other and to learn 
how to measure the wavelengths of spectrum 
lines. In particular, you will measure the wave- 
lengths of the hydrogen spectrum and relate 
them to the structure of the hydrogen atom. 

Before you begin, review carefully Sec. 
19.1 of text Chapter 19. 



Observing spectra 

You can observe diffraction when you look at 
hght that is reflected from a phonegraph rec- 
ord. Hold the record so that hght from a distant 
source is almost parallel to the record's sur- 
face, as in the sketch below. Like a diffraction 
grating, the grooved surface disperses light 
into a spectrum. 



4 



i' 



Creating spectra 

Materials can be made to give off light (or be 
"excited") in several diff"erent ways: by heat- 
ing in a flame, by an electric spark between 
electrodes made of the material, or by an elec- 
tric current through a gas at low pressure. 

The hght emitted can be dispersed into a 
spectrum by either a prism or a diff"raction 
grating. 

In this experiment, you will use a diffrac- 
tion grating to examine hght from various 
sources. A diff"raction grating consists of many 
very fine parallel grooves on a piece of glass or 
plastic. The grooves can be seen under a 400- 
power microscope. 

In experiment 33 (Young's Experiment) 
you saw how two narrow slits spread hght of 
different wavelengths through diff'erent an- 
gles, and you used the double sht to make 
approximate measurements of the wave- 
lengths of light of diff'erent colors. The dis- 
tance between the two shts was about 0.2 mm. 
The distance between the lines in a diffrac- 
tion grating is about 0.002 mm. And a grating 
may have about 10,000 grooves instead of 
just two. Because there are more hnes and 
they are closer together, a grating diffracts 
more light and separates the different wave- 
lengths more than a double-slit, and can be 
used to make very accurate measurements 
of wavelength. 



Use a real diff"raction grating to see spec- 
tra simply by holding the grating close to your 
eye with the hnes of the grating parallel to a 
distant hght source. Better yet, arrange a sht 
about 25 cm in front of the grating, as shown 
below, or use a pocket spectroscope. 

' ■ • .--Source 










d \'re.zT 



Look through the pocket spectroscope at a 
fluorescent light, at an ordinary (incandescent) 
light bulb, at mercury-vapor and sodium-vapor 
street lamps, at neon signs, at hght from the 
sky (but don't look directly at the sun), and at 
a flame into which various compounds are in- 
troduced (such as salts of sodium, potassium, 
strontium, barium, and calcium). 
Ql Which color does the grating diff'ract into 
the widest angle and which into the narrow- 
est? Are the long wavelengths diffracted at a 



Experiment 44 



147 



wider angle than the short wavelengths, or 
vice-versa? 

Q2 The spectra discussed in the Text are (a) 
either emission or absorption, and (b) either 
hne or continuous. What different kinds of 
spectra have you observed? Make a table show- 
ing the type of spectrums produced by each 
of the hght sources you observed. Do you detect 
any relationship between the nature of the 
source and the kind of spectra it produces? 

Photographing the spectrum 

A photograph of a spectrum has several ad- 
vantages over visual observation. A photo- 
graph reveals a greater range of wavelengths; 
also it allows greater convenience for your 
measurement of wavelengths. 

When you hold the grating up to your eye, 
the lens of your eye focuses the diffracted rays 
to form a series of colored images on the retina. 
If you put the grating in front of the camera 
lens (focused on the source), the lens will 
produce sharp images on the film. 

The spectrum of hydrogen is particularly 
interesting to measure because hydrogen is the 
simplest atom and its spectrum is fairly easily 
related to a model of its structure. In this ex- 
periment, hydrogen gas in a glass tube is 
excited by an electric current. The electric 
discharge separates most of the H2 molecules 
into single hydrogen atoms.) 

Set up a meter stick just behind the tube 
(Fig. 19-1). This is a scale against which to 
observe and measure the position of the spec- 
trum hnes. The tube should be placed at about 
the 70-cm mark since the spectrum viewed 
through the grating will appear nearly 70 cm 
long. 

From the camera position, look through 
the grating at the glowing tube to locate the 
positions of the visible spectral hnes against 
the meter stick. Then, with the grating fas- 
tened over the camera lens, set up the camera 
with its lens in the same position your eye was. 
The lens should be aimed perpendicularly at 
the 50 cm mark, and the grating hnes must be 
parallel to the source. 

Now take a photograph that shows both 
the scale on the meter stick and the spectral 




Fig. 19-1 

hnes. You may be able to take a single exposure 
for both, or you may have to make a double 
exposure— first the spectrum, and then, with 
more hght in the room, the scale. It depends 
on the amount of hght in the room. Consult 
your teacher. 

Analyzing the spectrum 

Count the number of spectral hnes on the 
photograph, using a magnifier to help pick 
out the faint ones. 

Q3 Are there more hnes than you can see 
when you hold the grating up to your eye? If 
you do see additional hnes, are they located 
in the visible part of the spectrum (between 
red and violet) or in the infrared or ultraviolet 
part? 

The angle d through which hght is diffrac- 
ted by a grating depends on the wavelength 
X of the hght and the distance d between hnes 
on the grating. The formula is a simple one: 

X = d sin 6. 

To find 6, you need to find tan 6 = xll as 
shown in Fig. 19-2. Here x is the distance of 
the spectral hne along the meter stick from the 
source, and t is the distance from the source 
to the grating. Use a magnifier to read x from 
your photograph. Calculate tan 9, and then 
look up the corresponding values of 6 and sin 6 
in trigonometric tables. 

To find d, remember that the grating space 
is probably given as hnes per inch. You must 
convert this to the distance between hnes in 
meters. One inch is 2.54 x 10"^ meters, so if 
there are 13,400 hnes per inch, then d is 



148 Experiment 44 




(^ ^Oiyy.^A by 



t 



X -^ 



o^ red (('(^lit Soured 

Fig. 19-2 Different images of the source are formed on 
of diffracted light. The angle of diffraction is equal to the 
ment angle of the source in the photograph so 

(2.54 X 10-2) / (1.34 X 10^) - 1.89 x 10-« meters. 

Calculate the values of A. for the various 
spectral hnes you have measured. 
014 How many of these lines are visible to the 
eye? 

QS What would you say is the shortest wave 
length to which your eye is sensitive? 
QQ What is the shortest wavelength that you 
can measure on the photograph? 

Compare your values for the wavelengths 
with those given in the text, or in a more com- 
plete list (for instance, in the Handbook of 
Chemistry and Physics). The differences be- 
tween your values and the pubUshed ones 
should be less than the experimental uncer- 
tainty of your measurement. Are they? 

This is not all that you can do with the re- 
sults of this experiment. You could, for ex- 
ample, work out a value for the Rydberg 
constant for hydrogen (mentioned in Text 
Sec. 19.2). 

