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Full text of "The Nucleus, Project Physics Text and Handbook Volume 6"

The Project Physics Course 



Text and Handbook 



6 



The Nucleus 



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The Project Physics Course 



Text and Handbook 

1M 






UNIT 





The Nucleus/^ 









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, California, 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, publishers, agents, and individ- 
uals for use of their copyrighted material. 



Special Consultant to Project Physics 

Andrew Ahlgren, Harvard(3raduate School of 
Education 

A partial list of staff and^onsultants to Harvard 
Project Physics appears/and page iv. 

This Text-Handbook, Unit 6, is one of the many 
instructional 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. 



P. 6 Becquerel, Henri, in Magie, William Francis, 
A Source Book in Physics, copyright® 1964 by 
Harvard University Press, pp. 610-611. 

P. 9 Curie, Pierre and Marie, "Sur une substance 
nouvelle radio-active, contenue dans la pechblende," 
Comptes Rendus Des Seances De L'Academie Des 
Sciences, Vol. 127, pp. 175 and 1215. 

P. 12 Curie, Marie, in Madame Curie, A Biography 
by Eve Curie, translated by Vincent Sheean, 
copyright 1938 by Doubleday & Co., Inc., p. 170. 

P. 53 Rutherford, Ernest, "Collision of Alpha 
Particles with Light Atoms. IV. An Anomalous Effect 
in Nitrogen," Philosophical Magazine, Series VI, 
Vol. 37, Apr. 1919, p. 587. 

P. 55 Chadwick, James, "The Existence of a 
Neutron," Proceedings of the Royal Society of 
London, Vol. CXXXVI, May 1932, p. 697. 

P. 56 Chadwick, James, in "Letters to the Editor," 
Nature, Vol. 129, No. 3552, Feb. 27, 1932, p. 312. 
Reprinted by permission. 

P. 83 Hahn, Otto and Strassman, F., "On the 
Determination and Behavior of the Alkaline Earth 
Metals Resulting from Uranium Irradiated with 
Neutrons," Die N aturwissenschaften. Vol. 27, 
Jan. 1939, p. 15. 

P. 114 From V. Weisskopf, "Why Basic Science?" 
in the Bulletin of the American Academy of Arts and 
Sciences, Vol. XXIV, number 1, October 1970, p. 8. 



Copyright © 1970, Project Physics 

All Rights Reserved 

SBN 03-084502-5 

1234 039 98765432 

Project Physics is a registered trademark 



Picture Credits, Text Section 

Cover photo : High Energy Physics Group, 
University of Maryland. 

P. viii Questar photo taken by a Project Physics 
student. 

P. 2 and 3 Yankee Atomic Electric, Rowe, 
Massachusetts. 

P. 6 Bumdy Library, Norwalk, Conn. 

P. 10 (top left) The Smithsonian Institution; 
(top right) Institut de Physique Nucleaire, Paris; 
(center) courtesy of Mrs. Eve Curie Labouisse. 
Photo from Labor atoire Curie, Institut de 
Physique Nucleaire; (bottom) Culver Pictures, 
Inc., N.Y.C. 

P. 11 Brown Brothers. 

P. 13 (left) Tracerlab, Waltham, Mass. 

P. 14 Cambridge Electron Accelerator photo 
by Hick Levy. 

P. 18 Atomic Energy Commission, Savannah 
River Plant. 

P. 30 Professor K. T. Bainbridge, Physics Dept., 
Harvard University. 

P. 33 Brown Brothers. 

P. 36 (top) Cavendish Laboratory, Cambridge 
University, Cambridge, England; (bottom) Pro- 
fessor Alfred O. C. Nier, University of Minnesota. 

P. 38 (top left) Bumdy Library, Norwalk, Conn, 
(bottom) British Crown Copyright. Science 
Museum, London. 

P. 40 U.S. Atomic Energy Commission, Oak 
Ridge. 

P. 44 News Office, Columbia University. 

P. 45 Dr. Parker E. Moreland, Jr., Chemistry 
Div., Argonne National Laboratory. 

P. 47 T. R. Hayes, Southern Methodist 
University. 

P. 48 Professor M. S. Livingston, Dept. of 
Physics, Massachusetts Institute of Technology, 
and Director, Cambridge Electron Accelerator, 
Harvard University. 

P. 52 (bottom) Sir P. M. S. Blackett, London. 

P. 54 Nobel Foundation, Stockholm. 

P. 60 Courtesy of the Los Alamos Scientific 
Laboratory. 

P. 61 Brookhaven National Laboratory. 

P. 62, 63 (a) (b) Stanford University; (c) (d) 
Public Information Office, CERN, Geneva, Switz- 
erland; (e) Brookhaven National Laboratory. 

P. 65 (top) Cavendish Laboratory, University 
of Cambridge; (middle) Professor W. E. Hazen, 
University of Michigan; (bottom) Professor W. B. 
Fretter, Berkeley. 



P. 66 (top left and bottom) Brookhaven National 
Laboratory; (top right) High Energy Physics 
Group, University of Maryland. 

P. 67 (aU except diagram top right). Introduc- 
tion to the detection of nuclear particles in a bubble 
chamber. The Ealing Press, Cambridge, Mass. 

P. 69 Introduction to the detection of nuclear 
particles in a bubble chamber. The Ealing Press, 
Cambridge, Mass. 

P. 70 Professor Carl Anderson, Cahfornia 
Institute of Technology. 

P. 71 French Embassy Press and Information 
Division, N.Y.C. 

P. 74 Westinghouse Electric Corp. 

P. 82 AEC, Savannah River Plant. 

P. 83 American Institute of Physics. 

P. 87 (top) Argonne National Laboratory; 
(center and bottom) Office of Public Relations, 
The University of Chicago. 

P. 89 Air Force Cambridge Research Laboratories. 

P. 90 (top) Niagara Mohawk Power Corporation, 
Syracuse, N.Y.; (bottom) Commonwealth Edison 
Company. 

P. 91 (top) Massachusetts Institute of Tech- 
nology; (bottom, right) Oak Ridge National 
Laboratory. 

P. 92 Bechtel Corporation, San Francisco. 

P. 93 (top and middle) joint AEC-NASA photo; 
(bottom) Lawrence Radiation Laboratory, 
Livermore. 

P. 96 Princeton University. 

P. 97 (drawing, "Les Saintes-Maries") Oskar 
Reinhart Collection, Winterthur. 

P. 103 (top) Brookhaven National Laboratory. 

P. 104 Brookhaven National Laboratory. 

Picture Credits, Handbook Section 

Cover: (cartoon) Andrew Ahlgren; (alpha 
particle tracks in cloud chamber) Professor J. K. 
B0ggild, Niels Bohr Institute, Copenhagen; 
(autoradiograph of leaves) from Photographs of 
Physical Phenomena, Kodanska, Tokyo, 1968. 

P. 143 Atomic Energy Commission photograph. 

P. 147 Alan Dunn, © 1965 The New Yorker 
Magazine, Inc. 

P. 176 Courtesy of Doctor S. J. Adelstein, 
Peter Bent Brigham Hospital, Boston, Mass. 

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 following pages) have each contributed in some way to the develop- 
ment 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 Erode, 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. Calif. 
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 
Kenneth Ford. University of California, Irvine 
(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 



Prologue 1 

Chapter 21 Radioactivity 

Becquerel's discovery 5 

Other radioactive elements are discovered 8 

The penetrating power of the radiation : a, ji and 7 rays 12 

The charge and mass of a, y3 and 7 rays 15 

The identity of a rays : Rutherford's "mousetrap" 16 

Radioactive transformations 17 

Radioactive decay series 19 

Decay rate and half -life 21 

Chapter 22 Isotopes 

The concept of isotopes 31 

Transformation rules 32 

Direct evidence for isotope of lead 34 

Positive rays 35 

Separating isotope 36 

Summary of a useful notation for nuclides; nuclear reactions 39 

The stable isotopes of the elements and their relative abundances 41 

Atomic masses 45 

Chapter 23 Probing the Nucleus 

The problem of the structure of the atomic nucleus 49 

The proton-electron hypothesis of nuclear structure 49 

The discovery of artificial transmutation 51 

The discovery of the neutron 53 

The proton-neutron theory of the composition of atomic nuclei 58 

The neutrino 59 

The need for particle accelerators 60 

Nuclear reactions 68 

Artificially induced radioactivity 70 

Chapter 24 Nuclear Energy; Nuclear Forces 

Conservation of energy in nuclear reactions 75 

The energy of nuclear binding 76 

Nuclear binding energy and stabiUty 77 

The mass-energy balance in nuclear reactions 79 

Nuclear fission: discovery 81 

Nuclear fission: controlling chain reactions 84 

Nuclear fission : large-scale energy release and some of its consequences 88 

Nuclear fusion 95 

Fusion reactions in stars 97 

The strength of nuclear forces 98 

The liquid-drop nuclear model 99 

The shell model 101 

Biological and medical applications of nuclear physics 102 

Epilogue 106 

A Perspective on the Project Physics Course m 

Contents — Handbook Section i25 

Index/Text Section 177 

Index/Handbook Section 18O 

Answers to End-of-Section Questions 183 

Brief Answers to Study Guide Questions Inside back cover 



i^.-f 



n<- 




•■i'v 




The energy released by nuclear reactions within stars makes them visible to us over 
vast distances. The sun, a typical star, converts the mass of over 4 billion kg of hydro- 
gen into an equivalent amount of radiant energy each second. 



UNIT 



6 



The Nucleus 



CHAPTERS 
21 
22 
23 
24 



Radioactivity 

Isotopes 

Probing the Nucleus 

Nuclear Energy; Nuclear Forces 



PROLOGUE In Unit 5 we learned that the atom consists of a very 
small, positively charged nucleus surrounded by electrons. Experiments 
on the scattering of a particles showed that the nucleus has dimensions 
of the order of 10"" m. Since the diameter of an atom is of the order 
of 10"^" m, the nucleus takes up only a minute fraction of the volume 
of an atom. The nucleus, however, contains nearly all of the mass of 
the atom, as is also shown by the scattering experiments. The existence 
of the atomic nucleus and its properties raised new questions. Is the 
nucleus itself made up of still smaller units? If so, what are these units 
and how are they arranged in the nucleus? What methods can be used 
to get answers to these questions? What experimental evidence do we 
have to guide us? 

We saw in Unit 5 that the study of the properties and structure of 
atoms needed new physical methods. The methods that could be used 
to study the properties of bodies of ordinary size, that is, with dimen- 
sions of the order of centimeters or meters, could not yield information 
about the structure of atoms, ^t is reasonable to expect that it is still 
more difficult to get information telling us what goes on inside the 
nucleus, which is such a small part of the atom. New kinds of experi- 
mental data must be obtained. New theories must be devised to help 
us correlate and understand the data. In these respects the study of 
the nucleus is still another step on the long road from the very large 
to the very small along which we have traveled in this course. In Unit 6 
we shall dig deeper into the problem of the constitution of matter by 
studying the atomic nucleus. 

One of the first and most important steps to an understanding of 
the atomic nucleus was the discovery of radioactivity in 1896. Our 
discussion of nuclear physics will, therefore, start with radioactivity. 
We shall see how the study of radioactivity led to additional discoveries, 



The Nucleus 



The Yankee Atomic Electric nuclear 
power station in Rowe, Massachusetts. 



to the developnnent of nnethods for getting at the nucleus, and to ideas 
about the constitution of the nucleus. In fact, the discovery that the 
atom has a nucleus was a consequence of the study of radioactivity. 
We shall exannine the interaction between experiment and theory, and 
the step-by-step development of ideas about the nucleus. We shall try 
to see how particular experimental results led to new ideas, and how 
the latter, in turn, led to new experiments. This historical study is 
especially useful and interesting because nuclear physics is a new 
branch of physics, which has developed over a relatively short period 
of time. The reports and papers through which discoveries have been 
made known are readily available. The research is still going on, and at 
an ever-increasing rate. Progress in nuclear physics Is closely related 
to modern technology, which both supplies tools for further research 
and applies some of the research in practical ways. Some of these 
practical applications have serious economic and political con- 
sequences. Newspapers report about them almost daily, and it is the 
citizen's duty to inform himself as well as he can about them in order 
to participate effectively in the decisions that affect his life. 

Now that the use and control of nuclear technology is often 
front-page news, it may be hard to realize that the study of the atomic 
nucleus is connected with a chance discovery made in 1896. But it was 
that discovery which touched off the whole enterprise that we call 
nuclear physics, and It is there that we shall start. 





Installation of the reac- 
tor vessel head at the 
Yankee Atomic Electric 
station. 



21.1 Becquerel's discovery 5 

21.2 Other radioactive elements are discovered 8 

21.3 The penetrating power of the radiation: a, ft and y rays 12 

21.4 The charge and mass of a, f3 and y rays I5 

21.5 The identity of a rays: Rutherford's "mousetrap" fg 

21.6 Radioactive transformations 17 

21.7 Radioactive decay series 19 

21.8 Decay rate and half-life 21 



Above is a photograph of the polished 
surface of a uranium-bearing rock, 
photographed in reflected light. Below 
is an autoradiograph of the same sur- 
face made by placing the rock directly 
on a piece of film, packaging both in a 
light-tight container, and allowing the 
film to be exposed for about fifty 
hours. The whitish areas on that print 
correspond to radioactive areas on 
the rock. 




CHAPTER TWENTY-ONE 



Radioactivity 



21.1 Becquerel's discovery 



A legendary chapter in physics began with the discovery of the 
phenomenon known as "radioactivity" early in 1896 by the French 
physicist Henri Becquerel. It was another of those "accidents" that 
illustrate how the trained and prepared mind is able to respond to 
an unexpected observation. 

Only two months before, in November 1895, Rontgen had 
discovered x rays. In doing so, he had unwittingly set the stage for 
the discovery of radioactivity. Rontgen had pointed out that x rays 
came from the glowing spot on a glass tube where a beam of 
cathode rays (high-speed electrons) was hitting. (See Sees. 18.2 
and 18.6.) When the cathode-ray beam was turned off, the spot of 
light on the face of the glass tube disappeared, and also 
the X rays coming from that spot stopped. 

The emission of light by the glass tube when it is excited by 
the cathode ray beam is an example of the phenomenon called 
fluorescence, and was well known before Rontgen's work. A 
considerable amount of research had been done on fluorescence 
during the latter part of the nineteenth century. A substance is 
said to be fluorescent if it immediately emits visible light when 
struck by visible light of shorter wavelength, or by invisible 
radiations such as ultraviolet light, or by the beam of electrons 
that make up cathode rays. Fluorescence stops when the exciting 
light is turned off. (The term phosphorescence is generally applied 
to a related phenomenon, the emission of visible light which 
continues after the exciting light is turned off.) 

Rontgen's observation that the x rays also came from the spot 
which showed fluorescence raised the suspicion that there was a 
close connection between x rays and fluorescence or phosphores- 
cence. Becquerel was fortunate in having the necessary materials 
and training to study this problem. In addition, he was the son 
and grandson of physicists who had made important contributions 
in the field of fluorescence and phosphorescence. In his Paris 
laboratory he had devised an instrument for examining materials 



SG 21.1 




^lASS 



X-ray production by bombardment 
of electrons (cathode rays) on glass. 



Rontgen also showed that one 
method of detecting the presence 
of X rays was to let them expose a 
well-wrapped photographic plate. 
(See Sec. 18.6) 



6 



Radioactivity 




Henri Becquerel (1852-1908) received 
the 1903 Nobel Prize in physics (for 
the discovery of natural radioactivity) 
along with Pierre and Marie Curie (for 
the discovery of the radioactive ele- 
ments radium and polonium). 



