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The Project Physics Course Text and Handbook

Models of the Atom

/•. ••

The Project Physics Course

Text and Handbook

UNIT

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.

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

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.]

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.

SG 17.1

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

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

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.

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

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

1740

1760

1780

1800

1820

1840

1860

1880

1900

Some of the current representations
of a water molecule.

The Chemical Basis of the Atomic Theory

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

Elements known by 1872

Atomic

Name
hydrogen

Symbol
H

Mass*
1.0

Name

Symbol

Mass*

cadmium

112.4

D lithium

6.9

indium

114.8(113)

beryllium

9.0

tin

118.7

boron

10.8

antimony

121.7

carbon

12.0

tellurium

127.6(125)

nitrogen

14.0

O iodine

126.9

oxygen

16.0

D cesium

132.9

O fluorine

19.0

barium

137.3

D sodium

23.0

didymium(**)

(138)

magnesium

24.3

cerium

140.1

aluminum

27.0

erbium

167.3(178)

silicon

28.1

lanthanum

138.9(180)

phosphorus

31.0

tantalum

180.9(182)

sulfur

32.1

tungsten

183.9

O chlorine

35.5

osmium

190.2(195)

D potassium

39.1

iridium

192.2(197)

calcium

40.1

platinum

195.1(198)

titanium

47.9

gold

197.0(199)

vanadium

50.9

mercury

200.6

chromium

52.0

thallium

204.4

manganese

54.9

lead

207.2

iron

55.8

bismuth

209.0

cobalt

58.9

thorium

232.0

nickel

58.7

uranium

238.0(240)

copper

63.5

zinc

65.4

arsenic
selenium

74.9

79 0

D alkaline metals

O bromine
n rubidium

Br
Rb

79.9
85.5

O halogens

strontium

87.6

•Atomic masses g

ven are modern values. Where 1

yttrium

88.9

these differ greatly from those

accepted In

zirconium

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

106.4

silver

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

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.

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

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.

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—*

Ill

V i VI

VII VIII

Higher oxides
and hydrides

R2O

RjOa

RO2
H4R

R205
H3R

RO3
H2R

R207

RO,

H(l)

Li(7)

Be(9.4)

B(ll)

C(12)

N(14)

0(16)

F(19)

Na(23)

Mg(24)

Al(27.3)

Si(28)

P(3I)

S(32)

Cl(35.5)

K(39)

Ca(40)

-(44)

Ti(48)

V(SI)

Cr(52)

Mn(55)

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

iCu(63)l

Zn(6S)

-(68)

-(72)

A«(75)

Se(78)

Br{80)

Rb(85)

Sr(87)

?Yt(88)

Zr(90)

Nb(94)

Mo(96)

-(100)

Ru(104),Rh(104),
Pd(106)..\«(108)

lAg(108)!

Cd(112)

ln(ll3)

Sn(118)

Sb(122)

Te(l25)

1(127)

C8(133)

Ba(I37)

?Di(138)

?Ce(140)

?Er(I78)

?U(I80)

Ta(l82)

W(184)

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

|Au(199)l

Hg(200)

Tl(204)

Pb(207)

Bi(208)

Th(231)

U(240)

Section 17.5

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.

I 50

30!

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.

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

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

III

VII

1.0080

4.0026

6.939

9.012

10.811

12.011

14.007

15.999

18.998

20.183

U
3

B
5

0
6

Ne
10

22.990

24.31

26.98

28.09

30.97

32.06

35.45

39.95

Al
13

Si
14

P
15

S
16

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

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

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

•

0»

57-71

(223)

226.05

Fr
87

+
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

metals

227

232.04

231

238.03

(237)

(242)

(243)

(245)

(249)

(253)

(255)

(256)

(253)

(257)

\ctmide

metals

100

101

102

103

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

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.

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.

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

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

Chlorine

35.45

Oxygen

16.00

8.00

Copper

63.54

31.77

Zinc

65.37

32.69

Aluminum

26.98

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;

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?