More interesting perhaps is to calculate 
some of the energy levels for the excited hydro- 
gen atom. Using Planck's constant (h = 6.6 x 
10-3"), the speed of hght in vacuum (c = 3.0 
X 10» m/sec), and your measured value of the 
wavelength A of the separate hnes. you can 
calculate the energy of photons' various wave- 
lengths, E = hf=hclK emitted when hydrogen 
atoms change from one state to another. The 
energy of the emitted photon is the difference 
in energy between the initial and final states 



the film by different colors 
apparent angular displace- 



tan d=- 



f. 



n =5 
n -4 

n ^3 



A- 

'ground staiC 'f°'^ _) 



*o ^2 



o-f hydrogen octom 



i. 



nsf 



Fig. 19-3 
of the atom. 

Make the assumption (which is correct) 
that for all hnes of the series you have observed 
the final energy state is the same. The energies 
that you have calculated represent the energy 
of various excited states above this final level. 

Draw an energy-level diagram something 
hke the one shown here (Fig. 19-3.). Show on it 
the energy of the photon emitted in transition 
from each of the excited states to the final 
state. 

Q7 How much energy does an excited hydro- 
gen atom lose when it emits red hght? 



ACTIVITIES 



SCIENTISTS ON STAMPS 

As shown here, scientists are pictured on the 
stamps of many countries, often being honored 
by other than their homeland. You may want 
to visit a stamp shop and assemble a display 
for your classroom. 

See also "Science and the Artist," in the 
Unit 4 Handbook. 




MEASURING IONIZATION, 
A QUANTUM EFFECT 

With an inexpensive thyratron 885 tube, you 
can demonstrate an effect that is closely re- 
lated to the famous Franck-Hertz effect. 

Theory 

According to the Rutherford-Bohr model, an 
atom can absorb and emit energy only in cer- 
tain amounts that correspond to permitted 
"jumps" between states. 

If you keep adding energy in larger and 
larger "packages," you will finally reach an 
amount large enough to separate an electron 
entirely from its atom— that is, to ionize the 
atom. The energy needed to do this is called 
the ionization energy. 

Now imagine a beam of electrons being 
accelerated by an electric field through a re- 
gion of space filled with argon atoms. This is 
the situation in a thyratron 884 tube with its 
grid and anode both connected to a source 
of variable voltage, as shown schematically 
in Fig. 19-4). 

+ X)0 



cathodt-' 




fi'lomtut 



Fig. 19-4 



In the form of its kinetic energy each elec- 
tron in the beam carries energy in a single 
"package." The electrons in the beam colhde 
with argon atoms. As you increase the acceler- 
ating voltage, the electrons eventually become 
energetic enough to excite the atoms, as in the 
Franck-Hertz effect. However, your equipment 
is not sensitive enough to detect the resulting 
small energy absorptions. So nothing seems to 
happen. The electron current from cathode to 
anode appears to increase quite linearly with 
the voltage, as you would expect— until the 



150 



Activities 



electrons get up to the ionization energy of 
argon. This happens at the ionization poten- 
tial V,, which is related to the ionization en- 
ergy E, and to the charge q^ on the electron 
as follows: 

£, = q^V; 

As soon as electrons begin to ionize argon 
atoms, the current increases sharply. The 
argon is now in a different state, called an ion- 
ized state, in which it conducts electric cur- 
rent much more easily than before. Because 
of this sudden decrease in electrical resistance, 
we may use the thyratron tube as an "elec- 
tronic switch" in such devices as stroboscopes. 
(A similar process ionizes the air so that it can 
conduct Ughtning.) As argon ions recapture 
electrons, they emit photons of ultraviolet and 
of visible violet hght. When you see this violet 
glow, the argon gas is being ionized. 

For theoretical purposes, the important 
point is that ionization takes place in any gas 
at a particular energy that is characteristic 
of that gas. This is easily observed evidence of 
one special case of Bohr's postulated discrete 
energy states. 

Equipment 

Thyratron 884 tube 

Octal socket to hold the tube (not essential 
but convenient) 
Voltmeter (0-30 volts dc) 
Ammeter (0-100 milhamperes) 
Potentiometer (10,000 ohm, 2 watts or 
larger) or variable transformer, 0-120 
volts ac 

Power supply, capable of dehvering 50-60 
mA at 200 volts dc 

Connect the apparatus as shown schemat- 
ically in Fig. 19-7. 

Procedure 

With the potentiometer set for the lowest avail- 
able anode voltage, turn on the power and wait 
a few seconds for the filament to heat. Now in- 
crease the voltage by small steps. At each new 
voltage, call out to your partner the voltmeter 
reading. Pause only long enough to permit your 
partner to read the ammeter and to note both 



readings in your data table. Take data as rapid- 
ly as accuracy permits: Your potentiometer 
will heat up quickly, especially at high cur- 
rents. If it gets too hot to touch, turn the power 
off and wait for it to cool before beginning 
again. 

Watch for the onset of the violet glow. 
Note in your data table the voltage at which 
you first observe the glow, and then note what 
happens to the glow at higher voltages. 

Plot current versus voltage, and mark the 
point on your graph where the glow first ap- 
peared. From your graph, determine the first 
ionization potential of argon. Compare your 
experimental value with pubhshed values, 
such as the one in the Handbook of Chemistry 
and Physics. 

What is the energy an electron must have 
in order to ionize an argon atom? 

MODELING ATOMS WITH MAGNETS 

Here is one easy way to demonstrate some of 
the important differences between the Thom- 
son "raisin pudding" atom model and the 
Rutherford nuclear model. 

To show how alpha aprticles would be 
expected to behave in colhsions with a Thom- 
son atom, represent the spread-out "pudding" 
of positive charge by a roughly circular ar- 
rangement of small disc magnets, spaced four 
or five inches apart, under the center of a 
smooth tray, as shown in Fig. 19-5. Use tape 




Fig. 19-5 The arrangement of the mag nets for a Thom- 
son atom". 



or putty to fasten the magnets to the under- 
side of the tray. Put the large magnet (repre- 
senting the alpha particle) down on top of the 
tray in such a way that the large magnet is 
repelled by the small magnets and sprinkle 
onto the tray enough tiny plastic beads to make 
the large magnet shde freely. Now push the 
"alpha particle" from the edge of the tray 
toward the "atom." As long as the "alpha par- 
ticle" has enough momentum to reach the 
other side, its deflection by the small mag- 
nets under the tray will be quite small — never 
more than a few degrees. 

For the Rutherford model, on the other 
hand, gather all the small magnets into a ver- 
tical stack under the center of the tray, as 
shown in Fig. 19-6. Turn the stack so that it 



Activities 
nuclecLS 



151 




Fig. 19-6 The arrangement of the magnets for a "Ruth- 
erford atom." 

repels "alpha particles" as before. This "nu- 
cleus of positive charge" now has a much 
greater effect on the path of the "alpha par- 
ticle." 

Have a partner tape an unknown array of 
magnets to the bottom of the tray — can you 
determine what it is hke just by scattering the 
large magnet? 