As it turned out, and will be shown 
in Sec. 21.3, the Becquerel rays 
are not x rays. 



in complete darkness a small fraction of a second after they had 
been exposed to a brilliant light. The question occurred to Becquerel: 
When bodies are made to fluoresce (or phosphoresce) in the visible 
region with sufficient intensity, do they also emit x rays in addition 
to the light-rays? He tested a number of substances by exposing 
them to sunlight; his method of checking whether they also emitted 
invisible x rays followed Rontgen's idea: to see if a well- wrapped 
photographic plate was exposed by such invisible rays. One of the 
samples Becquerel used happened to be a salt of the metal 
uranium, a sample of potassium-uranyl sulfate. In his words: 

I wrapped a . . . photographic plate . . . with two 
sheets of thick black paper, so thick that the plate did not 
become clouded by exposure to the sun for a whole day. 
I placed on the paper a crust of the phosphorescent 
substance, and exposed the whole thing to the sun for 
several hours. When I developed the photographic plate 
I saw the silhouette of the phosphorescent substance in 
black on the negative. If I placed between the phosphores- 
cent substance and the paper a coin or a metallic screen 
pierced with an open-work design, the image of these 
objects appeared on the negative. The same experiment 
can be tried with a thin sheet of glass placed between the 
phosphorescent substance and the paper, which excludes 
the possibility of a chemical action resulting from vapors 
which might emanate from the substance when heated 
by the sun's rays. 

We may therefore conclude from these experiments 
that the phosphorescent substance in question emits 
radiations which penetrate paper that is opaque to 
light 

In his published paper, Becquerel was careful to conclude from 
his experiment only that "penetrating radiations" were emitted 
from the phosphorescent substance. He did not write that the 
substance emitted x rays while it phosphoresced, because he had 
not fully verified that the radiations were x rays (though the 
radiations were transmitted through the black paper, just as 
X rays are), or that they were actually related to the phosphorescence 
(though he strongly suspected that they were). Before he could 
investigate these possibilities, he made this discovery: 

. . . among the preceding experiments some had been 
made ready on Wednesday the 26th and Thursday the 
27th of February [1896]; and as on those days the sun only 
showed itself intermittently, I kept my arrangements all 
prepared and put back the holders in the dark in the 
drawer of the case, and left in place the crusts or uranium 
salt. Since the sun did not show itself again for several 
days, I developed the photographic plates on the 1st of 
March, expecting to find the images very feeble. On the 
contrary, the silhouettes appeared with great intensity. I 
at once thought that the action might be able to go on in 
the dark. . . . 

Further experiments verified this surprising thought: even 



Section 21.1 



when the uranium compound was not being excited by sunUght to 
phosphoresce, it continually emitted something that could penetrate 
black paper and other substances opaque to light, such as thin 
plates of aluminum or copper. Becquerel found that all the 
compounds of uranium — many of which were not phosphorescent 
at all — and metallic uranium itself had the same property. The 
amount of action on the photographic plate did not depend on what 
the particular compound of uranium was, but only on the amount 
of uranium present in it! 

Becquerel also found that the persistent radiation from a 
sample of uranium did not appear to change, either in intensity or 
character, with the passing of time. Nor was a change in the 
activity observed when the sample of uranium or of one of its 
compounds was exposed to ultraviolet light, infrared light, or x rays. 
Moreover, the intensity of the uranium radiation (or "Becquerel 
rays," as they came to be known), was the same at room tem- 
perature (20 °C), at 200°C and at the temperature at which oxygen 
and nitrogen (air) liquefy, about -190°C. Thus, these rays seemed 
to be unaffected by ordinary physical (and chemical) changes. 

Becquerel also showed that the radiations from uranium 
produced ionization in the surrounding air. They could discharge 
a positively or negatively charged body such as an electroscope. 
So the uranium rays resemble x rays in two important respects: 
their penetrating power and their ionization power. Both kinds of 
rays were invisible to the unaided eye. but both affected photo- 
graphic plates. Still, x rays and Becquerel rays differed in at least 
two important ways: compared to x rays, these newly discovered 
rays from uranium needed no cathode ray tube or even light to 
start them, and they could not be turned off. Becquerel showed 
that even after a period of three years a given piece of uranium 
and its compounds continued to emit radiations spontaneously. 

The years 1896 and 1897 were years of high excitement in 
physics, to a large extent because of the great interest in the 
recently discovered x rays and in cathode rays. It quickly 
became evident that x rays could be used in medicine and they were 
the subject of much research. In comparison the properties of the 
Becquerel rays were less spectacular, and little work was done on 
them in the period from the end of May 1896 until the end of 1897. 
In any case, it seemed that somehow they are special cases of x-ray 
emission. Even Becquerel himself turned his attention to other 
work. But attention began to be attracted by the fact that the 
invisible rays from the uranium and its compounds appeared 
spontaneously without special preparation or electric devices. 

Two questions were asked: first, what was the source of the 
energy creating the uranium rays and making it possible for them 
to penetrate opaque substances? And second, did any other of the 
seventy or more elements known then have properties similar to 
those of uranium? The first question was not answered for some 
time, although it was considered seriously. The second question 
was answered early in 1898 by the Curies, who by doing so, opened 
a whole new field of research in physical science. 




1 


' |! 


i ! 




// \\ 


I 


i 


^ \ 


^1 

i 

—A 
v 




The ionizing effect of the Becquerel 
rays could be demonstrated with a 
charged electroscope (upper sketch). 
When a sample of uranium is held 
near the electroscope leaves (lower 
sketch), the rays cause gas molecules 
in the air to ionize— that is, to become 
electrically charged. Ions, with a 
charge opposite to that on the leaves 
drift to the leaves and neutralize 
their charge. The time taken for the 
leaves to fall is a measure of the rate 
of ionization of the gas, and hence of 
the activity of the uranium source. 



Radioactivity 



Q1 Why was Becquerel experimenting with a uranium com- 
pound? Describe his experiment. 

Q2 How did uranium compounds have to be treated in order 
to emit the "Becquerel rays"? 

Q3 What were the puzzling properties of the "Becquerel 
rays"? In what ways were they similar to x rays? 



21.2 Other radioactive elements are discovered 

One of Becquerel's colleagues in Paris was the physicist Pierre 
Curie, who had recently married a Polish-bom physicist, Marie 
Sklodowska. Marie Curie undertook a systematic study of the 
Becquerel rays and looked for other elements and minerals that 
might emit them. Using a sensitive electrometer which her 
husband had recently invented, she measured the small electric 
current produced when the rays ionized the air. This current was 
assumed to be (and actually is) proportional to the intensity of the 
rays. With this new technique, she could give a numerical value to 
the ionizing effect produced by the rays, and these values were 
reproducible within a few percent from one experiment to the 
next with the same sample. 

One of her first results was the discovery that the element 
thorium (Th) and its compounds emitted radiations with properties 
similar to those of the uranium rays. (The same finding was made 
independently in Germany by Gerhardt C. Schmidt, at about the 
same time.) The fact that thorium emits rays like those of uranium 
was of great importance; it showed that the mysterious rays were 
not a property peculiar just to one element. The discovery spurred 
the search for still other elements that might emit similar rays. 
The fact that uranium and thorium were the elements with the 
greatest known atomic masses indicated that the very heavy 
elements might have special properties different from those of the 
lighter elements. 

The evident importance of the problems raised by the discovery 
of the uranium and thorium rays, led Pierre Curie to lay aside his 
researches in other fields of physics and work with his wife on 
these new problems. They began on a herculean task. First they 
found that the intensity of the emission from any thorium 
compound was directly proportional to the fraction by weight of the 
metallic element thorium present. (Recall that Becquerel had found 
a similar result for uranium compounds.) Moreover, the amount of 
radiation was independent of the physical conditions or the 
chemical combination of the active elements. These results led the 
Curies to the conclusion that the emission of the rays depended 
only on the presence of atoms of either of the two elements 
uranium or thorium. Atoms of other elements that were present 
were simply inactive, or absorbed some of the radiation. 

These ideas were especially important because they helped 
the Curies interpret their later experiments. For example, in their 
studies of the radioactivity of minerals they examined pitchblende. 



Section 21.2 



9 



an ore containing about 80 percent uranium oxide (UgOg). They 
found that the emission from pitchblende, as measured by its 
effect in ionizing air, was about four or five times as great as that 
to be expected from the amount of uranium in the ore. The other 
elements known at the time to be associated with uranium in 
pitchblende, such as bismuth and barium, had been shown to be not 
radioactive. If emission of rays is an atomic phenomenon, the 
unexpected activity of pitchblende could be explained only by the 
presence of another element in pitchblende, an element more 
active than uranium itself. 

To explore this hypothesis, the Curies applied chemical 
separation processes to a large sample of pitchblende to try to 
isolate this hypothetical active substance. After each separation 
process, the products were tested, the inactive part discarded, and 
the active part analyzed further. Finally, the Curies obtained a 
highly active product which presumably consisted mainly of the 
unknown element. In a note titled "On a New Radioactive Substance 
Contained in Pitchblende," which they submitted to the French 
Academy of Sciences in July of 1898, they reported: 

By carrying on these different operations . . . finally 
we obtained a substance whose activity is about 400 
times greater than that of uranium. . . . 

We believe, therefore, that the substance which we 
removed from pitchblende contains a metal which has 
not yet been known, similar to bismuth in its chemical 
properties. If the existence of this new metal is confirmed, 
we propose to call it polonium, after the name of the 
native country of one of us. 

Six months after the discovery of polonium, the Curies 
chemically separated another substance from pitchblende and 
found the emission from it so intense as to indicate the presence 
of still another new element even more radioactive than polonium! 
This substance had an activity per unit mass 900 times that of 
uranium, and was chemically entirely different from uranium, 
thorium or polonium. Spectroscopic analysis of this substance 
revealed spectral lines characteristic of the inactive element 
barium, but also a line in the ultraviolet region that did not seem 
to belong to any known element. The Curies reported their belief 
that the substance, "although for the most part consisting of 
barium, contains in addition a new element which produced radio- 
activity and, furthermore, is very near barium in its chemical 
properties." For this new element, so extraordinarily radioactive, 
they proposed the name radium. 

A next step in making the evidence for the newly discovered 
elements more convincing was to determine their properties, 
especially their atomic masses. The Curies had made it clear that 
they had not yet been able to isolate either polonium or radium in 
pure metallic form, or even to obtain a pure sample of a compound 
of either element. From the substance containing the strongly 
radioactive substance that they called radium, they had separated 
a part consisting of barium chloride mixed with a presumably very 



In this note the term "radioactivity" 
was used for the first time. 



Compare the positions of polonium 
(Po) and bismuth (Bi) in the 
Periodic Table on p. 27. 



Compare the positions of barium (Ba) 
and radium (Ra) in the 
Periodic Table. 




a. Marie Curie 

b. c. Marie and Pierre 
d. Marie, Irene and Pierre 

all three won Nobel prizes 



Pierre Curie (1859-1906) studied at the Sorbonne in 
Paris. In 1878 he became an assistant teacher in 
the physical laboratory there, and some years later, 
professor of physics. He was well known for his 
research on crystals and magnetism. He married 
Marie Sklodowska in 1895 (she was 28 years old). 
After their marriage, Marie undertook her doctoral 
research on radioactivity. In 1898 Pierre joined his 
wife in this work. Their collaboration was so 
successful that in 1903 they were awarded the Nobel 
Prize in physics, which they shared with Becquerel. 
Pierre Curie was run over and killed by a horse-drawn 
vehicle in 1906. Marie Curie was appointed to his 
professorship at the Sorbonne. the first woman to 
have this post. 

In 1911 she was awarded the Nobel Prize in 
chemistry for the discovery of the two new elements, 
radium and polonium. She is the only person who 
has won two Nobel prizes in science. (Linus Pauling 
also won two Nobel prizes- one for chemistry and 
one for peace). The rest of her career was spent in 
the supervision of the Paris Institute of Radium, a 
center for research on radioactivity and the use of 
radium in the treatment of cancer. 

Marie Curie died in 1934 of leukemia, a form 
of cancer of the leukocyte-forming cells of the body, 
probably caused by over-exposure to the radiations 
from radioactive substances. 




5 



K 



(\ 



m 



12 



Radioactivity 



The present yield of radium from 
one ton of high-grade uranium ore 
is about 0.2 g. 



SG 21.2 



small quantity of radium chloride. Additional separations gave an 
increasing proportion of radium chloride. The difficulty of this task 
is indicated by the Curies' remark that radium "is very near 
barium in its chemical properties," for it is very difficult to separate 
elements whose chemical properties are similar. Moreover, to obtain 
their highly radioactive substances in usable amounts, they had to 
start with a very large amount of pitchblende. 

With an initial 100-kg shipment of pitchblende (from which the 
uranium salt had been removed to be used in the manufacture of 
glass) the Curies went to work in an abandoned woodshed at the 
School of Physics where Pierre Curie taught. Having failed to 
obtain financial support, the Curies made their preparations 
without technical help in this "laboratory." Marie Curie wrote later: 

I came to treat as many as twenty kilograms of matter 
at a time, which had the effect of filling the shed with 
great jars full of precipitates and liquids. It was killing 
work to carry the receivers, to pour off the liquids and to 
stir, for hours at a stretch, the boiling material in a smelt- 
ing basin. 

From the mixture of radium chloride and barium chloride they 
produced, only the average atomic mass of the barium and radium 
could be computed. At first an average value of 146 was obtained, 
as compared with 137 for the atomic mass of barium. After many 
additional purifications which increased the proportion of radium 
chloride, the average value for atomic mass rose to 174. Continuing 
the tedious purification process for four years, during which she 
treated several tons of pitchblende residue, Marie Curie was able 
to report in July 1902 that she had isolated 0.1 gram of radium 
chloride, so pure that spectroscopic examination showed no evidence 
of any remaining barium. She calculated the atomic mass of 
radium to be 225 (the present-day value is 226.03). The activity 
of radium is more than a million times that of the same mass 
of uranium. 

Q4 How is the radioactive emission of an element affected by 
being combined into different chemical compounds? 

Q5 Why did the Curies suspect the existence of another 
radioactive material in uranium ore, in addition to uranium itself? 

Q6 What was the main difficulty in producing a pure sample 
of the element radium? 



21.3 The penetrating power of the radiation: a, 13 and y rays 



Once the extraordinary properties of radium became known, 
they excited interest both inside and outside the scientific world, 
and the number of people studying radioactivity increased rapidly. 
The main question that attracted attention was: what are the 
mysterious radiations emitted by radioactive bodies? 



Section 21.3 



13 



In 1899, Ernest Rutherford, whose theory of the nuclear atom 
has been discussed in Chapter 19, started to seek answers to 
this question. Rutherford found that a sample of uranium emits at 
least two distinct kinds of rays — one that is very readily absorbed, 
which he called for convenience a rays (alpha rays), and the other 
more penetrating, which he called /3 rays (beta rays). In 1900 the 
French physicist P. Villard observed that the emission from radium 
contained rays much more penetrating than even the /3 rays; this 
type of emission was given the name y (gamma) rays. The 
penetrating power of the three types of rays, as known at the time, 
is compared in the table below, first published by Rutherford 
in 1903: 



See the article "Rutherford" 
Reader 6. 



Appropriate thickness of aluminum required to reduce 
the radiation intensity to one-half its initial value 



RADIATION TYPE 

a 

a 

y 



THICKNESS OF ALUMINUM 
0.0005 cm 
0.05 
8 



So it turned out that the Becquerel rays were more complex 
than had been thought even before the nature of a, (3 and y rays 
were ascertained. Of the three kinds of rays, the a rays are the 
most strongly ionizing and the y rays the least. The power of 
penetration is inversely proportional to the power of ionization. 
This is to be expected: the penetrating power of the a rays from 
uranium is low because they expend their energy very rapidly in 
causing intense ionization. Alpha rays can be stopped — that is, 
completely absorbed — by about 0.006 cm of aluminum, by a sheet 
of ordinary writing paper, or by a few centimeters of air. Beta rays 
are completely stopped only after traveling many meters in air, or 
a centimeter in aluminum. Gamma rays can pass through many 
centimeters of lead, or through several feet of concrete, before 
being almost completely absorbed. One consequence of these 
properties of the rays is that heavy and expensive shielding is 
sometimes needed in the study or use of radiations, especially y 



SG 21.2 

The absorption of ^ rays gives rise to 
many modern practical applications 
of radioactivity. One example is the 
thickness gauge illustrated in the 
photograph and draw/ing below. 
Sheet metal or plastic is reduced in 
thickness by rolling. The thickness 
is measured continuously and 
accurately by determining the 
intensity of the /3 rays that pass 
through the sheet. The rollers are 
adjusted so that the desired sheet 
thickness is obtained. 