(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?

(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

hydrogen

lithium

beryllium

boron

carbon

nitrogen

oxygen

fluorine

sodium

MELTING

BOILING

POINT

-259°C

-253°C

186

1340

1280

2970

2300

2550

>3350

4200

-210

-196

-218

-183

-223

-188

880

ATOMIC

MELTING

BOILING

NUMBER

NAME

POINT

magnesium

651

1107

aluminum

660

2057

silicon

1420

2355

phosphorus

280

sulfur

113

445

chlorine

-103

-35

potassium

760

calcium

842

1240

titanium

1800

>3000

vanadium

1710

3000

chromium

1890

2480

manganese

1260

1900

iron

1535

3000

cobalt

1495

2900

nickel

1455

2900

copper

1083

2336

zinc

419

907

arsenic

814

615

selenium

217

688

bromine

-7

rubidium

700

strontium

774

1150

yttrium

1490

2500

zirconium

1857

>2900

niobium

2500

3700

molybdenum

2620

4800

ruthenium

2450

2700

rhodium

1966

2500

palladium

1549

2200

silver

961

1950

cadmium

321

767

indium

156

2000

tin

232

2270

antimony

631

1380

tellurium

452

1390

iodine

114

184

cesium

670

barium

725

1140

lanthanum

826

cerium

804

1400

erbium

tantalum

3000

4100

tungsten

3370

5900

osmium

2700

>5300

iridium

2454

>4800

platinum

1774

4300

gold

1063

2600

mercury

-39

357

thallium

302

1460

lead

327

1620

bismuth

271

1560

thorium

1845

4500

uranium

1133

ignites

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.

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

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.

(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

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

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).

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

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

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.

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

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.

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.

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

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

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.

£»/ 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?

(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.)

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

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?

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

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.

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

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

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

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^-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„

6562.08

6562.10

+0.02

4860.8

4860.74

-0.06

4340

4340.1

+ 0.1

H«

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?

"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?

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

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

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.)

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

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.

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

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;

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 = — ^

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

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

mi/r = — -
2v

Inmv

and

,,_ n'h^

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

mv _ 1^ q'e

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

n'h'

47^/77-1

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

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

Paschen

series

Brackett
series

'ii

Pfund
series

... X -

iiit i

0.0

-0.87 X 10-

-1.36

-2.42

-5.43

n=i JjiiH

■21.76

Section 19.9

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.

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.

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

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)

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

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.

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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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

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?

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?

(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.

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

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

(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);

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?

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.

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

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

Some Ideas From Modern Physical Theories

SPtBD Sfi/A/?ei>

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 =

Thus the total mass tti of a body is its rest mass mo plus KEIc-:

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^

If we use the symbol E for the total energy of a body, E = Eo + KE,
we could then write

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

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^ •

"' /

/.•

(b) \v

^ /1^

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?

x = A

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

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.

■■\-.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

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

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.

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®

©®©®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 more general 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' t;" v"

= 1 + 1/2 ^ -f 3/8 -^ + 5/16 ^ +
c^ c* c®

35/128-^

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?

(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/^ still 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?

(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?

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

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).

(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

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)

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

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

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

Bq,v,

or, rearranging to get v by itself,

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

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.

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. = 0 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?

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

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

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.

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

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=-

n =5
n -4

n ^3

A-

'ground staiC 'f°'^ _)

*o ^2

o-f hydrogen octom

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

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

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

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

17.15 (a) 0.88 gram CI

(b) 3.14 grams I

(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

(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-^

(d) 2.3 X 10-'' cm

18.13 (a) 2x = n\

(b) 2x = any odd number of half wavelengths

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

(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

(d) Rest mass

20.7 (a) 1.2 X 10-22 kg m/sec

(b) 1.1 X 10-22 kgm/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

(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

HOLT, RINEHART AND WINSTON, INC.

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