With this magnet analogue you can do 
some quantitative work with the scattering 
relationships that Rutherford investigated. 
(See text Sec. 19.3 and Film Loop 48, "Ruther- 
ford Scattering" at the end of this Handbook 
chapter.) Try again with different sizes of 
magnets. Devise a launcher so that you can 
control the velocity of your projectile magnets 
and the distance of closest approach. 



..-J^ 



(XlplT<X 

porticle 




Fig. 19-7 



1) Keep the initial projectile velocity v con- 
stant and vary the distance b (see Fig. 19-7); 
then plot the scattering angle (/> versus b. 

2) Hold b constant and carry the speed of the 
projectile, then plot </> versus v. 

3) Try scattering hard, nonmagnetized discs 
off each other. Plot 4> versus b and (/> versus 
V as before. Contrast the two kinds of scatter- 
ing-angle distributions. 



"BLACK BOX" ATOMS 

Place two or three different objects, such as a 
battery, a small block of wood, a bar magnet, 
or a ball bearing, in a small box. Seal the box, 
and have one of your fellow students try to tell 
you as much about the contents as possible, 
without opening the box. For example, sizes 
might be determined by tilting the box, rela- 
tive masses by balancing the box on a support, 
or whether or not the contents are magnetic 
by checking with a compass. 

The object of all this is to get a feeling for 
what you can or cannot infer about the struc- 
ture of an atom purely on the basis of sec- 
ondary evidence. It may help you to write a re- 
port on your investigation in the form you may 
have used for writing a proof in plane geome- 
try, with the property of the box in one column 
and your reason for asserting that the property 
is present in the other column. The analogy 
can be made even better if you are exception- 
ally brave: Don't let the guesser open the box, 
ever, to find out what is really inside. 



152 



Activities 



ANOTHER SIMULATION 

OF THE RUTHERFORD ATOM 

A hard rubber "potential-energy hill" is avail- 
able from Stark Electronics Instruments, Ltd., 
Box 670, Ajax, Ontario, Canada. When you roll 
steel balls onto this hill, they are deflected in 



somewhat the same way as alpha particles 
are deflected away from a nucleus. The poten- 
tial-energy hill is very good for quantitative 
work such as that suggested for the magnet 
analogue in the activity "Modehng atoms with 
magnets." 



FILM LOOPS 



FILM LOOP 48: RUTHERFORD 
SCATTERING 

This film simulates the scattering of alpha par- 
ticles by a heavy nucleus, such as gold, as in 
Ernest Rutherford's famous experiment. The 
film was made wdth a digital computer. 

The computer program was a sHght modi- 
fication of that used in film loops 13 and 14, 
on program orbits, concerned with planetary 
orbits. The only difference is that the operator 
selected an inverse-square law of repulsion 
instead of a law of attraction such as that of 
gravity. The results of the computer calcula- 
tion were displayed on a cathode-ray tube and 
then photographed. Points are shown at equal 
time intervals. Verify the law of areas for the 
motion of the alpha particles by projecting the 
film for measurements. Why would you expect 
equal areas to be swept out in equal times? 

All the scattering particles shown are near 
a nucleus. If the image from your projector is 
1 foot high, the nearest adjacent nucleus would 
be about 500 feet above the nucleus shown. 
Any alpha particles moving through this large 
area between nuclei would show no appre- 
ciable deflection. 

We use the computer and a mathematical 
model to tell us what the result will be if we 
shoot particles at a nucleus. The computer 
does not "know" about Rutherford scattering. 
What it does is determined by a program placed 
in the computer's memory, written in this 
particular instance in a language called For- 
tran. The programmer has used Newton's laws 
of motion and has assumed an inverse-square 
repulsive force. It would be easy to change 
the program to test another force law, for ex- 




ample F = Klr^. The scattering would be com- 
puted and displayed; the angle of deflection 
for the same distance of closest approach 
would be different than for inverse-square 
force. 

Working backward from the observed 
scattering data, Rutherford deduced that the 
inverse-square Coulomb force law is correct 
for all motions taking place at distances 
greater than about 10~'*m from the scattering 
center, but he found deviations from Cou- 
lomb's law for closer distances. This suggested 
a new type of force, called nuclear force. 
Rutherford's scattering experiment showed 
the size of the nucleus (supposedly the same as 
the range of the nuclear forces) to be about 
10"^^m, which is about 1/10,000 the distance 
between the nuclei in soUd bodies. 



Chapter 



20 



Some Ideas from Modern Physical Theories 



ACTIVITIES 



STANDING WAVES ON A BAND-SAW 
BLADE 

Standing waves on a ring can be shown by 
shaking a band-saw blade with your hand. 
Wrap tape around the blade for about six 
inches to protect your hand. Then gently shake 
the blade up and down until you have a feehng 
for the lowest vibration rate that produces re- 
inforcement of the vibration. Then double the 
rate of shaking, and continue to increase the 
rate of shaking, watching for standing waves. 
You should be able to maintain five or six 
nodes. 

TURNTABLE OSCILLATOR PATTERNS 
RESEMBLING DE BROGLIE WAVES 

If you set up two turntable oscillators and a 
Variac as shown in Fig. 20-1, you can draw 
pictures resembhng de Broglie waves, Hke 
those shown in Chapter 20 of your text. 

Place a paper disc on the turntable. Set 
both turntables at their lowest speeds. Before 
starting to draw, check the back-and-forth 
motion of the second turntable to be sure the 
pen stays on the paper. Turn both turntables 
on and use the Variac as a precise speed con- 
trol on the second turntable. Your goal is to 
get the pen to follow exactly the same path 
each time the paper disc goes around. Try 
higher frequencies of back-and-forth motion 
to get more wavelengths around the circle. 




For each stationary pattern that you get, check 
whether the back-and-forth frequency is an 
integral multiple of the circular frequency. 

STANDING WAVES IN A WIRE RING 

With the apparatus described below, you can 
set up circular waves that somewhat resemble 
the de Broghe wave models of certain electron 
orbits. You will need a strong magnet, a fairly 
stiff wire loop, a low-frequency oscillator, and 
a power supply with a transistor chopping 
switch. 

The output current of the oscillator is 
much too small to interact with the magnetic 
field enough to set up visible standing waves 
in the wire ring. However, the oscillator cur- 
rent can operate the transistor switch to con- 
trol ("chop") a much larger current from the 
power supply (see Fig. 20-2). 



OSc'iHcdjr 




Fig. 20-1 



Fig. 20-2 The signal from the oscillator controls the 
transistor switch, causing it to turn the current from the 
power supply on and off. The "chopped" current in 
the wire ring interacts with the magnetic field to pro- 
duce a pulsating force on the wire. 