14 



Radioactivity 



The rays ionize and, consequently, 
break down molecules in living cells. 



rays, to protect people from harmful effects of the rays. In some 
cases these "radiation shields" are as much as 10 feet thick. 
Shown below is one example of shielding around a target at the 
output of an electron accelerator (where y rays are created by 
a method different from radioactivity, as you shall see later in 
this unit). 

Q7 List a, /3 and y rays in order of the penetrating ability. Why 
is penetrating power inversely related to ionizing power? 



Shielding around an experimental 
area through which passes a beam 
from a high-energy particle ac- 
celerator (The Cambridge Electron 
Accelerator). 




Section 21.4 



15 



21.4 The charge and mass of a, /3 and y rays 

Another method used to study the rays was to direct them 
through a magnetic field to see if they were deflected or deviated 
from their initial directions by the action of the field. This method, 
which came to provide one of the most widely used tools for the 
study of atomic and nuclear events, is based on the now familiar 
fact that a force acts on a charged particle when it moves across 
a magnetic field. As was discussed in Sec. 14.13, this force acts 
always at right angles to the direction of motion of the charged 
particle. The particle experiences a continual deflection and, if sent 
into a uniform field at right angles, moves along the arc of a circle. 
(It might be wise to review that section now.) 

This property had been used in the 1890's by J. J. Thomson in 
his studies of cathode rays. He showed that these rays consist of 
very small negatively charged particles, or electrons (Chapter 18). 
Becquerel, the Curies and others found that the a, jS and y rays 
behaved differently from one another in a magnetic field. The 
behavior of the rays is illustrated in the diagram in the margin. 

Suppose that some radioactive material, such as a sample of 
uranium, is placed at the end of a narrow hole in a lead block; 
a narrow beam consisting of a, /3 and y rays escapes from the 
opening. If the beam enters a strong, uniform magnetic field (as 
in the last 2 drawings in the margin), the three types of rays 
will go along paths separated from one another. The y rays 
continue in a straight line without any deviation. The fi rays will 
be deflected to one side, moving in circular arcs of differing radii. 
The a rays will be deflected slightly to the other side, moving in a 
circular arc of large radius, but are rapidly absorbed in the air. 

The direction of the deflection of the /3 rays in such a magnetic 
field is the same as that observed earlier in Thomson's studies of 
the properties of cathode rays. It was concluded, therefore, that the 
P rays, like cathode rays, consist of negatively charged particles. 
(The negative charge on the P particles was confirmed by the 
Curies in 1900; they caused the beam of the particles to enter an 
electroscope, which became negatively charged.) Since the direction 
of the deflection of the a rays was opposite to that of the /3 rays, it 
was concluded that the a rays consist of positively charged 
particles. Since the y rays were not deflected, it was concluded 
that they were neutral, that is, had no electric charge; no conclusion 
could be drawn from this type of experiment as to whether the 
y rays are, or are not, particles. 

The deflection of a charged particle in electric and magnetic 
fields depends on both its charge and mass. Therefore, the ratio 
of charge to mass for /3 particles can be calculated from measured 
deflections in fields of known intensity. 

Becquerel, investigating /3 particles in 1900, used a procedure 
which was essentially the same as that used by J. J. Thomson in 
1897 to obtain a reliable value for the ratio of charge q^ to mass 
me for the particles in cathode rays. (The fact that there was a 



a, 13 and y rays are separated from a 
sample of radioactive material by their 
passage through a magnetic field. 




No magnetic field. 



t(J, 



Ar 



Weak magnetic field. 




Stronger magnetic field. 




Very strong magnetic field. 



y: 




16 



Radioactivity 



consistent single value establishing quantitatively the existence 
of the electron; (see Sec. 18.2.) By sending /3 rays through electric 
and magnetic fields, Becquerel was able to calculate the speed of 
the ^3 particles. He obtained a value of qlm for /3 particles which 
was in close enough agreement with that found by Thomson for 
the electron to permit the deduction that the /3 particles 
are electrons. 





(a) Electric field only 

Electric and magnetic fields can be 
set up perpendicularly so that the 
deflections they cause in a beam 
of charged particles will be in op- 
posite directions. Particles moving 
at one certain speed will not be 
deflected, because the electric and 
magnetic forces on it balance. 

SG 21.4-21.6 



See Rutherford's essay The Nature 
of the Alpha Particle" in Reader 6. 




(b) Magnetic field only 



(c) Both electric and magnetic field 



The nature of the a radiation was more difficult to establish. 
It was necessary to use a very strong magnetic field to produce 
measurable deflections of a rays. The value of qlm found for a 
particles (4.8 x 10' coul/kg) was about 4000 times smaller than 
qlm for /3 particles. The reason for the small qlm value could be a 
small value of q or a large value of m. Other evidence available 
at the time indicated that q for an a particle was not likely to be 
smaller than for a /3 particle. It was therefore concluded that m. 
would have to be much larger for the a particle than for the 
/3 particle. 

The value of qlm. given above for oc particles is just one half 
that of qlm found earlier for a hydrogen ion (see Table 17.4). The 
value would be explained in a reasonable way if the a particle were 
like a hydrogen molecule minus one electron (H.,+). or else if it were 
a helium atom (whose mass was known to be about four times that 
of a hydrogen atom) without its two electrons (He^^). Other 
possibilities might have been entertained — for example, bare 
nuclei of carbon, nitrogen or oxygen would have about the same 
q/m ratio. In fact, however, the right identification turned out 
to be that of a particles with He^^, and we turn now to the clever 
experiment that provided the final proof. 

Q8 What was the evidence that /3 particles are electrons? 
Q9 What observation led to the suggestion that a particles are 
much more massive than ^8 particles? 

21.5 The identity of a rays: Rutherford's "mousetrap" 

It was known that the gas helium was always found imprisoned 
in radioactive minerals. In addition. Sir William Ramsey and 
Frederick Soddy had discovered, in 1903, that helium was given 
off from a radioactive compound, radium bromide. This led 
Rutherford to advance the hypothesis that the a particle is a doubly- 
ionized heliuin atom — a He atom minus its two electrons — or, as we 
would now say, the nucleus of a helium atom. In a series of 
experiments from 1906 to 1909 he succeeded in proving the 
correctness of his hypothesis in several different ways. The last 



Section 21.6 



17 



and most convincing of these experiments was made in 1909, with 
T. D. Royds, by constructing what Sir James Jeans later called 
"a sort of mousetrap for a particles." 

The experiment used the radioactive element radon (Rn). Radon 
had been discovered by Pierre Curie and Andre Debierne in 1901; 
they had found that a gas was given off from radium. A small 
amount of the gas collected in this way was found to be a strong or 
emitter. The gas was shown to be a new element and was called 
"radium emanation" and later "radon." Ramsey and Soddy then 
found that when radon is stored in a closed vessel, helium always 
appears in the vessel also. Thus helium is given off not only by 
radium but also by radon. 

Now Rutherford and Royds put a small amount of radon in a 
fine glass tube with a wall only one-hundredth of a millimeter 
thick. This wall was thin enough so that a particles could pass 
through it, but radon itself could not. The tube was sealed into a 
thick-walled, outer glass tube which had an electric discharge 
section at the top. (See sketch A in the margin.) The air was 
pumped out of the outer tube and the apparatus was allowed to 
stand for about a week. During this time, while a particles from 
the radon passed through the thin walls of the inner tube, a gas 
was found gradually to collect in the previously evacuated space 
(sketch B). Mercury was then pumped in at the bottom to compress 
the gas and confine it in the discharge tube (sketch C). When a 
potential difference was applied to the electrodes of the discharge 
tube, an electric discharge was produced in the gas. The resulting 
light was examined with a spectroscope, and the spectral lines 
seen turned out to be characteristic of helium. (In a separate 
control experiment, helium gas itself was put in the inner, thin- 
walled tube, and did not leak through the wall of the inner tube.) 

Now it was clear to Rutherford how to interpret his results: he 
could safely conclude that the helium gas that collected in the outer 
tube was formed from a particles that had passed into the outer tube. 

But Rutherford's result implied conclusions more important 
than just the identity of a particles. Apparently, an atom of an 
element (radon) can spontaneously emit a fragment (an a particle) 
that is the nucleus of another element (helium). A startling idea, 
but only the beginning of more startling things to come. 

Q10 How did Rutherford know that the gas which appeared in 
the tube was helium? 



21.6 Radioactive transformations 

The emission of a and (B particles raised difficult questions with 
respect to existing ideas of matter and its structure. The rapid 
development of chemistry in the nineteenth century had made the 
atomic-molecular theory of matter highly convincing. According 
to this theory, a pure element consists of identical atoms, which are 
indestructible and unchangeable. But if a radioactive atom emits 



Msa^*^e n«£. 



^6»5S TUB£- 




VHPVMP ^^ 






Rutherford's "mousetrap" for iden- 
tifying particles. 












18 



Radioactivity 




The water is being boiled by the heat 
given off by a small capsule of cobalt 
60. This capsule, the first ever made to 
produce heat from radioactive cobalt, 
was generating heat at the rate of 
360 watts when this photo was taken. 



Here He stands for the helium atom 
formed by the doubly-charged o 
particle when it picks up two 
electrons. 



as substantial a fragment as an a particle (shown to be an ionized 
helium atom), can the radioactive atom remain unchanged? That 
did not seem plausible. Rather, it seemed that there must be a 
transformation in which the radioactive atom is changed to an 
atom of a different chemical element. 

If an atom emits an a particle, a substantial part of its mass 
will be carried away by the a. particle. What about the atoms which 
emit /3 particles? The jS particle (shown to be an electron) is far 
less massive than the a particle; but its mass is not zero, and so a 
radioactive atom must also undergo some change when it emits a 
)8 particle. It was again difficult to escape the conclusion that 
radioactive atoms are, in fact, subject to division (into two parts of 
markedly unequal mass) — a conclusion contrary to the basic concept 
that the atom is indivisible. 

Another fundamental question arose in connection with the 
energy carried by the rays emitted by radioactive substances. As 
early as 1903 Rutherford and Soddy, and Pierre Curie and a young 
co-worker, A. Laborde, noted that a sample of radium kept itself 
at a higher temperature than its surroundings merely by reabsorbing 
some of the energy of the a particles emitted by atoms inside the 
sample. (Curie and Laborde found that one gram of radium can 
produce about 0.1 kilocalories of heat per hour.) A sample of radium 
thus has the property that it can continue to release energy year 
after year, for hundreds and even thousands of years. 

The continuing release of such a quantity of heat could not be 
explained by treating radioactivity as an ordinary chemical reaction. 
It was clear that radioactivity did not involve chemical changes in 
the usual sense: energy was emitted by samples of pure elements; 
energy emission by compounds did not depend on the type of 
molecule in which the radioactive element was present. The origin 
of the production of heat had to be sought in some deep changes 
within the atoms of radioactive elements, rather than in chemical 
reactions among atoms. 

Rutherford and Soddy proposed a bold theory of radioactive 
transformation to explain the nature of these changes. They 
proposed that when a radioactive atom emits an a or a /3 particle, 
it really breaks into two parts — the a or fi particle that was emitted, 
and a heavy leftover part which is physically and chemically 
different from the "parent" atom. There was a good deal of evidence 
for the last part of the assumption. For example, the formation of 
radon gas from radium was known as mentioned earlier. When the 
atomic mass of radon was determined, it turned out to be smaller 
than that of radium by just 4 atomic mass units, the mass of an 
a particle. 

The idea of radioactive transformation can be represented by an 
"equation" similar to the kind used to represent chemical reactions. 
For example, if we use the symbols Ra and Rn to represent atoms 
of radium and radon, we can express the transformation of radium 
into radon as: 

Ra * Rn + He 



Section 21.7 



19 



The process of transformation can be described as the transforma- 
tion or "disintegration" or "decay" or "transmutation" of radium 
into radon, with the emission of an a particle. 

Many decay processes in addition to the example just cited had 
been found and studied, by the Curies, by Rutherford and his 
co-workers, and by others, and these processes fitted easily into the 
kind of scheme proposed by Rutherford and Soddy. For example, 
Radon is radioactive also, emitting another a particle and thereby 
decaying into an atom of an element which was called "radium A" 
at the time. Radium A was later shown to be polonium (Po). 



Rn 



Po + He 



Polonium is a solid, and it too is radioactive. In fact, the 
original "parent" radium atoms undergo a series or chain of 
transformations into new, radioactive, "daughter" elements, ending 
finally with a "daughter" element which is non-radioactive or stable. 

Q11 Why was radioactive decay believed not to be an ordinary 
chemical reaction? 

Q12 Give an example of a radioactive transformation. Why is it 
contrary to the ideas of nineteenth-century chemistry? 



Rutherford and Soddy received 
Nobel Prizes in chemistry for their 
work on the radioactive trans- 
formation of one element into 
another. 



SG 21.7 



21.7 Radioactive decay series 



The decay of radium and its daughters was found eventually to 
lead to a stable end-product which was identified by its chemical 
behavior as lead. The chain beginning with radium has 10 
members, some emitting a particles and others emitting (3 particles. 
Some gamma rays are emitted during the decay series, but gamma 
rays do not appear alone; they are emitted only together with an a 
particle or a )S particle. Rutherford and Soddy also suggested that, 
since radium is always found in uranium ores, radium itself may 
be a member of a series starting with uranium as the ancestor of 
all the members. Research showed that this is indeed the case. 
Each uranium atom may in time give rise to successive daughter 
atoms, radium being the sixth generation and stable lead 
the fifteenth. 

The table on p. 27 shows all the members of the so-called 
uranium-radium series. The meaning of some of the symbols will 
be discussed in later sections. The number following the name of 
an element, as in uranium 238. indicates the atomic mass. Notice 
that there are heavier and lighter varieties of the element, for 
example, uranium 238 and 235, polonium 218, 214, and 210. Much 
more will be said about these varieties in the next chapter. 

Each member of the series differs physically and chemically 
from its immediate parent or daughters; it should, therefore, be 
possible to separate the different members in any radioactive 
sample. This is by no means impossible to do, but the separation 



Two other naturally occurring 
radioactive series have been found; 
one starts with thorium 232 and the 
other with uranium 235. (See 
SG 22.7 and 22.8, Chapter 22.) 



20 



Radioactivity 




^ i<l> %o Ito 



SG 21.8 



problem was made difficult by the fact that the different radioactive 
species decay at different rates, some very slowly, some rapidly, 
others at intermediate rates. These rates and their meaning will 
be discussed in the next section, but the fact that the rates differ 
gives rise to important effects that can be discussed now. 

An interesting example is supplied by that portion of the 
uranium series which starts with the substance called polonium 
218. A pure sample of polonium 218 may be collected by exposing 
to the gas radon a piece of ordinary material such as a thin foO of 
aluminum. Some of the radon atoms decay into polonium 218 atoms 
which then stick to the surface of the foil. The graph at the left 
shows what becomes of the polonium 218. Polonium 218 (Po^'^) 
decays into lead 214 (Pb^^^), which decays into bismuth 214 (Bi^'^), 
which decays into polonium 214 (not shown), then lead 210, etc. If 
the original sample contains 1,000,000 atoms of polonium 218 when 
it is formed, after twenty minutes it will contain about 10,000 Po^^* 
atoms, about 660,000 Pb^'" atoms, about 240,000 Bi^^'' atoms and 
about 90,000 Pb^'° atoms. The number of Po^'^ atoms is negligibly 
small because most of the Po^^* changes into Pb^*" in a small 
fraction of a second. 