The wire ring must be of non-magnetic 
metal. Insulated copper magnet wire works 
well: Twist the ends together and support the 



Activities 



155 



ring at the twisted portion by means of a bind- 
ing post, Fahnestock clip, thumbtack, or ring- 
stand clamp. Remove a httle insulation from 
each end for electrical connections. 

A ring 4 to 6 inches in diameter made of 
22-guage enameled copper wire has its lowest 
rate of vibration at about 20 cycles/sec. Stiffer 
wire or a smaller ring will have higher charac- 
teristic vibrations that are more difficult to see. 

Position the ring as shown, with a section 
of the wire passing between the poles of the 
magnet. When the pulsed current passes 
through the ring, the current interacts with 
the magnetic field, producing alternating 
forces which cause the wire to vibrate. In 
Fig. 20-2, the magnetic field is vertical, and the 
vibrations are in the plane of the ring. You 
can turn the magnet so that the vibrations are 
perpendicular to the ring. 

Because the ring is clamped at one point, 
it can support standing waves that have any 
integral number of half wavelengths. In this 
respect they are different from waves on a free 
wire ring, which are restricted to integral 
numbers of whole wavelengths. Such waves 
are more appropriate for comparison to an 
atom. 

When you are looking for a certain mode of 
vibration, position the magnet between ex- 
pected nodes (at antinodes). The first "charac- 
teristic, or state" "mode of vibration," that the 
ring can support in its plane is the first har- 
monic, having two nodes: the one at the point 



of support and the other opposite it. In the sec- 
ond mode, three nodes are spaced evenly 
around the loop, and the best position for the 
magnet is directly opposite the support, as 
shown in Fig. 20-3. 




Fig. 20-3 

You can demonstrate the various modes 
of vibration to the class by setting up the mag- 
net, ring, and support on the platform of an 
overhead projector. Be careful not to break 
the glass with the magnet, especially if the 
frame of the projector happens to be made of 
a magnetic material. 

The Project Physics Film Loop "Vibrations 
of a Wire," also shows this. 



INDEX 



I 



INDEX/TEXT SECTION 



Actinide series, 24 
Alchemy, 6-7 
Alkaline earth family, 19 
Alpha particle, 66-67, 68 
Anode, 34 
Argon, 85 
Aristotle, 4-5, 7 
Atom, 3, 11-14, 29 

compound, 13 

hydrogen, 72, 74 

levels, 83-85 

mass, 14-15, 17, 28, 33 

mercury, 79 

model, 12, 13, 66, 71, 75, 78, 
107 

number, 24-25, 55 

stationary states of, 72 

structure, 33-35, 54-55, 83 

theory of, 4, 8 
Atomic bomb, 45 
Atomic mass unit, 40 
Atomic number, 24-25 
Atomic physics, 113 
Atomic theory, 86, 88-89 
Atomic-volume, of elements, 21 
Atomism, 3, 5, 16 

Balmer, Johann Jakob, 63, 77, 78, 

83 
Barium platinocyanide, 48 
Battery, 25-26 

Bohr, Niels, 34, 70, 71-75, 76, 106, 
117 

inadequacy of theory, 86, 88-89 

model, 55, 58, 83 

periodic table, 86 

quantization rule, 73 

theory, 75, 77-79, 82 
Born, Max, 104, 106, 113 
Boyle, Robert, 7, 116 
Brownian motion, 45 
Bunsen, Robert W., 61 

California Institute of Technology, 

40,47 
Cambridge Electron Accelerator, 

98 
Cambridge University, 35, 104 
Cathode, 34 

rays, 34, 36-37, 40 
Cavendish, Henry, 7 
Cavendish Laboratory, 35 
Charge, nuclear, 69-71 

total, 28 
Chemical formula, 16 
Chemistry, 7 
Colhsion, elastic, 79 
Columbia University, 40, 47 



Compounds, 8, 29 
Compton, Arthur H., 100 
Conductors, 25 
Coulomb, 28, 35, 58 
Crookes, Sir William, 34 
tube, 34 

Dalton, John, 13 

atomic theory, 8, 11-14, 25 

compounds, 29 

element symbols, 10 

model, 12 

A New System of Chemical Phi- 
losophy, 11 
Davisson, C. J., 102 
Davy, Humphrey, 26 
De Broglie, Louis, 101, 102, 103, 
105 

waves, 101, 102, 103, 109 
Delphi, shrine of, 2 
Democritus, 3, 4, 116 
Deterministic, 114 
Diffraction, 106 

grating, 50 

pattern, 94, 102, 111 

X-ray, 51 
Dirac, P. A. M., 105, 106 
Dobereiner, Johann Wolfgang, 18 
Dublin Institute for Advanced 

Studies, 105 
Dynamite, 80 

Einstein, Albert, 43, 45, 95, 96, 98, 
114 

photoelectric effect, 43-44, 46- 
47 
Electricity 

and matter, 25-26, 28-29 
Electrodes, 26 
Electrolysis, 25, 26, 28 
Electromagnetic theory, of light, 

42 
Electromagnetic wave, 35 
Electron, 37, 100 

charge of, 37-38 

kinetic energy of, 41 

momentum of, 101 

orbits of, 82-86 

shells, 84 

subshells, 85 

velocity, 109 

volts (eV), 79, 82 
Electroscope, 50 
Elements, 4 

atomic mass of, 14-15 

atomic-volume, 21 

combining capacity, 17 

family of, 18-19 



159 



four basic, 5 

known by 1872 (table), 16 

melting and boiling tempera- 
tures of (table), 31 

noble, 24 

order among, 18-19 

properties of, 16-18 

rare earth, 24 

transition, 24 

triads, 18 
Elements of Chemistry (Lavoisier), 

7-8 
Empedocles, 4 
Energy, kinetic, 41, 79, 98 

levels, 85 

potential, 42, 98 
Epicurus, 5 
Escher, M. C, 115 
Esterman, I., 102 

Faraday, Michael, 26, 28, 29 
Fluoresce, 48 
Fluorescent lights, 34 
Formula, chemical, 16 
Franck, James, 79, 82 
Franck-Hertz experiment, 79, 82 
Fraunhofer, Joseph von, 61, 62 
Frequency, 41, 72 
threshold, 41 

Galileo, 116 
Gases, 25, 50 

noble, 19, 24 

spectra of, 59-63 
Gassendi, Pierre, 7 
Geiger, Hans, 66, 67, 68, 69 
Geiger counter, 69 
Geissler, Heinrich, 34 

tubes, 34 
Gell-Mann, Murray, 38 
Generator, high voltage, 52 

Van de Graaf, 52 
Germer, L. H., 102 
Goldstein, Eugene, 34 
Gravitational constant (G), 7 
Greeks 

and order, 2 
Guericke, 34 

Halogens, 19 

Heisenberg, Werner, 105, 106 

Herschel, John, 61 

Hertz, Heinrich, 40 

Hertz, Gustav, 79, 82 

Hittorf, Johann, 34 

Hydrogen 

atom, 72, 83 

spectral series of, 75, 77-79 

spectrum, 63-65 



Ionized gas, 50 

Ions, 26 

Institute of Advanced Studies, 

Princeton, 45 
Integers, 89 

Joule, 78 

K-shell, 83 

Kinetic energy, 41, 79, 98 
King William IV, 13 
Kirchhoff, Gustave R., 61, 62 

Lavoisier, Antoine, 7 

Elements of Chemistry, IS 
Law of conservation 

of definite proportions, 12 

of mass, 12 

of multiple proportions, 13 
Leucippus, 3, 4, 116 
Light wave, scattered, 100 
Lithium atom, 83 
Lord Rayleigh, 24 
L-shell, 83 
Lucretius, 3, 5 