A sample of pure, freshly separated radium (Ra 226) would also 

change in composition in a complicated way, but much more slowly. 
Eventually it would consist of a mixture of radium 226, radon 222, 
polonium 218, lead 214 and all the rest of the members of the chain 
down to, and including, stable "radium G" (lead 206). 

Similarly, a sample of pure uranium may contain, after a time, 
14 other elements of which 13- all but the last, stable portion — 
contribute to the radioactive emission, each in its own way. In all 
such cases, a complicated mixture of elements results. After starting 
as a pure a emitter, a sample eventually emits many a particles, 
)3 particles and y rays, apparently continuously and simultaneously. 

It is evident that the separation of the different members of a 
radioactive chain wUl be difficult — especially if some members of 
the chain decay rapidly. The determination of the chemical nature 
and the radioactive properties of each member required great 
experimental ingenuity. One successful method depended on the 
skillful chemical purification of a particular radioactive substance, 
as the Curies had done with radium and polonium. For example, 
suppose that a sample has been obtained from which all the radio- 
active atoms except those of radium 226 have been removed. The 
sample immediately starts to give off radon gas. The latter can be 
drawn off and its properties examined before it becomes seriously 
contaminated by the disintegration of many of its atoms into 
polonium 218. If this is done, it turns out that radon decays 
(through several transformations) into lead much more quickly 
than radium decays into radon. 

Q13 Give at least three reasons for the difficulty of separating 
decay products. 

Q14 If you start with a sample made entirely of pure uranium 



Section 21.8 



21 



238 atoms, what emission is observed at the start? How will the 
emission change as time goes on? 



21.8 Decay rate and half-life 

In the last section we saw that of 1,000,000 polonium 218 atoms 
present in a freshly prepared sample of that radioactive substance, 
only about 10,000 would remain after twenty minutes, the rest 
having decayed into atoms of lead 214. It would take only three 
minutes following the preparation of the pure sample of Po^** or 
fifty percent of the atoms originally present in the sample to have 
decayed. In the case of radium (Ra^^^), however, it would take 1620 
years for half of the radium atoms in a freshly prepared sample of 
radium to be transformed into radon atoms. 

These two examples illustrate the experimental fact that 
samples of radioactive elements show great differences in their 
rates of decay. These different rates are the result of averages of 
many individual, different decay events going on at random in a 
sample. Looking at one atom of any radioactive element, one never 
can tell when it will decay; some may decay as soon as they are 
produced, while others may never decay. Still, it has been found 
experimentally that there is a numerical value that describes the 
decay of a large group of atoms of one kind; a value which is 
unchangeable and always the same for any group of atoms of that 
kind. That value is the fraction of those atoms that decay per 
second. This number is almost completely independent of all 
physical and chemical conditions, such as temperature, pressure, 
and form of chemical combination. These remarkable properties of 
radioactivity deserve special attention, and the meaning of the 
italicized statement above will be discussed in detail because it is 
basic to our understanding of radioactivity. 

Say, for example, that 1/1000 of the atoms in a freshly-prepared 
pure sample decay during the first second. Then we expect that 
1/1000 of the remaining atoms will decay during the next second, 
and 1/1000 of the atoms remaining after 10 seconds will decay 
during the eleventh second, and so on — in fact, during any sub- 
sequent second of time, 1/1000 of the atoms remaining at the 
beginning of that second will decay — at least until the number of 
remaining atoms becomes so small that statistical predictions start 
to become very uncertain. 

Since the fraction of the atoms that decay per unit time is a 
constant for each element, the number of atoms that decay per 
unit time will decrease in proportion to the number of atoms 
remaining. Consequently, if the percentage of surviving, unchanged 
atoms is plotted as a function of time, a curve like the one on the 
next page is obtained. The number of atoms in a sample that decay 
per unit time is the activity of the sample. Thus, the graph on the 
next page also represents the way in which the measured activity 
of a sample would decrease with time. 



In 1898 the Curies obtained a total 
of about 200 grams of radium. 
Seventy years later (1968) 194 
grams of this remained as radium. 
The other six grams corresponded to 
16 X 10" radium atoms that have 
decayed into radon and sub- 
sequently into other elements 
during those 70 years. 



In a few cases, pressure and 
chemical combination have been 
found to make slight (and now 
well understood) differences in the 
rate of decay. 



SG 21.9, 21.10 



22 



Radioactivity 



If the daughter atoms were also 
radioactive, then the change of 
measured activity would of course 
be complicated, and not have so 
simple a form of graph. 



SG 21.11 



The curve that shows the number of atoms that have not 
decayed as a function of time approaches the time axis asymp- 
totically; that is, the number of survivors becomes small, but 
it may never become zero. This is another way of saying that we 
cannot assign any definite "life time" in which all of the original 
atoms for a sample will have decayed. 

However, it is possible to specify the time required for any 
particular /raction of a sample to decay — say 7 or j or 37%, for 
instance. For convenience in making comparisons, the fraction j 
has been chosen. The time required for the decay of one-half the 
original atoms of a pure sample, Rutherford called the half-life. 
Each kind of radioactive atom has a unique half-life, and thus the 
half-life of an element can be used to identify a radioactive 
element. As the table on p. 27 shows, a wide variety of half-lives, 
have been found. 

For uranium 238, the parent of the uranium series, the half-life 
is 4.5 billion years. This means that after 4.5 x 10^ years half of the 
uranium 238 atoms will have decayed. For polonium 214 the half- 
life is of the order of 10^ seconds. That is, in only 1/10,000 of a 
second, half of an original sample of Po-'^ atoms will have decayed. 
If pure samples of each, containing the same number of atoms, 
were available, the initial activity (atoms decaying per second) of 
polonium 214 would be very strong, and that of uranium 238 very 
feeble. If left for even a minute, though, the polonium would have 
decayed so thoroughly and hence the number of its surviving atoms 
would be so small, that at this point the activity due to polonium 
would now be less than the activity of the uranium. We can 
speculate that some radioactive elements, present in great 
quantities long ago, decayed so rapidly that no measurable traces 
are now left. On the other hand, many radioactive elements decay 
so slowly that during any ordinary experimentation time their 
decay rates seem to be constant. 

The principal advantage of the concept of half-life lies in the 
experimental result implied in the graph in the margin that for 
any element of half-life Ti, no matter how old a sample is. half 
of the atoms will still have survived after an additional time 
interval Ti. Thus, the half-life is not to be thought of as an 
abbreviation for "half a life." If one-half the original atoms remain 
unchanged after a time Ti, one-fourth (tX 2^) will remain after two 
consecutive half-life intervals 2Ti, one-eighth after 3Ti, and so on. 
Note how different the situation is for a population of. say, human 
beings instead of radioactive atoms. If we select a group of N„ 
babies, half the number may survive to their 70th birthday; of these 
N„/2 oldsters, none is likely to celebrate a 140th birthday. But of 




■cime. 



The Mathematics of Decay 

The activity of a sample, the number of 
disintegrations per second, the decay rate- 
these are alternative expressions for the same 
quantity. If we use the letter N to represent 
generally the number of atoms of a given kind 
present in a radioactive sample, then the 
activity is AA//Af, where AN is the number of 
atoms disintegrating in the time interval Af. 
If, in a time interval At, AN atoms disintegrate 
out of a total number N, the fraction of atoms 
disintegrating is AN/N. The fraction of atoms 
disintegrating per unit time is AN/N/At. (This 
same quantity can be thought of also as the 
ratio of the activity to the total number, 
AN/At/N.) This quantity, usually called K is 
analogous to the death rate in a human 
population. In the United States, for example, 
about 5,000 persons die each day out of a 
population of about 200,000,000. The death 
rate is therefore one person per 40,000 per 
day (or one person per day per 40,000). 

The beautifully simple mathematical 
aspect of radioactive decay is that the fraction 
of atoms decaying per second does not 
change with time. If initially there are N^ 
atoms, and a certain fraction k decay in one 
second, the actual number of atoms decaying 
in one second is KN^. Then, at any later time t, 
when there are only A/, atoms remaining, the 
fraction that decay in one second will still 
be X— but the number of atoms decaying in 
one second is now \N^, a smaller number 
than before. 

The constant fraction k of atoms decaying 
per unit time is called the decay constant. The 
value of this constant k can be found for each 
radioactive species. For example, k for radium 
is 1.36 X 10"" per second, which means that 
on the average 0.0000000000136 of the total 
number of atoms in any sample of radium will 
decay in one second. 

We can represent the fact that X is a 
constant by the expression 



\- 



AN/At 
N 



constant 



which we can rewrite as 



This form of the relation expresses clearly 
the fact that the decay rate depends directly 
on the number of atoms left. 

By using calculus, a relation of this type 
can be turned into an expression for N as a 
function of elapsed time t: 



^ = e- 



or A/j = /V„e-^' 



AN/At= constant x N 
or AN/At cc N 



where A/„ is the number of atoms at ? = 0, 
Ni is the number remaining unchanged at 
time t, and e is a mathematical constant that 
is approximately equal to 2.718. The factor 
e"'^' has the value 1 when f = 0, and decreases 
toward as f increases. Since the decay 
constant appears as an exponent, the decay 
is called "exponential" and takes the typical 
exponential form illustrated by the graph 
which frames page 22. 

The relationship between the half-life Tl 

■^ 2 

and the decay constant k can be derived as 

follows. We start by writing the exponential 

decay equation in logarithmic form. This is 

done by taking the logarithm of both sides of 

the equation: 

N 
log -rj^ ^ log e-^ 

= -kt log e 
After a time equal to the half-life Tl, the 
ratio A/t//Vo = i- So we can substitute i for 
A/,/A/o if we substitute Tl for t in the above 
equation, and get 

log (2) = -^7"^ log e 

The value of log (2) is -0.301 and the value 
of log e = 0.4343; hence 

-0.301 = -XTi (0.4343) 
and XTi = 0.693 

So the product of the decay constant and the 
half-life is always equal to 0.693. Knowing 
either one allows us to compute the other 
directly. 

For example, radium 226 has a decay 
constant X = 1 .36 x 10"" per second, so 

(1.36 X 10-" sec-') Tl = 0.693 

_ _ 0.693 

^ 1.36 X 10-" sec-' 
7i-5.10 X 10'° sec 

Thus the half-life of radium 226 is 5.10 x 10'° 
sec (about 1620 years). 



24 



Radioactivity 



SG 21.12-21.15 



The use of this statistical law, in 
practice, is justified because even 
a minute sample of a radioactive 
element contains very many atoms. 
For example, one-millionth of a 
gram of uranium contains 3 x 10''< 
atoms. 



No radioactive atoms with a half-life of 70 years. No/4 will have 
remained intact after 140 years, NJ8 after 210 years, etc. To put it 
differently, the statistical probability of survival for atoms is 
unchanged by the age they have already reached; in humans, of 
course, the probability of survival (say, for another year) depends 
strongly on age. 

We have been considering the behavior not of individual atoms, 
but of a very large number of them. As we saw in considering the 
behavior of gases in Chapter 11, this allows us to use laws of 
statistics to describe the average behavior of the group. If a hundred 
thousand persons were to flip coins simultaneously just once, we 
could predict with good accuracy that about one-half of them would 
get heads. But we could not accurately predict that one particular 
person in this crowd would obtain heads on a single flip. If the 
number of coins tossed is small, the observed count is likely to 
differ considerably from the prediction of 50% heads. From 
experiments in radioactivity we can predict that a certain fraction 
of a relatively large number of atoms in a sample will survive in 
any given time interval — say 2" will survive to reach the age T— but 
not whether a particular atom will be among the survivors. And as 
the sample of survivors decreases in size owing to disintegrations, 
our predictions become less precise. Eventually, when only a few 
unchanged atoms are left, we could no longer make useful 
predictions at all. In short, the disintegration law is a statistical 
law, and is thus applicable only to large populations of the 
radioactive atoms. Moreover, it makes no assumptions as to why 
the atoms disintegrate. 

In the discussion of the kinetic theory of matter we saw that 
it is a hopeless and meaningless task to try to describe the motions 
of each individual molecule; but we could calculate the average 
pressure of a gas containing a very large number of molecules. 
Similarly, in dealing with radioactivity we find that our inability 
to specify when each of the tremendous number of atoms in a 
normal sample will disintegrate makes a statistical treatment 
necessary — and useful. 

Q15 Why can one not specify the life time of a sample of 
radioactive atoms? 

Q16 How much of a substance will be left unchanged after a 
period equal to four times its half-life? 

Q17 If, after many many half-lives, only two atoms of a 
radioactive substance remain, what will happen during an 
additional period equal to one half-life? 



21.1 The Project Physics learning materials 
particularly appropriate for Chapter 21 include: 

Experiments 

Random Events 

Range of a and /3 Particles 

Half-life -I 

Half-life -II 

Radioactive Tracers 

Activities 

Magnetic Deflection of /3 Rays 
Measuring the Energy of a Radiation 
A Sweet Demonstration 
Ionization of Radioactivity 
Exponential Decay in Concentrations 

Reader Article 

The Nature of the Alpha Particle 

Transparencies 

Separation of a, /3, y Rays 
Rutherford's a-Particle "Mousetrap" 
Radioactive Disintegration Series 

In addition, the following Reader articles are 

appropriate to Unit 6 in general: 
Rutherford 

The Privilege of Being a Physicist 
One Scientist and His View of Science 
The Development of the Space-Time View 

of Quantum Electrodynamics 
Physics and Mathematics 
Where Do We Go From Here? 

21.2 Which of the Curies' discoveries would have 
been unlikely if they had used Becquerel's photo- 
graphic technique for detecting radioactivity? 

21.3 A spectroscopic examination of the y rays 
from bismuth 214 shows that rays of several 
discrete but different energies are present. The 
rays are said to show a "line spectrum." The 
measured wavelength corresponding to one of the 
lines is 0.016A. 

(a) Show that the energy of each of the y-ray 
photons responsible for that line is 

1.2 X i0-'3 J. (Hint- see Chapter 20.) 

(b) What is the equivalent energy in electron 
volts? 

21.4 Suppose that in the figure on p. 15 the 
magnetic field strength is 1.0 x 10"^N/ampm. 

(a) What would be the radius of curvature of 
the path of electrons entering the magnetic 
field with a speed of 1.0 x lO' m/sec? (The 
charge and mass of the electron are 

1.6 X 10~'" coul and 9.1 x lO'^^ kg 
respectively.) 

(b) If a particles entered the magnetic field 
with the same speed as the electrons in 
part (a), what would be the radius of 
curvature of their orbit? (The mass of an 
a particle is 6.7 x 10-27 kg.) 

(c) Compare your answers to parts (a) and (b). 



21.5 The electric field in the figure on p. 16 is 
produced by + charge at top plate, — charge at 
bottom. What is the sign of charges in beam going 
through tube? What is direction of magnetic field 
(into page or out of page)? 

21.6 If the electrons described in part (a) of 
SG 21.4 pass through crossed electric and 
magnetic fields as shown in part (c) of the 
figure on p. 16, 

(a) what must be the strength of the electric 
field to just balance the effect of a magnetic 
field of strength 1.0 x IQ-^N/ampm? 

(b) what voltage must be supplied to the electric 
field deflecting plates to produce the electric 
field strength of part (a) of this problem if 
the plates are 0.10 m apart? 

(c) what will happen to the a particles of 
SG 21.4 (b) moving through the crossed 
magnetic and electric fields of this problem? 

21.7 For each part below, select the most 
appropriate radiation(s): a, /3, or y. 

(a) most penetrating radiation 

(b) most easily absorbed by aluminum foil 

(c) most strongly ionizing radiation 

(d) may require thick "radiation shields" for 
protection 

(e) cannot be deflected by a magnet 

(f ) largest radius of curvature when traveling 
across a magnetic field 

(g) highest qlm value 

(h) important in Rutherford's and Royd's 

"mousetrap" experiment 
(i) involved in the transmutation of radium 

to radon 
( j ) involved in the transmutation of bismuth 

210 to polonium 210 

21.8 Suggest an explanation for the following 
observations: 

The Enghsh physicist Sir William Crookes 
discovered in 1900 that immediately after a 
strongly radioactive uranium-containing com- 
pound was purified chemically, the uranium 
compound itself showed much smaller activity, 
and the separate residue containing none of the 
uranium was strongly radioactive. 

Becquerel found, in 1901. that in such a case 
the uranium compound regained its original 
activity after several months, while the residue 
gradually lost most of its activity during the 
same time. 

21.9 A Geiger counter shows that the rate of 
emission of /3 particles from an initially pure 
sample of a radioactive element decreases to 
one-half the initial rate in 25 hours. 

(a) What fraction of the original number of 
radioactive atoms is still unchanged at 
that time? 

(b) What fraction of the original number will 
have disintegrated in 50 hours? 



25 




(c) What assumptions have you made in giving 
these answers? How might you check them? 

21.10 It took 10 years for 10 percent of the atoms 
of a certain freshly prepared sample of radioactive 
substance to decay. How much of the material 
that is left unchanged will decay in the next 

10 years? 

21.11 Suppose at time to a sample of pure radium 
consisted of 2.66 x 10^* atoms. (The half-life of 
radium is approximately 1600 years.) 

(a) If N, is the number of radium atoms in the 
sample at a time t, make a graph of N, vs 
time covering a period of 8000 years. 

(b) Show that at the end of 8000 years, 8.3 x lO^' 
radium atoms stUI remain in the sample 

(c) From your graph, estimate the number of 
radium atoms in the sample after 4000 years. 

21.12 The capsule containing cobalt 60, shown 
and described on p. 18, is reported to have an 
activity of 17,000 curies. One curie is defined as 
3.70 X 10'" disintegrations per second. 

(a) How much energy is released per dis- 
integration in the cobalt 60? 

(b) What would be the rate of heat production 
of that sample after 15 years? (The half- 
life of cobalt 60 is approximately 5 years.) 

21.13 Radioactive isotopes in quantities of 10 
micro-curies or less can be purchased for 
instructional purposes from the U.S. Atomic 
Energy Commission. How many disintegrations 
per second occur in a 10 micro-curie sample? 

21.14 Below are the observed disintegration rates 
(counting rates) as a function of time for a radio- 
active sample. 



(a) Plot the data, and determine the approximate 
half-life of this substance. 

(b) How many atoms decay each minute for 
each 10® atoms in this sample? (Use the 
relationship between X and T derived on 

p. 23.) Does this number remain constant? 

21.15 Rutherford and Soddy, working with 
samples of compounds of thorium, obtained 
results similar to those described in SG 21.8. 
Their results published in 1903, are shown below. 




(a) What is the half-life of thorium X? 

(b) In 1931 Rutherford was elevated to the 
British peerage, becoming "Baron Ruther- 
ford of Nelson." It is claimed that there is 

a connection between Rutherford's design of 
his coat of arms (shown below) and his 
work. What might the connection be? 



RUTHERFORD OF NELSON. 



TIME 



COUNTING 
RATE 
(counts/min) 



TIME 

(hr) 



COUNTING 
RATE 
(counts/min) 



0.0 




6.0 


1800 


0.5 


9535 


7.0 


1330 


1.0 


8190 


8.0 


980 


1.5 


7040 


9.0 


720 


2.0 


6050 


10.0 


535 


3.0 


4465 


11.0 


395 


4.0 


3300 


12.0 


290 


5.0 


2430 








26 















Periodic Table of the Elements* 




1 / 


f 


{^^ 




-^ 


Group—* 
Period 

1 


I 


II 


iJ . . 


III 


IV 


'K 


Yi' 


VII 





1.0080 
















.lk: 


^ 




/ 




4.0026 


1 


H 

1 












^ 

tV 


,0^ 


1^ 








He 
2 




6.939 


9.012 


^^, 


I / 

viK811 


12.011 


X4.007 


15.999 


18.998 


20.183 


2 


Li 


Be 










If 


. .'^ J B 


c / 


N 





F 


Ne 




3 


4 










r 


Va >^ , 


i^" 


5 


r 


7 


8 


9 


10 




22.990 


24.31 


26.98 


/4%.09 


30.97 


32.06 


35.45 


39.95 


3 


Na 
U 


Mg 
12 










} 


[y / 




A\/ 


Si 
14 


P 
IS 


S 
16 


CI 
17 


At 
18 




39.10 


40.08 


44.96 


47.90 


50.94 


52.00 


54.94 


55.85 


58.93 


Hs.n 


63.54 


65.37 


/4.72 


72.59 


74.92 


78.96 


79.91 


83.80 


4 


K 


Ca 


Sc 


Ti 


V 


Cr 


Mn 


Fe 


Co 


Ni 


Cu 


Zn/ 


Ga 


Ge 


As 


Se 


Br 


Kr 




19 


20 


21 


22 


23 


24 


25 


26 


27 


28 


29 


3JK 


31 


32 


33 


34 


35 


36 




85.47 


87.62 


88.91 


91.22 


92.91 


95.94 


(99) 


101.07 


102.91 


106.4 


107.87 


/I2.40 


114.82 


118.69 


121.75 


127.60 


126.9 


131.30 


5 


Rb 


Sr 


Y 


Zr 


Nb 


Mo 


Tc 


Ru 


Rh 


Pd 


Ag/ 


Cd 


In 


Sn 


Sb 


Te 


I 


Xe 




37 


38 


39 


40 


41 


42 


43 


44 


45 


46 


47/ 


48 


49 


50 


51 


52 


53 


54 




132.91 


137.34 




178.49 


180.95 


183.85 


186.2 


190.2 


192.2 


195.09 


/96.97 


200.59 


204.37 


207.19 


208.98 


210 


(210) 


222 


6 


Cs 


Ba 


* 


Hf 


Ta 


W 


Re 


08 


If 


Pt/ 


Au 


Hg 


Tl 


Pb 


Bi 


Po 


At 


Rn 




55 


56 


57-71 


72 


73 


74 


75 


76 


77 


r 


79 


80 


81 


82 


83 


84 


85 


86 




(223) 


226.05 


\ 










/ 














7 


Fr 


Ra 


't 










/ 
















87 


88 


89-103 












/ 





















•Rare- 


138.91 


140.12 


140.91 


144.27 


iy^) 


150.35 


151.96 


157.25 


158.92 


162.50 


164.93 


167.26 


168.93 


173.04 


174.97 


earth 


La 


Ce 


Pr 


Nd 


XPm 


Sm 


Eu 


Gd 


Tb 


Dy 


Ho 


Er 


Tra 


Yb 


Lu 


metals 


57 


58 


59 


60/ 


61 


62 


63 


04 


65 


66 


67 


68 


69 


70 


71 


t 


227 


232.04 


231 


28^.03 


(237) 


(242) 


(243) 


(245) 


(249) 


(249) 


(253) 


(255) 


(256) 


(253) 


(257) 


Actinide 


Ac 


Th 


Pa . 


-^ U 


Np 


Pu 


Am 


Cm 


Bk 


Cf 


E 


Fm 


Mv 


No 


Lw 


metals 


89 


90 


r1 


92 


93 


94 


95 


96 


97 


98 


99 


100 


101 


102 


103 



above the symbols are the average atomic masses (relative to carbon 12). 
names of the elements and their symbols are listed on the following pages. 




Uranium-radium decay series 



OLD NAME 


PRESENT NAME AND SYMB 


Uranium 1 


Uranium 238 


1 1238 
92 "J 


Uranium X, 


Thorium 234 


9oTh^»^ 


Uranium X^ 


Protactinium 234 


mPa''' 


Uranium II 


Uranium 234 


,,U^- 


Ionium 




Thorium 230 


soTh"" 


Radium 




Radium 226 


88Ra"« 


Radium 


Emanation 


Radon 222 


86Rn^" 


Radium 


A 


Polonium 218 


,,Po^'« 


Radium 


B 


Lead 214 


82 Pb^'^ 


Radium 


C 


Bismuth 214 


Bi2'^ 

83°' 


Radium 


C 


Polonium 214 


Pn2H 


Radium 


D 


Lead 210 


Ph210 
82 ~" 


Radium 


E 


Bismuth 210 


Ri2I0 
83^1 


Radium 


F 


Polonium 210 


84P0^"' 


Radium 


G 


Lead 206 


«,Pb^«« 



MODE OF 


HALF-LIFE 


DECAY 




a 


4.51 X iQs years 


/3,y 


24.1 days 


/S.-y 


1.18 minutes 


a 


2.48 X 10^ years 


a,y 


8.0 X 10^ years 


a,y 


1 620 years 


a 


3.82 days 


a 


3.05 minutes 


^.y 


26.8 minutes 


/3.y 


19.7 minutes 


a 


1.64 X 10-^ seconds 


^^y 


21.4 years 


P 


5.0 days 


a.-y 


138.4 days 


stable 





27 



List of the Elements 



Element £ 


>ymbol At 


omic Nun 


Actinium 


Ac 


89 


Aluminum 


Al 


13 


Americium 


Am 


95 


Antimony 


Sb 


51 


Argon 


Ar 


18 


Arsenic 


As 


33 


Astatine 


At 


85 


Barium 


Ba 


56 


Berkelium 


Bk 


97 


Beryllium 


Be 


4 


Bismuth 


Bi 


83 


Boron 


B 


5 


Bromine 


Br 


35 


Cadmium 


Cd 


48 


Calcium 


Ca 


20 


Californium 


Cf 


98 


Carbon 


C 


6 


Cerium 


Ce 


58 


Cesium 


Cs 


55 


Chlorine 


CI 


17 


Chromium 


Cr 


24 


Cobalt 


Co 


27 


Copper 


Cu 


29 


Curium 


Cm 


96 


Dysprosium 


Dy 


66 


Einsteinium 


Es 


99 


Erbium 


Er 


68 


Europium 


Eu 


63 


Fermium 


Fm 


100 


Fluorine 


F 


9 


Francium 


Fr 


87 


Gadolinium 


Gd 


64 


Gallium 


Ga 


31 


Germanium 


Ge 


32 


Gold 


Au 


79 


Hafnium 


Hf 


72 


Helium 


He 


2 


Holmium 


Ho 


67 


Hydrogen 


H 


1 


Indium 


In 


49 


Iodine 


I 


53 


Iridium 


Ir 


77 


Iron 


Fe 


26 


Krypton 


Kr 


36 


Lanthanum 


La 


57 


Lawrencium 


Lw 


103 


Lead 


Pb 


82 


Lithium 


Li 


3 


Lutetium 


Lu 


71 


Magnesium 


Mg 


12 


Mendelevium 


Md 


101 



Year of Isolation or Discovery and Origin of Name* 

1900 Greek aktis, ray 

1825 Latin alumen, substance with astringent taste 
1944 America 

15th century, Greek antimonos, opposite to solitude 

1894 Greek argos, inactive 

13th century, Greek arsenikon, valiant 
1940 Greek astatos, unstable 
1808 Greek barys, heavy 

1949 Berkeley, California 
1797 mineral, beryl 

15th century, German Weisse Masse, white mass 
1808 Arabic bawraq, white 

1826 Greek bromos, a stench 

1817 Latin cadmia, calamine, a zinc ore 
1808 Latin calcis, lime 

1950 State and University of California 
prehistoric, Latin carbo, coal 

1804 the asteroid Ceres, discovered 1803 

1860 Latin caesius, sky blue 

1808 Greek chloros. grass green 

1797 Greek chroma, color 

1735 Greek kobolos, a goblin 

prehistoric, Latin cuprum, copper 

1944 Marie and Pierre Curie 

1886 Greek dysprositos, hard to get at 

1952 Albert Einstein 

1843 Ytterby, a mining town in Sweden where first sample found 

1900 Europe 

1953 Enrico Fermi 
1886 Latin yiitere, to flow 
1939 France 

1886 Johan Gadolin, Finnish chemist 

1875 Gaul, or France 

1886 Germany 

prehistoric, Anglo-Saxon gold, symbol from Latin aurum 

1922 Hafnia, Latin for Copenhagen 

1895 Greek helios, the sun 

1879 Holmia, Latin for Stockholm 

1766 Greek hydro genes, water former 

1863 indigo-blue spectrum line 

1811 Greek iodes, violet-like 

1804 Latin iridis, rainbow 

prehistoric, Anglo-Saxon iren or isen. symbol from Latin /errum 

1898 Greek kryptos, hidden 

1839 Greek lanthanien, to be concealed 

1961 Ernest O. Lawrence, inventor of cyclotron 

Prehistoric, middle English led. symbol from Latin plumbum 

1817 Greek lithos. stone 

1905 Lutetia. ancient name of Paris 

1774 Latin magnes, magnet 

1955 Dmitri Mendeleev, who devised first Periodic Table 



28 



List of the Elements (cont.) 



Element S 


iymb< 


Mercury 


Hg 


Molybdenum 


Mo 


Neodymium 


Nd 


Neon 


Ne 


Neptunium 


Np 


Nickel 


Ni 


Niobium 


Nb 


Nitrogen 


N 


Nobelium 


No 


Osmium 


Os 


Oxygen 


O 


Palladium 


Pd 


Phosphorus 


P 


Platinum 


Pt 


Plutonium 


Pu 


Polonium 


Po 


Potassium 


K 


Praseodymium 


Pr 


Promethium 


Pm 


Protactinium 


Pa 


Radium 


Ra 


Radon 


Rn 


Rhenium 


Re 


Rhodium 


Rh 


Rubidium 


Rb 


Ruthenium 


Ru 


Samarium 


Sm 


Scandium 


Sc 


Selenium 


Se 


Silicon 


Si 


Silver 


Ag 


Sodium 


Na 


Strontium 


Sr 


Sulfur 


S 


Tantalum 


Ta 


Technetium 


Tc 


Tellurium 


Te 


Terbium 


Tb 


Thallium 


Tl 


Thorium 


Th 


Thulium 


Tm 


Tin 


Sn 


Titanium 


Ti 


Tungsten 


W 


Uranium 


U 


Vanadium 


V 


Xenon 


Xe 


Ytterbium 


Yb 


Yttrium 


Y 


Zinc 


Zn 


Zirconium 


Zr 



Symbol Atomic Number Year of Isolation or Discovery and Origin of Name* 

80 prehistoric, Latin Mercurius, the gold and planet 

42 1782 Greek mo/z/bdos. lead 

60 1885 Greek neos, new, and didymos, twin 

10 1898 Greek neos, new 

93 1940 planet Neptune 
28 1750 German Nickel, a goblin or devil 
41 1801 Niobe, daughter of Tantalus 

7 1772 Latin nitro, native soda, and gen, bom 
102 1957 Alfred Nobel 

76 1804 Greek osme, a smell, from the odor of its volatile tetroxide 

8 1774 Greek oxys. sharp, and gen, bom 

46 1803 planetoid Pallas, discovered 1801 

15 1669 Greek phosphoros, light bringer 
78 1735 Spanish plata, silver 

94 1940 Pluto, the second planet beyond Uranus 
84 1898 Poland, native country of co-discoverer Marie Curie 
19 1807 English potash, symbol Latin kalium 
59 1885 Greek praseos, leek green and didymos, a twin 

61 1947 Prometheus, fire bringer of Greek mythology 

91 1917 Greek protos first, and actinium because it disintegrates into it 
88 1898 Latin radius, ray 
86 1900 because it comes from radium 
75 1924 Latin Rhenus, Rhine province of Germany 
45 1804 Greek rhodon, a rose 

37 1860 Latin rubidus, red 
44 1845 Latin Ruthenia, Russia 

62 1879 Samarski, a Russian engineer 

21 1879 Scandinavian peninsula 
34 1817 Greek selene, moon 
14 1823 Latin silex, flint 

47 prehistoric, Anglo-Saxon seolfor, symbol from Latin argentum 

11 1807 Medieval Latin soda, symbol from Latin natrium 

38 1808 town of Strontian, Scotland 

16 prehistoric, Latin sulphur 

73 1802 Tantalus of Greek mythology 

43 1937 Greek technetos, artificial 
52 1782 Latin tellus, the earth 
65 1843 Ytterby, town in Sweden 

81 1862 Greek thallos, a young shoot 
90 1819 Scandinavian mythology, Thor 

69 1879 Latin Thule, most northerly part of the habitable world 
50 prehistoric, origin of name unknown, symbol Latin stannum 

22 1791 Greek mythology. Titans, first sons of the earth 

74 1783 Swedish tung sten, heavy stone, symbol from the mineral wolframite 

92 1789 Planet Uranus 

23 1830 goddess Vanadis of Scandinavian mythology 
54 1898 Greek xenos, strange 

70 1905 Ytterby, a town in Sweden 

39 1843 Ytterby, a town in Sweden 
30 prehistoric, German Zink, akin to Zinn. tin 

40 1824 Arabian Zerk, a precious stone 



* adapted from Alfred Romer, The Restless Atom, Science Study Series, Doubleday Co., N.Y. 