On the Nature of Things, 3 

Magnus, Albert, 17 
Manchester University, 66 
Marsden, 67, 68, 69 
Mass 

atomic, 14-15, 28, 33 

equivalent, 98 

law of conservation of, 12 

relativistic, 96 
Matter, and electricity, 25-26, 28- 
29 

model of, 4 

nature of, 1 

theory of, 5-6 
Maxwell, James C., 106 
McGill University, Montreal, 66 
Melville, Thomas, 59 
Mendeleev, Dmitri, 19, 20, 70, 116 

periodic table, 19-23 
Mercury atom, 79 
Metals, alkali, 18 
Metaphysics (Aristotle), 5 
Meteorology, 12 
Meyer, Lothar, 21 
Microscope 

electron, 109 

field-ion, 109 

light, 109 
Millikan, Robert A., 38, 40, 47 

oil drop experiment, 38, 39 
Model of atom 

Bohr, 55, 58, 71-75 



160 



mathematical, 78, 107 

physical, 107 

Rutherford, 66-69 

Thomson, 55, 56 
Momentum, 99 
Monolith, 1 
M-shell, 84 

Neutron, 50 
Newlands, J.A.R., 18 
A New System of Chemical Phi- 
losophy (Dalton), 11 
Newton, Isaac, 7, 116 
Nobel, Alfred B., 80 
Nobel Prize, 80, 100 

physics in, 40, 43, 49, 81 
Noble elements, 24 

gases, 24 
N-shell, 85 
Nuclear 

atom, 68 

charge, 69-71 

size, 69—71 

Oberlin College, 47 
Orbits, of electrons, 82-86 
Owens College, Manchester, En- 
gland, 35 

Particles, charged, 35 

wave-Uke, 101-103, 106 
Paschen, F., 64 
Periodicity, 33 
Periodic properties, 21 
Periodic table, 19-23, 23-25, 33, 

70, 82-86 
Photoelectric current, 41 

effect, 40, 41, 43-44, 46-47 
Photon, 43, 101, 111 

momentum of, 100 
Planck, Max, 47 

constant, 43, 46, 47, 72 
Pliicker, Julius, 34 
Potential energy, 42, 98 
Probability interpretation, 111-114 
Pro ton -neutron theory, 105 
Pupin, Michael, 48 

q/m value, 35, 37, 38, 54 
Quanta, 41, 46, 47, 55, 111 
Quantum, 43 

light, 99 

mechanics, 95, 106, 107, 113, 
114, 117 

numbers, 89 



physics, 47 

theory, 41, 88, 100, 112 
Quarks, 38 

Rontgen, Wilhelm K., 48, 50, 51 

On a New Kind of Rays, 48 

rays (Xrays), 50 
Radar, 108 
Radiation, duahsm of, 101 

particle-like, 99 
Ramsay, William, 24 
Rare-earth element, 24 
Relativistic mass, 96 
Relativity Theory, 95-99 
Rutherford, Ernest, 35, 66, 67, 117 

Bohr model, 71, 82 
Rydberg, J. R., 64 

constant, 77 

Scattering experiment, 66 
Schrodinger, Erwin, 105, 106, 107, 

111 
Scientific Revolution, 7 
Shells, 84 

Smith, Frederick, 48 
Spectra, 59-63 
Spectroscope, 61 
Spectrum analysis, 61 
Stationary states, 72 
Sub-shells, 85 

Thomson, J. J., 32, 35, 37, 40, 50, 
96, 117 

atom model, 55 

q/m experiment, 36 
Transition elements, 24 
Triads 

of elements, 18 

Ultraviolet light, 51 
Uncertainty principle, 110-111 
University of Chicago, 40 

Van de Graaf generator, 52 
Velocity, 109 

electron, 109 
Volta, Allessandro, 25 
Voltage, stopping, 42 

Wollaston, William, 61 
Wavelengths, 50, 51 

X ray, 48, 50, 51, 53, 54, 99, 100, 
102 
diffraction, 51 



161 



INDEX/HANDBOOK SECTION 



Accelerator, electron. Scientific American 
(January 1959), 131 

Activities : 

activities from Scientific American, 131 
"black box" atoms, 151-152 
cathode rays in a Crooke's tube, 143 
Dalton's Puzzle, 129 
electrolysis of water, 129 
lighting an electric lamp with a match, 144 
measurement of ionization, 149-150 
measuring q/m for the electron, 143 
modeling atoms with magnets, 150-151 
periodic table(s), 129-131 
scientists on stamps, 305 
single-electrode plating, 131 
standing waves on a band-saw blade, 154 
standing waves in a wire ring, 154-155 
Thomson model of the atom, 145 
turntable oscillator patterns resembling 

de Broglie laws, 154 
X-rays from a Crooke's tube, 143 

Alpha particles, scattering of, 153 

Argon, ionization energy of, 149-150 

Atom(s), "black box" (activity), 151-152 
copper, calculating mass and volume of, 128 
modeling with magnets (activity), 150-151 
Rutherford-Bohr model of, 146-148 
Thomson model of (activity), 145 
see also nucleus 

Atomic masses, relative (activity), 129 

Balanced particle, electric force on, 136 
Band-saw blade, standing waves on (activity), 

154 
Beta ray spectrometer, Scientific American 

(September 1958), 131 
"Black box" atoms (activity), 151-152 
de Broglie waves, 154 

Calibration, of coils, 134 

Carbon 14 dating. Scientific American (February 

1957), 131 
Cathode ray(s), and charge-to-mass ratio, 133- 
135 
in a Crooke's tube (activity), 143 
Charge-to-mass ratio, of electron, 143 
equation for, 133 
(experiment), 138-135 
Chemical change, and electric currents, 126—128 
Cloud chamber, diffusion. Scientific American 
(September 1952), 131 
plumber's friend. Scientific American (Decem- 
ber 1956), 131 
Wilson, Scientific American (April 1956), 131 
with magnet. Scientific American (June 1959), 
131 
Copper atom, calculating mass of, 127-128 
Coulomb's force law, 153 



Crooke's tube, cathode rays in (activity), 143 

x-rays from (activity), 143 
Current balance, in calibrating coils, 134 
Cyclotron, Scientific American (September 
1953), 131 

Dalton's Puzzle (activity), 129 
Davy, Humphry, and electrochemical reactions, 
126 
and sodium production by electrolysis, 132 
Diffraction angle, of light, formula for, 147-148 
Diffraction grating, 146-147 

Einstein, Albert 

Albert Einstein: Philosopher-Scientist, 143 

Out of My Later Years, 143 

photoelectric equation of, 141 

The World As I See It, 143 
Electric charge, computation of, 127 

measurement of (experiment), 136-138 
Electric currents, and chemical change, 126-128 
Electric force, on balanced particle, 136 
Electric lamp, lighting with a match (activity), 

144 
Electrolysis, (experiment), 126-128 

sodium production by (film loop), 132 

of water (activity), 129 
Electron, charge of, 141; (experiment) 136-138 

charge-to-mass ratio for (experiment), 
133-135 

measuring q/m for (activity), 143 
Electron micrograph, of latex spheres, 136 
Elementary charge, measurement of (experi- 
ment), 136-138 
Experiments : 

charge-to-mass ratio for an electron, 133-135 

electrolysis, 126-128 

measurements of elementary charge, 136—138 

photoelectric effect, the, 139-142 

spectroscopy, 146-148 

Faraday, and electrochemical reactions, 126 
Film loops: 

Production of sodium by electrolysis, 132 

"Rutherford scattering," 151, 153 
Fortran, 153 
Franck-Hertz effect, 149 

Gas discharge tubes, how to make, Scientific 

American (February 1958), 131 
Geiger counter, how to make. Scientific American 

(May 1969), 131 

Handbook of Chemistry and Physics, 148, 150 
High voltage reversing switch, 137 
Hydrogen, Rydberg constant for, 148 
Hydrogen spectrum, measuring wavelengths of 
(experiment), 146-148 



163 



Ionization, measurement of (activity), 149-150 
Ionization energy, 149 
Ionization potential, 150 

Isotopic experiments, Scientific American (May 
1960), 131 

Latex spheres, electron micrograph of, 136 
Light, calculation of diffraction angle, 147-148 
dispersion into a spectrum, 146-147 
effect on metal surface (experiment), 

139-142 
wave vs. particle models of, 139, 141-142 
Linear time chart of element discovery dates, 
129, 131 

Magnetic resonance spectrometer. Scientific 

American (April 1959), 131 
Magnets, modeling atoms with (activity), 

150-151 
"Mass of the Electron, The," Physics Laboratory 

Guide, 143 
Measurement of elementary charge (experiment), 

136-138 
Mercury spectrum, frequencies of, 140 
Milliken, oil drop experiment, 136 
Modeling atoms with magnets (activity), 

150-151 

Newton, laws of motion, 153 
Nuclear force, 153 
Nucleus, size of, 153 
see also Atom 

Out of My Later Years (Albert Einstein), 143 

Particle model, of hght, 139, 141-142 

Periodic Table(s), exhibit of (activity), 129-131 

Photoelectric effect, 144 

(experiment), 139-142 
Photoelectric equation, Einstein's, 141 
Physics Laboratory Guide, "The Mass of the 

Electron," 143 
Planck's constant, 142, 148 
Potential-energy hill, 152 
Pythagoras' theorem, 135 

"Raisin pudding" model of atom, 145, 150 
Rutherford nuclear atom model, 150-151 
Rutherford-Bohr model of atom, 146-148, 149 



Rutherford scattering (film loop), 151, 
Rydberg constant, for hydrogen, 148 



153 



Scientific American, activities from, 131 

Scintillation counter. Scientific American (March 
1953), 131 

Single-electrode plating (activity), 131 

Sodium, production by electrolysis (film loop), 
132 

Spectra, creation of, 146 
observation of, 146-147 

Spectrograph, astronomical. Scientific American 
(September 1956), 131 

Spectrograph, Bunsen's Scientific American (June 
1955), 131 

Spectroheliograph, how to make, Scientific Amer- 
ican (April 1958), 131 

Spectroscopy (experiment), 146—148 

Spectrum, analysis of, 147-148 
photographing of, 147 

Spectrum lines, measuring wavelengths of (ex- 
periment), 146-148 

Spinthariscope, Scientific American (March 
1953), 131 

Stamps, scientists depicted on (activity), 147 

Standing waves, on a band saw (activity), 154 
in a wire ring (activity), 154—155 

Subatomic particle scattering, simulating. Scien- 
tific American (August 1955), 131 

Thomson, J. J., and cathode rays, 133 

"raisin pudding" model of atom, 145, 150 
Thratron 884 tube, in ionization 
measurement activity, 149 
Threshold frequency, 142 
Turntable oscillator patterns (activity), 154 

"Ups and Downs of the Periodic Table," 129 

Vibration, modes of, 155 

Volta, and electrochemical reactions, 126 

Wave(s), de Broglie, 154 

model, of light, 139, 141-142 

standing, 154—155 
Water, electrolysis of (activity), 129 
World As I See It, The (Albert Einstein), 143 

X-rays from a Crooke's tube (activity), 143 



164 



Answers to End-of-Section Questions 



Chapter 17 

Q1 The atoms of any one element are identical and 

unchanging. 

Q2 Conservation of matter; the constant ratio of 

combining weights of elements. These successes lend 

strength to the atomic theory of matter and to the 

hypothesis that chemical elements differ from one 

another because they are composed of different 

kinds of atoms. 

Q3 No. 

Q4 It was the lightest known element — and others 

were rough multiples. 

Q5 Relative mass; and combining number, or 

"valence." 

Q6 2,4,5,1,2. 

Q7 Density, melting point, chemical activity, 

"valence." 

Q8 Because when the elements are arranged as they 

were in his table, there is a periodic recurrence of 

elements with similar properties; that is, elements 

with similar properties tend to fall in the same column 

of the table. 

Q9 increasing atomic mass. 

Q10 When he found that the chemical properties of the 

next heaviest element clearly indicated that it did not 

belong in the next column but in one further to the right. 

Q11 He was able to predict in considerable detail the 

properties of missing elements, and these predictions 

proved to be extremely accurate, once the missing 

elements were discovered and studied. 

Q12 Its position in the periodic table, determined by 

many properties but usually increasing regularly with 

atomic mass. Some examples are: hydrogen, 1; oxygen, 

8; uranium, 92. 

Q13 Water, which had always been considered a basic 

element, and had resisted all efforts at decomposition, 

was easily decomposed. 

Q14 New metals were separated from substances 

which had never been decomposed before. 

Q15 The amount of charge transferred by the current, 

the valence of the elements, and the atomic mass of 

the element. 

Q16 First, when two elements combine, the ratio of 

their combining masses is equal to the ratio of their 

values for A/v. Secondly, A/v is a measure of the amount 

of the material which will be deposited in electrolysis. 

Chapter 18 

Q1 They could be deflected by magnetic and electric 

fields. 