29 



22.1 The concept of isotopes 31 

22.2 Transformation rules 32 

22.3 Direct evidence for isotopes of lead 34 

22.4 Positive rays 35 

22.5 Separating isotopes 36 

22.6 Summary of a useful notation for nuclides; nuclear reactions 39 

22.7 The stable isotopes of the elements and their relative 
abundances 41 

22.8 Atomic masses 45 



Partially assembled mass spec- 
trograph in the laboratory of 
K.T. Bainbridge at Harvard Uni- 
versity. 




CHAPTER TWENTY-TWO 



Isotopes 



22.1 The concept of isotopes 

The discovery that there are three radioactive series, each 
containing apparently new substances, raised a serious problem. 
In 1910 there were still some empty spaces in the periodic table of SG 22.1 

the elements, but there were not enough spaces for the many new 
substances. The periodic table represents an arrangement of the 
elements according to their chemical properties and, if it could not 
include the radioactive elements, it would have to be revised, 
perhaps in some drastic and fundamental way. 

The clue to the puzzle lay in the observation that some of the 
newly found materials that cropped up as members of a radioactive 
series had chemical properties identical with those of well-known 
elements, although some of their physical properties were different. 
For example, the "great-granddaughter" of uranium was found to 
have the same chemical properties as uranium itself. When both 
were mixed together, the two could not be separated by chemical 
means. No chemist had detected, by chemical analysis, any 
difference between these two substances. But the two substances, 
now known as uranium 238 and uranium 234, do differ from each 
other in certain physical properties. As the lower table on p. 27 
shows, uranium 238 and 234 have quite different radioactive 
half-lives: 4.5 x 10^ years and 2.5 x 10^ years, respectively; and 
the mass of a uranium 234 atom must be smaller than that of a 
uranium 238 atom by the mass of one a particle and two ^3 particles. 
Another pair of radioactive substances, radium B and radium G, 
were found to have the same chemical properties as lead: when 
mixed with lead they could not be separated from it by chemical 
means. These substances are now known as lead 214 and lead 206, 
respectively. But lead 214 is radioactive and lead 206 is stable, and 
the lower table on p. 27 indicates that the atoms must differ from 
each other in mass by the mass of two a particles and four /3 
particles. There are many other examples of such physical dif- 
ferences among two or more radioactive substances with the same 
chemical behavior. 

31 



32 Isotopes 

Soddy suggested a solution that threw a flood of hght on the 
nature of matter and on the relationship of the elements in the 
periodic table. He proposed that a chemical element could be 
regarded as a pure substance only in the sense that all of its atoms 
have the same chemical properties. That is, a chemical element 
may in fact be a mixture of atoms, some having different radio- 
active behavior and diff'erent atomic masses, but all having the 
same chemical properties. This idea meant that one of the basic 
postulates of Dalton's atomic theory would have to be changed, 
namely the postulate that the atoms of a pure element are alike in 
all respects. According to Soddy, it is only in chemical properties that 
the atoms of a given element are identical. The several physically 
diff'erent species of atoms making up a particular element occupy 
the same place in the periodic table, that is, have the same atomic 
number Z. Soddy called them isotopes of the element, from the 
Greek isos and topos meaning same and place (same place in the 
periodic table). Thus uranium 238 and uranium 234 are isotopes of 
uranium; lead 214 and lead 206 are isotopes of lead. 

The many species of radioactive atoms in the three radioactive 

series were shown by chemical analysis to be isotopes of one or 

another of the last eleven elements in the periodic table — from lead 

to uranium. For example, the second and fifth members of the 

uranium series were shown to be isotopes of thorium, with Z = 90; 

the 8th, 11th and 14th members turned out to be isotopes of 

polonium (Z = 84). The old names and symbols given to the 

members of radioactive series upon their discovery were therefore 

rewritten to represent both the chemical similarity and physical 

difference among isotopes. The present names for uranium Xj and 
This shorthand notation is explained -^ • .„ ^ i ..t^ • oo/i j ..u • oorv / u 

(. ..«!.», «» ^-.^^ An lonmm, tor example, are thorium 234 and thorium 230 (as shown 

in the lower table on p. 27) A modern "shorthand" form for 

symbolizing any species of atom, or nuclide, is also given in the 

same table (for example, goTh"* and goTh"" for two of the isotopes 

of thorium). The subscript (90 in both cases for thorium) is the 

atomic number Z — the place number in the periodic table; the 

superscript (234 or 230) is the mass number A — the approximate 

atomic mass in amu. Note that the chemical symbol (such as Th) 

adds nothing to the information given by the subscript. 

Q1 Why wasn't it necessary, after all, to expand the periodic 
table to fit in the newly discovered radioactive substances? 

Q2 The symbol for the carbon 12 nuclide is gC*'. What is the 
approximate atomic mass of carbon 12? What is its position in the 
list of elements? 



further on page 40. 



22.2 Transformation rules 

Two questions then arose: how do changes in chemical nature 
come about as an atom undergoes radioactive decay? And, more 
specifically, what determines whether the atomic number Z 
increases or decreases in a given radioactive transformation? 

In 1913, the answers to these questions were given independently 



Section 22.2 



33 



by Soddy in England and by A. Fajans in Germany. They each 
proposed two rules which systematized all the relevant observations 
for natural radioactivity. We call them the transformation rules of 
radioactivity. Recall that by 1913 Rutherford's nuclear model of 
the atom was generally accepted. Using this model, one could 
consider a radioactive atom to have an unstable nucleus which 
emits an a or i8 particle (sometimes with emission of a y ray). 
Every nucleus has a positive charge Zq^, where Z is the atomic 
number and q^ is the magnitude of the charge of an electron. The 
nucleus is surrounded by Z electrons which make the atom as a 
whole electrically neutral and determine the chemical behavior of 
the atom. An a particle has an atomic mass of about 4 units and 
a positive charge of 2 units, +2qe. A ^3 particle has a negative charge 
of one unit, -qe, and very little mass compared with an a particle. 
The transformation rules may now be stated as follows: 

1. When a nucleus emits an a particle, the mass of the atom 
decreases by 4 atomic mass units, and the atomic number Z of the 
nucleus decreases by 2 units; the resulting atom belongs to an 
element two spaces back in the periodic table. 

2. When a nucleus emits a /3 particle, the mass of the atom is 
changed very little, but the atomic number Z increases by one unit: 
the resulting atom belongs to an element one place forward in the 
periodic table. When only a y ray is emitted, there is no change in 
the number corresponding to the atomic mass, and none in the 
atomic number. The lower table on p. 27 shows how these rules 
apply to the uranium-radium series, at least so far as the atomic 
number is concerned. 

The Rutherford- Bohr model of the atom helps us to understand 
why a change in chemical nature occurs as a result of a or /3 
emission. Emission of an a particle takes two positive charges from 
the nucleus, and the resulting new atom with its less positive 
nucleus can hold in its outer shells two fewer electrons than before, 
so two excess electrons drift away. The chemical behavior of atoms 
is controlled by the number of electrons, therefore the new atom 
acts chemically like an atom of an element with an atomic number 
two units less than that of the parent atom. On the other hand, in fi 
emission the nucleus — and with it the whole atom — becomes more 
positively charged, by one unit. The number of electrons that the 
atom can hold around the nucleus has increased by one, and after 
it has picked up an extra electron to become neutral again, the 
atom acts chemically as an atom with an atomic number one unit 
greater than that of the atom before the radioactive change occurred. 

By using the transformation rules, Soddy and Fajans were able 
to determine the place in the periodic table for every one of the 
substances (or nuclides) in the radioactive series; no revision of the 
periodic table was needed. Many of the nuclides between Z = 82 
(lead) and Z = 92 (uranium) are now known to contain several 
isotopes each. These results were expected from the hypothesis of 
the existence of isotopes, but direct, independent evidence was 
also sought — and it was obtained in 1914. 




Frederick Soddy (1877-1956), an 
English chemist, studied at Oxford, 
and went to Canada in 1899 to work 
under Rutherford at McGill University 
in Montreal. There the two worked 
out their explanation of radioactive 
decay. Soddy returned to England in 
1902 to work with Sir William Ramsay, 
the discoverer of the rare gases argon, 
neon, krypton and xenon. Ramsay 
and Soddy showed, in 1903, that 
helium was continually produced by 
naturally radioactive substances. In 
1921, Soddy was awarded the Nobel 
Prize in chemistry for his discovery 
of isotopes. He was a professor of 
chemistry at Oxford from 1 91 9 to 1 936. 



Example of a and 13 decay: 



SG 22.2, 22.3 



34 



Isotopes 



Q3 By how many units does the mass of an atom change 
during a decay? During /3 decay? 

Q4 By how many units does the charge of a nucleus change 
during a decay? During ft decay? 

Q5 What are the transformation rules of radioactivity? Give 
an actual example of how they apply. How do these rules follow 
from the Rutherford-Bohr model of the atom? 



22.3 Direct evidence for isotopes of lead 



( v^^A 



(li^'A 




ph 



20C> 



•>r^b^^j 



There are four naturally occurring 
lead isotopes: 

,,Pb-^ 

The first is found only as one of the 
isotopes of "ordinary" lead. Pb-"' is 
also found as the end product of a 
decay chain starting with actinium. 



SG 12.13 involves the fact that the 
decay of U'" is a distinct isotope of 
lead. 



Soddy knew that the stable end product of the uranium-radium 
series had the chemical properties of lead, and that the end product 
of the thorium series also had the chemical properties of lead. But 
he realized that these end products should have atomic masses 
different from that of ordinary lead (that is, lead that was not 
produced from a radioactive- series). This result follows from a 
simple calculation of the change in mass as an atom decays from 
the starting point of a radioactive series to the end point. The 
calculation may be simplified by ignoring beta decays in which no 
appreciable change in mass is involved. 

In the uranium series eight a particles, each with atomic mass 
of 4 units, are emitted. Therefore, the end product of the series 
starting from U^^** is expected to have an atomic mass close to 
238 -(8X4) = 206 units. In the thorium series, the end product 
derives from thorium 232, with an atomic mass of about 232 units, 
and six a particles are emitted along the way. It should therefore 
have an atomic mass close to 232 -(6x4) = 208 units. The average 
atomic mass of ordinary lead, found where there is no radioactive 
material evident, was known from chemical analysis to be 
207.2 units. 

The lead extracted from the mineral thorite, which consists 
mainly of thorium and contains only one or two per cent by mass of 
uranium, may be presumed to be the final product of the thorium 
series. The atomic mass of lead extracted from thorite should 
therefore be significantly different both from the atomic mass of 
lead extracted from a uranium mineral such as pitchblende, and 
from the atomic mass of ordinary lead. 

Here was a quantitative prediction, built on the transformation 
rules, which could be checked, and a number of chemists in 
Scotland, France, Germany, Austria and the United States attacked 
the problem. At Harvard University, T. W. Richards (later recipient 
of a Nobel Prize in chemistry) found atomic masses as low as 
206.08 for samples of lead from ores rich in uranium. Chemists in 
Austria found samples of lead, in the ore uraninite. with an atomic 
mass of 206.04. Soddy and others found samples of lead from 
thorite with atomic masses as high as 207.08 and 207.9. The results 
left no doubt that uranium was transformed into a light isotope of 
lead, and thorium into a heavier isotope of lead. 



Section 22.4 



35 



Q6 On what grounds was the existence of different atomic 
masses of lead predicted? 



22.4 Positive rays 



It was hard to show that stable elements may be mixtures of 
isotopes. By definition, isotopes cannot be separated by ordinary 
chemical methods. Any attempt to separate a pair of isotopes must 
depend on a difference in some behavior which depends, in turn, on 
the difference between their atomic masses. Moreover, except for 
the very lightest elements, the difference in atomic mass is small 
compared to the atomic masses themselves. For the lead isotopes 
discussed in the last section the difference was only two units in 
about 200 units, or about one per cent. Any difference in a physical 
property between two isotopes having such a small mass difference 
would be expected to be very small, making separation difficult to 
achieve. Fortunately, when the question of the possible existence of 
isotopes of stable elements arose, a method was available which 
could answer the question. This method, developed by J. J. Thomson 
and extended by A. J. Dempster and others, depended on the 
behavior of positively charged ions when these are traveling 
in electric and magnetic fields. 

In a cathode ray tube, electrons emitted from the cathode can 
knock electrons out of neutral atoms of gas with which they collide. 
It was thought that the positive ions produced in this way would 
accelerate toward the cathode and be neutralized there. In 1886, 
the German physicist Goldstein found that if a hole is made in 
the cathode, a ray passes through the cathode and emerges beyond 
it. The sketch in the margin is a schematic diagram of a discharge 
tube for producing such rays. If the cathode fits the tube tightly, 
so that no gas can enter the region behind it, and if the holes are 
so small that very little gas can get through them, a high vacuum 
can be produced on the right side, where the ray emerges. The ray 
then has quite a long range, and can be deflected by externally 
applied electric and magnetic fields. From the direction of the 
deflection, it could be concluded that the rays consist of positively 
charged particles. The rays were therefore called "positive rays," 
and were thought (correctly) to consist of positively charged ions 
of the atoms or molecules of the residual gas in the left side of 
the discharge tube. 

In this manner, Thomson prepared positive rays from different 
gases and used the observed deflection produced by external fields 
to determine the relative masses of the atoms of the gases. It was 
a crucially important method as we shall see. Rather than describe 
the details of Thomson's early apparatus we shall describe an 
improved type of instrument based on the early form, and one that 
is still in common use. 

The modern instrument typically consists of two main parts: 
the first part accelerates and then selects a beam of ions all moving 



^AS llOtET 




VACUUM 



Discharge tube for producing a beam 
of positive ions. The low-pressure gas 
between anode and cathode is ionized 
by the action of the electric field. The 
positive ions are accelerated by the 
electric field toward the cathode; 
there some of them will pass through 
a small hole and enter the well- 
evacuated region beyond, on the right 
side. That is where an external elec- 
tric or magnetic field can be applied. 



36 



Isotopes 




J. J. Thomson (1856-1940) at work in 
the Cavendish Laboratory. 




Some mass spectrometers are port- 
able; small ones similar to this are 
carried aloft for analysis of the upper 
atmosphere. 



with the same speed; in the second part these ions pass through a 
magnetic field which deflects them from a straight path into several 
different curved paths determined by their relative masses. Ions of 
different mass are thus separated to such an extent that they can 
be detected separately. By analogy with the instrument that 
separates light of different wavelengths, the instrument that 
separates ions of different masses was called a mass spectrograph. 
Its operation (including how it can be used to measure qlm of ions) 
is explained on the opposite page. The details show what an 
ingenious and pretty piece of equipment this really is. 

Thomson obtained results in his measurements of q/m for 
positive rays which were quite different from those that had been 
obtained for qlm of cathode-ray particles or /3 particles. Both the 
speeds of the ions and values of qlm were found to be smaller for 
gases with heavier molecules. These results are consistent with the 
idea that the positive rays are streams of positively ionized atoms 
or molecules. 