Q2 The mass of an electron is about 1800 times smaller 

than the mass of a hydrogen ion. 

Q3 (1) identical electrons were emitted by a variety 

of materials; and (2) the mass of an electron was much 

smaller than that of an atom. 

Q4 All other values of charge he found were multiples 

of that lowest value. 

Q5 Fewer electrons are emitted, but with the same 

average energy as before. 



Q6 The average kinetic energy of the emitted electrons 

decreases until, below some frequency value, none 

are emitted at all. • ■ i . 

Qj ^ Light source 



Evacuated tube 




Q8 The energy of the quantum is proportional to the 

frequency of the wave, E — hf. 

Q9 The electron loses some kinetic energy in escaping 

from the surface. 

QIC The maximum kinetic energy of emitted electrons 

is 2.0 eV. 

Q11 When x rays passed through material, say air, 

they caused electrons to be ejected from molecules, 

and so produced + ions. 

Q12 (1) Not deflected by magnetic field; (2) show 

diffraction patterns when passing through crystals; 

(3) produced a pronounced photoelectric effect. 

Q13 (1) Diffraction pattern formed by "slits" with 

atomic spacing (that is, crystals); (2) energy of quantum 

in photoelectric effect; (3) their great penetrating power. 

Q14 For atoms to be electrically neutral, they must 

contain enough positive charge to balance the negative 

charge of the electrons they contain; but electrons are 

thousands of times lighter than atoms. 

Q15 There are at least two reasons: First, the facts 

never are all in, so models cannot wait that long. 

Secondly, it is one of the main functions of a model to 

suggest what some of the facts (as yet undiscovered) 

might be. 

Chapter 19 

Q1 The source emits light of only certain frequencies, 

and is therefore probably an excited gas. 

Q2 The source is probably made up of two parts: an 

inside part that produces a continuous spectrum; and 

an outer layer that absorbs only certain frequencies. 

Q3 Light from very distant stars produces spectra 

which are identical with those produced by elements 

and compounds here on earth. 

Q4 None (he predicted that they would exist because 

the mathematics was so neat). 

Q5 Careful measurement and tabulation of data on 

spectral lines, together with a liking for mathematical 

games. 



165 



Q6 At this point In the development of the book, one 
cannot say what specifically accounts for the correct- 
ness of Balmer's formula (the explanation requires 
atomic theory which is yet to come). But the success of 
the formula does indicate that there must be something 
about the structure of the atom which makes it emit 
only discrete frequencies of light. 
Q7 They have a positive electric charge and are 
repelled by the positive electric charge in atoms. The 
angle of scattering is usually small because the nuclei 
are so tiny that the alpha particle rarely gets near 
enough to be deflected much. However, once in a while 
there is a close approach, and then the forces of 
repulsion are great enough to deflect the alpha particle 
through a large angle. 

Q8 Rutherford's model located the positively charged 
bulk of the atom in a tiny nucleus — in Thomson's model 
the positive bulk filled the entire atom. 
Q9 It is the number, Z, of positive units of charge found 
in the nucleus, or the number of electrons around the 
nucleus. 

Q10 3 positive units of charge (when ail 3 electrons 
were removed). 

Q11 Atoms of a gas emit light of only certain fre- 
quencies, which implies that each atom's energy can 
change only by certain amounts. 
Q12 None. (He assumed that electron orbits could 
have only certain values of angular momentum, which 
Implied only certain energy states.) 
Q13 All hydrogen atoms have the same size because 
in all unexcited atoms the electron is in the innermost 
allowable orbit. 

Q14 The quantization of the orbits prevents them 
from having other arbitrary sizes. 
Q15 Bohr derived his prediction from a physical model, 
from which other predictions could be made. Balmer 
only followed out a mathematical analogy. 
Q16 According to Bohr's model, an absorption line 
would result from a transition within the atom from a 
lower to a higher energy state (the energy being ab- 
sorbed from the radiation passing through the material). 
Q17 (a) 4.0 eV (b) 0.1 eV (c) 2.1 eV. 
Q18 The electron arrangements in noble gases are 
very stable. When an additional nuclear charge and an 
additional electron are added, the added electron Is 
bound very weakly to the atom. 

Q19 Period I contains the elements with electrons in 
the K shell only. Since only two electrons can exist in the 



K shell. Period I will contain only the two elements with 
one electron and two electrons respectively. Period II 
elements have electrons in the K (full) and L shells. The L 
shell can accommodate 8 electrons, so those elements 
with only one through eight electrons in the L shell 
will be in Period II. And so forth. 
Q20 It predicted some results that disagreed with 
experiment; and it predicted others which could not be 
tested in any known way. It did, however, give a satis- 
factory explanation of the observed frequency of the 
hydrogen spectral lines, and it provided a first physical 
picture of the quantum states of atoms. 



Chapter 20 

Q1 It increases, without limit. 

Q2 It increases, approaching ever nearer to a limiting 

value, the speed of light. 

Q3 Photon momentum is directly proportional to the 

frequency of the associated wave. 

Q4 The Compton effect is the scattering of light (or 

x-ray) photons from electrons in such a way that the 

photons transfer a part of their energy and momentum 

to the electrons, and thus emerge as lower frequency 

radiation. It demonstrated that photons resemble 

material particles in possessing momentum as well as 

energy; both energy and momentum are conserved in 

collisions involving photons and electrons. 

Q5 By analogy with the same relation for photons. 

Q6 The regular spacing of atoms in crystals is about 

the same as the wavelength of low-energy electrons. 

Q7 Bohr invented his postulate just for the purpose. 

Schrodinger's equation was derived from the wave 

nature of electrons and explained many phenomena 

other than hydrogen spectra. 

Q8 It is almost entirely mathematical — no physical 

picture or models can be made of it. 

Q9 It can. But less energetic photons have longer 

associated wavelengths, so that the location of the 

particle becomes less precise. 

Q10 It can. But the more energetic photons will 

disturb the particle more and make measurement of 

velocity less precise. 

Q11 They are regions where there is a high probability 

of quanta arriving. 

Q12 As with all probability laws, the average behavior 

of a large collection of particles can be predicted 

with great precision. 



166 



staff and Consultants (continued) 



Sidney Rosen, University of Illinois, Urbana 
John J. Rosenbaum, Livermore High School, 

Calif. 
William Rosenfeld, Smith College, Northampton, 

Mass. 
Arthur Rothman, State University of New York, 

Buffalo 
Daniel Rufolo, Clairemont High School, San 

Diego, Calif. 
Bernhard A. Sachs. Brooklyn Technical High 

School, N.Y. 
Morton L. Schagrin, Denison University, Granville, 

Ohio 
Rudolph Schiller, Valley High School, Las Vegas, 

Nev. 
Myron O. Schneiderwent, Interlochen Arts 

Academy, Mich. 
Guenter Schwarz, Florida State University, 

Tallahassee 
Sherman D. Sheppard, Oak Ridge High School, 

Tenn. 
William E. Shortall, Lansdowne High School, 

Baltimore, Md. 
Devon Showley, Cypress Junior College, Calif. 
William Shurcliff. Cambridge Electron 

Accelerator, Mass. 
Katherine J. Sopka, Harvard University 
George I. Squibb, Harvard University 
Sister M. Suzanne Kelley, O.S.B., Monte Casino 

High School, Tulsa, Okla. 
Sister Mary Christine Martens, Convent of the 

Visitation, St. Paul, Minn. 



Sister M. Helen St. Paul, O.S.F., The Catholic 

High School of Baltimore, Md. 
M. Daniel Smith, Earlham College, Richmond, 

Ind. 
Sam Standring, Santa Fe High School, Santa Fe 

Springs, Calif. 
Albert B. Stewart, Antioch College, Yellow 

Springs, Ohio 
Robert T. Sullivan, Burnt Hills-Ballston Lake 

Central School, N.Y. 
Loyd S. Swenson, University of Houston, Texas 
Thomas E. Thorpe, West High School, Phoenix, 

Ariz. 
June Goodfield Toulmin, Nuffield Foundation, 

London, England 
Stephen E. Toulmin, Nuffield Foundation, London, 

England 
Emily H. Van Zee, Harvard University 
Ann Venable, Arthur D. Little, Inc., Cambridge, 

Mass. 
W. O. Viens, Nova High School, Fort Lauderdale, 

Fla. 
Herbert J. Walberg, Harvard University 
Eleanor Webster, Wellesley College, Mass. 
Wayne W. Welch, University of Wisconsin, 

Madison 
Richard Weller, Harvard University 
Arthur Western, Melbourne High School, Fla. 
Haven Whiteside, University of Maryland, College 

Park 
R. Brady Williamson, Massachusetts Institute of 

Technology, Cambridge 
Stephen S. Winter, State University of New York, 

Buffalo 



167 



Brief Answers to Study Guide Questions 



Chapter 17 

17.1 Information 

17.2 80.3% zinc; 19.7% oxygen 

17.3 47.9% zinc 

17.4 13.9 times mass of H atom; same 

17.5 986 grams nitrogen; 214 grams hydrogen 

17.6 9.23 times mass of H atom 

17.7 (a) 14.1 

(b) 28.2 

(c) 7.0 

17.8 Derivation 

17.9 Na;1 Al;3 P;5 Ca; 2 Sn;4 

17.10 (a) Ar— K; Co— Ni; Te— I; Th— Pa; U— Np; 

Es — Fm; IVId — No 
(b) Discussion 

17.11 Graph 

17.12 Graph; discussion 

17.13 8.0 grams; 0.895 gram 

17.14 (a) 0.05 gram Zn 

(b) 0.30 gram Zn 

(c) 1.2 gram Zn 

17.15 (a) 0.88 gram CI 

(b) 3.14 grams I 

(c) Discussion 

(d) Discussion 

17.16 Discussion 

17.17 Discussion 

17.18 Discussion 

17.19 35.45 grams 

17.20 Discussion 

17.21 Discussion 

17.22 1,3,5 
2,4 



Chapter 18 

18.1 Information 

18.2 (a) 2.0 X 10" m/sec 
(b) 1.8 X lOiicoul/kg 

18.3 Proof 

18.4 Discussion 

18.5 Discussion 

18.6 2000 A; ultraviolet 

18.7 4 X 10-19 joule; 4 X 10-18 joule 

18.8 2.6 X 10-19; 1.6 eV 

18.9 4.9 X lOiVsec 

18.10 (a) 6 X lOiVsec 

(b) 4 X 10-19 joule 

(c) 2.5 X 10-0 photons 

(d) 2.5 photons/sec 

(e) 0.4 sec 

(f) 2.5 X 10-10 photon 

(g) 6.25 X 1017 electrons/sec; 0.1 amp 

18.11 1.3 X 101' photons 

18.12 (a) 6.0 X 1023 electrons 

(b) 84 X 10-' copper atoms/cm-^ 

(c) 1.2 X lO-"cm» 

(d) 2.3 X 10-'' cm 

18.13 (a) 2x = n\ 

(b) 2x = any odd number of half wavelengths 

(c) cos e - 2d/\ for first order 

18.14 1.2xi0i9/sec 

18.15 Discussion 

18.16 1.2 X 105 volts; 1.9 X 10-" joule; 1.2 X 10^ eV 

18.17 Glossary 

18.18 Discussion 



Chapter 19 

19.1 Information 

19.2 Discussion 

19.3 Five listed in Text, but theoretically an Infinite 
number. 

Four lines in visible region. 

19.4 /7 = 8; \ = 3880 A 
n = 10;\ = 3790A 
n = 12; \ = 3740 A 

19.5 (a) Yes 

(b) n, = oo 

(c) Lyman series 910 A; Balmer series 3650 A; 
Paschen series 8200 A 

(d) 21.8 X 10-19 joule, 13.6 eV 

19.6 Discussion 

19.7 Discussion 

19.8 2.6 X 10-14 m 

19.9 (a) Discussion 
(b) 10-V1 

19.10 3.5 m 

19.11 Derivation 

19.12 Discussion 

19.13 List 

19.14 Diagram 

19.15 Discussion 

19.16 Discussion 

19.17 Discussion 

19.18 Discussion 

19.19 Discussion 

19.20 Discussion 

19.21 Discussion 

19.22 Essay 

19.23 Discussion 



Chapter 20 

20.1 Information 

20.2 0.14cor4.2 X 10' m/sec 

20.3 3.7 X 10-14 newtons 

20.4 p = m.,v and KE = m„vV2 

20.5 (a) Changes are too small 
(b) 1.1 X 10-12 kg 

20.6 (a) 2.7 X 10^3 joules 

(b) 3.0 X 101G kg 

(c) 5 X 10-"% 

(d) Rest mass 

20.7 (a) 1.2 X 10-22 kg m/sec 

(b) 1.1 X 10-22 kgm/sec 

(c) 2.4 X 10-22 kg m/sec 

(d) 1.1 X 10-22 kgm/sec 

20.8 p = 1.7 X 10-27 kg m/sec; i/ = 1.9 x 10^ m/sec 

20.9 Discussion 

20.10 Diagram 

20.11 6.6 X 10-5 m/sec 

20.12 3.3 X 10-33 m 

20.13 \ becomes larger 

20.14 Discussion 

20.15 3 X 10-31 m 

20.16 Discussion 

20.17 (a) 3.3 X 10-25 m/sec 

(b) 5.0 X 10-8 m/sec 

(c) 3.3 X 10-G m/sec 

(d) 3.3 X 10G m/sec 

20.18 Discussion 

20.19 Discussion 

20.20 Discussion 

20.21 Discussion 

20.22 Discussion 

20.23 Discussion 

20.24 Discussion 



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