Of course it would be very desirable if the values of q and m 
could be separately determined. The magnitude of q must be a 
multiple of the electron charge q^, that is, it can only be q^, or 2qe, 
or Sq^, 4qe, .... The greater the charge on an ion, the greater the 
magnetic force will be and, therefore, the more curved the path of 
the ions. So we expect that in the apparatus shown on p. 37, a 
doubly ionized atom (an ion with charge +2q'e) will follow a path 
with half the radius of that of a singly ionized atom of similar type; 
a triply ionized atom will trace out a semi-circular path with one- 
third the radius, etc. Thus, for each type of atom analyzed, the 
path with the largest radius will be that taken by the ions with the 
single charge qg. Since q is therefore known for each of the paths, 
the mass of the ions can be determined from the values of qlm 
found for each path. 

Thus, study of positive rays with the mass spectrograph made 
it possible to measure for the first time the masses of individual 
atoms. (With the electrolysis methods that had been available 
before, described in Sec. 17.7, it was possible to obtain only average 
masses for very large numbers of atoms.) The uncertainty of mass 
determinations made with modem mass spectrographs can be less 
than one part in a hundred thousand, that is, less than 0.001 
percent. The difference in the masses of the isotopes of an element 
is thus easily detected, because in no case is it less than about 
0.3 percent. 



Q7 The radius of curvature of the path of an ion beam in a 
magnetic field depends on both the mass and speed of the ions. 
How must a mass spectograph be constructed to allow separation 
of the ions in a beam by mass? 



22.5 Separating isotopes 



In Thomson's original instrument the uncertainty in measured 
mass of ions was about one percent, but this was small enough to 



Principles of the operation of the mass 
spectrograph. 



The magnetic separation of isotopes begins by 
electrically charging the atoms of a sample of 
material, for example by means of an electric 
discharge through a sample of gas. The 
resulting ions are then further accelerated 
by means of the electric potential difference 
between the lower pair of electrodes, and a 
beam emerges. 

Before the different isotopes in the beam can 
be separated, there is usually a preliminary 
stage that allows only those ions with a 
certain velocity to pass through. In one type, 
the ion beam initially enters a region of 
crossec^ magnetic fields B and E, produced 
by current in coils and charged plates as 
shown. There, each ion experiences a magnetic 
force of magnitude qvB and an electric force 
of magnitude qE. The magnetic and electric 
forces act on an ion in opposite directions, 
and only for ions of a certain speed will the 
forces be balanced, allowing them to pass 
straight through the crossed fields and the 
hole in the diaphragm below them. For each of 
these ions, qvB = qE; so their speed v = E/B. 
Because only ions with this speed in the 
original direction remain in the beam, this 
portion of the first part of the apparatus is 
called a velocity selector. 

The separation of isotopes in the beam is now 
accomplished in another magnetic field of 
strength B'. As the beam enters this field, the 
magnetic field causes a centripetal force to 
act on each ion, deflecting it into a circular 
arc whose radius R depends upon the ion's 
charge-to-mass ratio. That is, qvB' = mv^/R, 
and so q/m = v/B'R. 

The divided beams of ions fall on either 
a photographic plate (in a mass spectrograp/?) 
or a sensitive ion current detector (in a mass 
spectrometer), allowing the radii R of their 
deflections to be calculated from the geometry 
of the apparatus. Since v, B' , and R can be 
determined from measurements, the charge- 
to-mass ratio of each beam of ions can be 
directly calculated. 

Because this method uses electric and 
magnetic fields, it is called the electromagnetic 
method of separation of isotopes. 



'Beah 



(vi£.Lt>«5 E. 







(Direction of B' is into 
plane of page 









38 



Isotopes 




Francis William Aston (1877-1945) 
studied chemistry at the University 
of Birmingham. In 1910 he went to 
Cambridge to work under J. J. Thom- 
son. He was awarded the Nobel Prize 
in chemistry, in 1922, for his work on 
isotopic mass determinations with the 
mass spectrograph. In disagreement 
with Rutherford, Aston pictured a 
future in which the energy of the atom 
would be tapped by man. In his Nobel 
acceptance speech he also spoke of 
the dangers involved in such a possi- 
bility. (Aston lived just long enough- 
by three months-to learn of the ex- 
plosion of the nuclear bombs.) 



permit Thomson to make the first observation of separated isotopes. 
He introduced a beam of neon ions from a discharge tube containing 
chemically pure neon into his mass spectrograph. The atomic mass 
of neon had been determined as 20.2 atomic mass units by means 
of the usual chemical methods for determining the atomic (or 
molecular) mass of a gas. Sure enough, at about the position on 
the photographic plate where ions of atomic mass 20 were expected 
to arrive, a dark line was observed when the plate was developed. 
But, in addition, there was also present nearby a faint line such as 
would indicate the presence of particles with atomic mass 22. No 
chemical element or gaseous compound was known which had this 
atomic or molecular mass. The presence of this line suggested, 
therefore, that neon might be a mixture of two isotopes, one with 
atomic mass 20, and the other with atomic mass 22. The average 
chemical mass 20.2 would result if neon contained about ten times 
as many atoms of atomic mass 20 as those of atomic mass 22. 

The tentative evidence from this physical experiment that neon 
has two isotopes was so intriguing that Thomson's associate, 
F. W. Aston, looked for ways to sharpen the case for the existence 
of isotopes. It was well known from kinetic theory (see Sec. 11.5) 
that in a mixture of two gases with different molecular masses, the 
average molecular kinetic energy is the same for both. Therefore 
the lighter molecules have a higher average speed than the heavier 
molecules and collide more often with the walls of a container. If 
the mixture is allowed to diffuse through a porous wall from one 
container into another, the slower, heavier molecules are less likely 
to reach and pass through the wall. The portion of the gas sample 
that does not get through the wall will, therefore, contain more of the 
heavier molecules than the portion that does pass through the wall. 

Aston allowed part of a sample of chemically pure neon gas to 
pass through such a wall. One pass accomplished only a slight 
separation of the lighter and heavier molecules, so a portion of the 
gas which had passed through the wall was passed through a 
porous wall again, and the same process was repeated many tiines. 
Aston measured the average atomic mass of each fraction of the 
gas by chemical means and found values of 20.15 atomic mass 
units for the fraction that had passed through the wall many times, 
and 20.28 units for the fraction that had been left behind in many 
tires. The difference in average atomic mass indicated that the 
neon was, indeed, a mixture of isotopes. 



Two views of one of Aston's earlier 
mass spectrographs. The electro- 
magnet was used to deflect a beam 
of charged atoms. Compare with 
sketch given on preceding page. 



<% 





Section 22.6 



39 



But even more impressive was the change in the relative 
intensities of the two traces (for atomic masses 20 and 22) in the 
mass spectrograph. The hne corresponding to ions with 22 atomic 
mass units was more prominent in the analysis of the fraction of 
the gas that had been left behind, showing that this fraction was 
"enriched" in atoms of mass 22. The optical emission spectrum of 
the enriched sample was the same as that of the original neon 
sample — proving that no substance other than neon was present. 

These results of separating isotopes at least partially by gas 
diffusion encouraged Aston to improve the method of determining 
the atomic masses of the isotopes of many elements other than 
neon. Today, the number and the atomic masses of virtually all 
naturally found isotopes of the whole list of elements have been 
determined. As an example, the figure below shows the mass 
spectrograph record obtained for the element germanium, indicating 
that this element has five isotopes. A picture of this kind is called 
a "mass spectrogram." 

i III I 

A photographic record of the mass spectrum of germanium, showing 
the isotopes of mass numbers 70, 72, 73, 74, and 76. 

Both the electromagnetic method and the gas-diffusion method 
of separating isotopes have been modified for large-scale applica- 
tions. The electromagnetic method shown in principle on p. 37 is 
used by the United States Atomic Energy Commission to provide 
samples of separated isotopes for research. The gas diffusion 
method used by Aston in achieving a small degree of separation of 
the neon isotopes has been developed on an enormous scale to 
separate the isotopes of uranium in connection with the manufacture 
of nuclear bombs and the production of nuclear power. 

Q8 What were three experimental results that supported the 
belief in the existence of two isotopes of neon? 

Q9 Isotopes at a given speed are separated by the electro- 
magnetic method in a mass spectrograph because more massive 
ions are deflected less than lighter ions going at the same speed. 
Why are isotopes separated in diffusing through a porous wall? 



Although we cannot measure the 
mass of a neutral atom in a mass 
spectrograph (why not?), it is the 
custom to compute and list isotopic 
masses for neutral atoms, based on 
the measurement on ions. 



SG 22.5 



22.6 Summary of a useful notation for nuclides; nuclear reactions 



It will be useful to summarize and recapitulate some ideas 
and notations. Because of the existence of isotopes, it was no longer 
possible to designate an atomic species only by means of the atomic 
number Z alone. To distinguish among the isotopes of an element 
some new symbols were introduced. One is the mass number, A, 
defined as the whole number closest to the measured atomic mass 
(see table on p. 42). For example, the lighter and heavier isotopes 



40 




The Atomic Energy Commission's 
Gaseous Diffusion Plant at Oai< Ridge, 
Tennessee. The long buildings right 
of center made up the first plant. 



The current international convention 
is to write both Z and A values on 
the left: ^^X. For purposes of clarity 
in this introductory text, the former 
convention, /X\ is used. 



of neon are characterized by the pairs of values: Z — 10, A = 20, 
and Z = 10, A = 22. (An element which consists of a single isotope 
can, of course, also be characterized by its Z and A values.) 

These values of Z and A are determined by the properties of the 
atomic nucleus: according to the Rutherford-Bohr model of the 
atom, the atomic number Z is the magnitude of the positive charge 
of the nucleus in elementary charge units. The mass number A 
is very nearly equal to (but a bit less than) the atomic mass of the 
nucleus because the total mass of the electrons around the nucleus 
is very small compared to the mass of the nucleus. 

The term nuclide is used to denote an atomic species charac- 
terized by particular values of Z and A. An isotope is then one of a 
group of two or more nuclides, all having the same atomic number 
Z but different mass numbers A. A radioactive atomic species is 
called a radioactive nuclide, or radionuchde for short. A nuchde is 
usually denoted by the chemical symbol with a subscript at the 
lower left giving the atomic number, and a superscript at the upper 
right giving the mass number. In the symbol zX^ for a certain 
nuclide, Z stands for the atomic number, X stands for the chemical 
symbol, and A stands for the mass number. For example, ^Be^ is the 
nuclide beryllium with atomic number 4 and mass number 9; the 
symbols joNe^" and loNe^^ represent the neon isotopes discussed 
above. The Z-value is the same for all the isotopes of a given 
element (X), and so is often omitted — except when it is needed for 



Section 22.7 



41 



balancing equations (as you will shortly see). Thus we often write 
Ne^o for ,oNe2«, ^^ y^^s for ^^U^^^ 

The introduction of the mass number and the symbol for a 
nuclide makes it possible to represent radioactive nuclides in an 
easy and consistent way (as was done in the lower table on p. 27). 
In addition, radioactive decay can be expressed by a simple 
"equation" representing the changes that occur in the decay 
process. For example, the first step in the uranium-radium series, 
namely the decay of uranium 238 into thorium 234, may be written: 



,U^ 



„Th23 



Me' 



The symbol 2He'' stands for the helium nucleus (a particle); the 
other two symbols represent the initial and final atomic nuclei, 
each with the appropriate charge and mass number. The arrow 
stands for "decays into." The "equation" represents a nuclear 
reaction, and is analogous to an equation for a chemical reaction. 
The atomic numbers on the two sides of the equation must balance 
because the electric charge of the nucleus must be conserved: 
92 = 90 + 2. Also, the mass numbers must balance because of 
conservation of mass: 238 = 234 + 4. 

For another example, we see from the table of the uranium- 
radium series on p. 27, that goTh^^" (thorium 234) decays by jS 
emission, becoming giPa^^* (protactinium 234). Since a /3 particle 
(electron) has charge -^e and has an extremely small mass, the 
symbol _ie° is used for it. This 13 decay process may then be 
represented by the equation: 




There is also an antineutrino (t) 
given off together with the /j 
particle. The neutrino and anti- 
neutrino are two particles that will 
be discussed briefly in Sec. 23.6. 
Z and A are both zero for neutrinos 
and gamma rays: „*'" oT" 



Th-^ 



^Pa^^^ + .^e^ + oi^" 



Q10 Write the complete symbol for the nuclide with atomic 
mass 194 and atomic number 78. Of which element is it an isotope? 

Q11 Complete the following equation for a-decay. Tell what 
law or rule you have relied on. 

zX-^ — > oHe' + Z-2X • 

Q12 In the same way, complete the following equation for /3- 
decay: 

^X^ — ^ .^eO+.X-^+oPO 



SG 22.6-22.9 



22.7 The stable isotopes of the elements and their relative 
abundances 



Mass spectra, such as the one of germanium shown on p. 39 
have now been determined for all the elements that have at least 
one stable isotope. These are the elements with atomic numbers 
between 1 (hydrogen) and 83 (bismuth). A few of the results are 
listed on p. 42. The table also includes isotopes of the unstable 
(radioactive) elements uranium and thorium because they have 



42 



Isotopes 



such long half-lives that they are still present in large quantities 
in some rocks. Uranium has three naturally occurring isotopes, one 
of which, U^^^ has the remarkable properties (to be discussed) that 
have made it important in military and political affairs as well as 
in science and industry. As can be seen in the table, the relative 
abundance of U^^'^ is very low, and it must first be separated from 
the far more abundant U"^ before it can be used in some applica- 
tions. Such applications and some of their social effects will be 
discussed in Chapter 24. 

Of the elements having atomic numbers between 1 and 83, 
only about one-fourth are single species; the others all have two or 

Relative natural abundances and masses of some nuclides 



The 


masses are given 


in atomic mass 


; units (amu) based on gC'^ 


= 12.000000 




CHEMICAL 


ATOMIC 


MASS 


RELATIVE 


MASS OF 


ELEMENT 


SYMBOL 


NUMBER 


NUMBER 


ABUNDANCE 


NEUTRAL ATOM 






Z 


A 


% 


(amu) 


Hydrogen 


H 


1 


1 


99.98 


1.007825 






1 


2 


0.02 


2.014102 


Helium 


He 


2 


4 


100.00 


4.002604 


Lithium 


Li 


3 


6 


7.42 


6.015126 






3 


7 


92.58 


7.016005 


Beryllium 


Be 


4 


9 


100.00 


9.012186 


Carbon 


C 


6 


12 


98.89 


12.000000 






6 


13 


1.11 


13.003354 


Nitrogen 


N 


7 


14 


99.63 


14.003074 






7 


15 


0.37 


15.000108 


Oxygen 





8 


16 


99.76 


15.994915 






8 


17 


0.04 


16.999134 






8 


18 


0.20 


17.999160 


Neon 


Ne 


10 


20 


90.92 


19.992440 






10 


21 


0.26 


20.993849 






10 


22 


8.82 


21.991385 


Aluminum 


Al 


13 


27 


100.00 


26.981535 


Chlorine 


CI 


17 


35 


75.53 


34.968855 






17 


37 


24.47 


36.965896 


Platinum 


Pt 


78 


190 


0.01 


189.9600 






78 


192 


0.78 


191.9614 






78 


194 


32.90 


193.9628 






78 


195 


33.80 


194.9648 






78 


196 


25.30 


195.9650 






78 


198 


7.21 


197.9675 


Gold 


Au 


79 


197 


100.00 


196.9666 


Lead 


Pb 


82 


204 


1.50 


203.9731 






82 


206 


23.60 


205.9745 






82 


207 


22.60 


206.9759 






82 


208 


52.30 


207.9766 


Thorium 


Th 


90 


232 


100.00 


232.0382 


Uranium 


U 


92 


234 


0.006 


234.0409 






92 


235 


0.720 


235.0439 






92 


238 


99.274 


238.0508 



Mass of bare nucleus of hydrogen: 1.00727 amu 
Mass of electron; 0.000549 amu 




VL.'va£5 :>c :::iZ'-C'<S 



Chart of the known nuclides. 

Each black square represents a stable, natural nuclide. 
Each open square represents a known unstable nuclide, 
with only a small number of these found naturally, the 
rest being man made. Note that all isotopes of a given 
element are found in a vertical column centered on the 
element's atomic number Z. (As will be seen in the next 
chapter, the Z number is the number of protons in the 
nucleus, and A-Z, the difference between the atomic mass 
and atomic number, is the number of neutrons.) 



44 



Isotopes 























30 






































20 






































10 
















p 
















/ 


\ 




n 


o— 


J^ 










V 


\ 





38 



39 40 41 
Atomic mass 



42 



Record of determination of abun- 
dance of the isotopes of potassium in 
a mass spectrometer. In a mass spec- 
trometer the current due to the ions 
is detected (see p. 37). Comparison of 
the current due to each isotope per- 
mits fairly precise estimates of the 
relative abundances of the isotopes. 




The American chemist H. C. Urey 
received the 1934 Nobel Prize in 
chemistry for his discovery of "heavy" 
hydrogen. 



more isotopes. As a result, the 83 elements together actually are 
made up of 284 naturally-occurring nuclides. All but 25 of these 
nuclides are stable. Many elements have only one stable nuclide, 
others have several, and tin has the greatest number, ten. Carbon 
and nitrogen each have two, and oxygen has three. The table on 
p. 42 shows that the isotope C* has a very high relative abundance, 
the isotopes O'^ and O'^ being relatively rare. 

There are 25 naturally occurring unstable nuclides not 
associated with the decay chains of the heavy radionuclides. They 
show only a small degree of radioactivity. The most common of 
these light nuclides is igK**, an isotope of potassium that has a 
relative abundance of only 0.012%. This isotope, which emits )8 
particles, has so lengthy a half-life (1.3 x 10** years) that its 
presence makes it very useful for determining the ages of certain 
rocks. Such information, coupled with information on the decay of 
U^^^, can be used to estimate the age of the earth. 

Hydrogen, the lightest element, has two stable isotopes, of which 
the heavier one, with atomic mass number 2, has a relative 
abundance of only 0.02%. The hydrogen isotopes are exceptional in 
that the rare isotope has an atomic mass twice that of the common 
isotope. As a result, the differences between the properties of the 
two isotopes are more marked than in any other pair of isotopes. 
The hydrogen isotope of atomic mass number 2 has therefore been 
given its own name, deuterium, with the symbol D; sometimes it 
is called "heavy hydrogen." It occurs in so-called "heavy water" or 
"deuterium oxide," for which the formula is written (iH^20 or D2O. 

Heavy water differs from ordinary water in some important 
respects: its density is 1.11 gram per cm^ as compared with 1.00 for 
ordinary water; at one atmosphere pressure it freezes at 3.82t and 
boils at 101.42T; (the corresponding temperatures for ordinary 
water being 0°C and 100°C). Naturally occurring water contains 
only about 1 atom of H^ per 7000 atoms of H', but methods have 
been developed for enriching the fraction of H^ and also for 
producing nearly pure D2O in large amounts. Heavy water is 
important in some types of devices for the controlled release of 
nuclear energy, as will be explained in Chapter 24. 

Interesting and important regularities have been discovered 
among the natural abundances, and some are stOl sources of 
puzzles. The number of nuchdes with the various combinations of 
even and odd values of Z and A are listed below. It is evident that 
naturally occurring nuclides with even Z and even A are much 
more numerous than those with any other combination. Elements 

Some Interesting Data Concerning Naturally Occurring Nuclides 





NUMBER OF 


NUMBER OF NUCLIDES 


AVERAGE NO. 




STABLE 




OF ISOTOPES 




ELEMENTS 


Odd A Even A TOTAL 


PER ELEMENT 


OddZ 


40 


53 8 61 


1.5 


Even Z 


43 


57 166 223 


5.2 



Total 



83 



110 



174 



284 



3.4 



Section 22.8 



45 



with even Z have, on the average, more isotopes per element than 
those with odd Z. Every theory of the nucleus has to try to account 
for these regularities, which are related to the stability of atomic 
nuclei. Information of this kind is analogous to observations of the 
positions of planets, to data on chemical compounds, and to atomic 
spectra. All of these provide material for the building of theories 
and models. 

Q13 What is deuterium? 
Q14 What is "heavy water"? 

Q15 Neon actually has three isotopes (see table on p. 42). 
Why did Thomson and Aston find evidence for only two isotopes? 

22.8 Atomic masses 

The masses of most of the stable nuclides have been determined, 
and the results are of fundamental importance in quantitative work 
in nuclear physics and its applications. The standard of mass 
adopted by physicists for expressing the atomic mass of any 
nuclide was slightly different from that used by chemists for the 
chemical atomic weights. The chemists' scale was defined by 
assigning the value 16.0000 atomic mass units to ordinary oxygen. 
But, as can be seen in the table on p. 42, oxygen is a mixture of 
three isotopes, two of which, O'^ and O^^ have very small abun- 
dances. For isotopic mass measurements, the value 16.0000 was 
assigned to the most abundant isotope, 0'^ and this mass was used 
as the standard by physicists. For some years, up to 1960, the 
atomic mass unit, 1 amu, was defined as 1/16 of the mass of a 
neutral O^** atom. Since 1960, O'*^ has been replaced by C'^ as the 
standard, and the atomic mass unit is now defined by both physi- 
cists and chemists as 1/12 of the mass of a neutral C'^ atom. The 
main reason for the choice of carbon is that mass-spectrographic 
measurements of atomic masses are much more accurate than the 
older chemical methods. Carbon forms an exceptional variety of 
compounds, from light to very heavy, which can be used as 
comparison standards in the mass spectrograph. 

The results that have been obtained for the atomic masses of 
some elements of special interest are Usted in the table on p. 42. 
Atomic masses can be determined with great accuracy, and, when 
expressed in atomic mass units, they all turn out to be very close to 
integers. For each nuclide, the measured mass differs from an 
integer by less than 0.06 amu. This result is known as Aston's 
whole-number rule, and provides the justification for using the 
mass number A in the symbol zX"^ for a nuclide or atom. As you 
will see in the next chapter, the explanation or physical basis for 
this rule is connected with the structure of the nucleus. 




This is a pliotograph of the oscillo- 
scope display of a high-resolution 
mass spectrometer when both hydro- 
gen and helium are present. The high 
peak, on the left, indicates the He^ 
isotope of mass 3.016030 amu. The 
other peak indicates H^ the extra- 
heavy hydrogen isotope, otherwise 
known as tritium, whose mass is 
3.016049 amu. The mass difference 
between the two nuclides is therefore 
about two parts in 300,000. It is easily 
observable. 



SG 22.10-22.12 



Q16 What nuclide is the current standard for atomic mass? 
Why has it been chosen? 



22.1 The Project Physics learning materials 
particularly appropriate for Chapter 22 include 
the following Transparencies: 

Radioactivity Displacement Rules 
Mass Spectrometer 
Chart of Nuclides 
Nuclear Equations 

22.2 Soddy's proposal of isotopes meant that not 
all atoms of the same element are identical. 
Explain why this proposal does not require that 
the atoms of a given element show differences in 
chemical behavior. 

22.3 After Soddy's proposal of the existence of 
isotopes, how could one go about determining 
whether an apparently new element was really 
new and should be given a separate place in the 
periodic table, or was simply an isotope of an 
already known element? 

22.4 At the National Bureau of Standards, in 
1932, a gallon of liquid hydrogen was slowly 
evaporated until only about 1 gram remained. 
This residue allowed the first experimental check 
on existence of the "heavy" hydrogen isotope H^. 

(a) With the help of the kinetic theory of matter, 
explain why the evaporation should leave in 
the residue an increased concentration of 
the isotope of greater atomic mass. 

(b) Why should the evaporation method be 
especially effective with hydrogen? 

22.5 A mass spectrograph similar to that sketched 
below causes singly charged ions of chlorine 37 to 
travel a semi-circular path and strike a photo- 
graphic plate (in the magnetic field at the right). 




From the equation on p 37: 

(a) show that the path radius 
is inversely proportional to 
the ion mass. 

(b) if the path diameter for chlorine ions is 
about 1.0 m, how far apart will the traces 
of CI''" and CP^ be on the photographic 
plate? 

(c) what would be the diameter of the orbit of 
lead 208 ions if the same electric and 



magnetic field intensities were used to 
analyze a sample of lead? 
(d) the problems of maintaining a uniform 
magnetic field over surfaces larger than 
1 square meter are considerable. What 
separation between lead 207 and lead 208 
would be achieved if the diameter of the 
orbit of lead 208 were held to 1.000 meter? 

22.6 Supply the missing data indicated by these 
transformation "equations:" 

(a) ,Pb2'2 > Bi2'2 + ? 

(b) ,Bi2'2 » +_,e'' 

(c) ■ ? > Ph">^ + Me* 

22.7 A radioactive series, originally called the 
actinium series, is now known to start with the 
uranium isotope 92^!^^^. This parent member 
undergoes transmutations by emitting in succes- 
sion the following particles: a, /3, a, /3, a, a, a, a, 
^3, a, /3. The last of these disintegrations yields 
gjPb^*"^, which is stable. From this information, 
and by consulting the periodic table, determine 
the complete symbol for each member of the 
series. List the members of the series in a column, 
and beside each member give its mode of decay 
(similar to what was done in the Table on page 27). 

22.8 In the following diagram of the thorium 
series, which begins with 9oTh^'^ the symbols used 
are those that were originally assigned to the 
members of the sequence: 

« ? & 

? ? ? 






84"rhC 



V » pThD 



^^8 (stable) 



Supply the missing data; then by consulting the 
periodic table replace the old symbols with the 
present ones. Indicate where alternative possi- 
bilities exist in the series. 

22.9 From g^Pu"', an isotope of plutonium 
produced artificially by bombarding uranium in 
a nuclear reactor, a radioactive series has been 
traced for which the first seven members are 
9,Pu--", ssAm^^', mNp"", 9,Pa^'-'\ ...U-*^ <H,Th"».and 
ggRa"*. Outline the disintegration series for these 
first seven members, showing the modes of decay 
as in the preceding question. 

22.10 A trace of radioactivity found in natural 
carbon makes it possible to estimate the age of 
materials were once living. The radioactivity of 
the carbon is due to the presence of a small 
amount of the unstable isotope, carbon 14. This 
isotope is created mainly in the upper atmosphere 
by transformation (induced by cosmic rays) of the 
stable isotope carbon 13 to carbon 14. 



46 



UDY GUIDE 



The rate of production of carbon 14 from carbon 
13 matches the rate of beta-decay of carbon 14 
into nitrogen 14, so the percentage of total carbon 
in the atmosphere consisting of carbon 14 is 
relatively constant. Now when carbon dioxide is 
used by plants in photosynthesis, the cell in- 
corporates the isotopes of carbon in the same 
proportions as exist in the atmosphere. The 
activity of the carbon at that point amounts to 
15.3 beta emissions per minute per gram of 
carbon. When the interaction of the living plant 
with the atmosphere stops, for example, when a 
branch is broken off a living tree for use as a tool, 
the radioactivity begins to decrease at a rate 
characteristic of carbon 14. This rate has been 
measured, and the half-life of carbon is known to 
be 5760 years. So if the activity is measured at 
some later time, and if the half-life of carbon 14 
is known, then one can use the decay curve given 
on page 22 to determine the time elapsed since 
the branch was taken from the tree. For example, 
suppose the activity was found to have dropped 
from the normal rate of 15.3 to 9.2 beta emissions 
per minute per gram of carbon. Knowing the 
half-life, determine the time elapsed. 

Repeat the procedure in SG 22.10 to calculate 
the age of charcoal found in an ancient Indian 
fire pit, if the activity of the carbon in the charcoal 
is now found to be 1.0 beta emissions per minute 
per gram of carbon. What assumption are you 
making in this part of the problem? 

22.11 (a) Find the average atomic mass of carbon 
by calculating the "weighted average" 
of the atomic masses of the two natural 
carbon isotopes. (Use the data of the 
table on p. 42.) 

(b) Find the average atomic mass of 
lithium. 

(c) Find the average atomic mass of 
ordinary lead. 



22.12 The mass of a neutral hehum atom is 
4.00260 amu, and that of an electron is 0.00055 
amu. From these data find the mass of the a 
particle in amu. 

22.13 The age of a rock containing uranium can 
be estimated by measuring the relative amount 
of U^^** and Pb^"® in a sample of the rock. Consider 
a rock sample which is found to contain 3 times 
as many U"** atoms as Pb-"® atoms. 

(a) What fraction of the U"* contained in the 
sample when it was formed has decayed? 

(b) Refer to the graph on p. 22 and estimate the 
fraction of a half-hfe needed for that 
fraction of the U"* to decay. 

(c) How old is the rock? 

(d) For this simple method to work it is 
necessary to assume that each U^^* atom 
that decays appears as a Pb^"® atom— 

in other words that the half-Uves of all the 
intermediate substances in the uranium 
chain are negUgible compared to that of 
U^^^. Is this assumption a valid one? 




A 14,000-year-old burial site being un- 
covered by an archeological team near the 
Aswan Reservoir. The age of the burial site 
is determined by carbon-14 dating (de- 
scribed in SG 22.10) of scraps of wood or 
charcoal found in it. 



47 



23.1 The problem of the structure of the atomic nucleus 49 

23.2 The proton-electron hypothesis of nuclear structure 49 

23.3 The discovery of artificial transmutation 51 

23.4 The discovery of the neutron 53 

23.5 The proton-neutron theory of the composition of atomic nuclei 58 

23.6 The neutrino 59 

23.7 The need for particle accelerators 60 

23.8 Nuclear reactions 68 

23.9 Artificially induced radioactivity 70 



Ernest O. Lawrence (left) and M. S. 
Livingston (right) are shown standing 
beside the magnet for one of the earli- 
est cyclotrons. Lawrence and Living- 
ston invented the cyclotron in 1931, 
thereby initiating the development of 
high-energy physics in the United 
States. 




CHAPTER TWENTY-THREE 



Probing the Nucleus 



23.1 The problem of the structure of the atomic nucleus 



The discoveries of radioactivity and isotopes raised new 
questions about the structure of atoms — questions which involved 
the atomic nucleus. We saw in Sec. 22.2 that the transformation 
rules of radioactivity could be understood in terms of the 
Rutherford- Bohr model of the atom. But that model said nothing 
about the nucleus other than that it is small, has charge and mass, 
and may emit an a or a )8 particle. This implies that the nucleus has 
a structure which changes when a radioactive process occurs. The 
question arose: can we develop a theory or model of the atomic 
nucleus that will explain the facts of radioactivity and the existence 
of isotopes? 

The answer to this question makes up much of nuclear physics. 
The problem of nuclear structure can be broken into two questions: 

(1) what are the building blocks of which the nucleus is made, and 

(2) how are the nuclear building blocks put together? Answers to 
the first question are considered in this chapter. In the next chapter 
we shall take up the question of how the nucleus is held together. 
The attempt to solve the problem of nuclear structure, although not 
yet completed, has not only led to many new basic discoveries and 
to large-scale practical applications, but also has had important 
social and political consequences, stretching far beyond physics 
into the life of society in general. Some of these consequences will 
be discussed in Chapter 24. 



SG 23.1 



The Project Physics supplemental 
unit Elementary Particles goes one 
step further, into the nature and 
structure of the subatomic particles 
themselves. 



23.2 The proton-electron hypothesis of nuclear structure 



The emission of a and (3 particles by radioactive nuclides 
suggested that a model of the nucleus might be constructed by 
starting with a and /3 particles as building blocks. Such a model 
would make it easy to see, for example, how a number of a par- 
ticles could be emitted, in succession, in a radioactive series. But 
not all nuclei are radioactive, nor do all have masses that are 



49 



SG 23.2 



50 



Probing the Nucleus 



Proton — from the Greek "protos" 
(first). It is not known who suggested 
the name originally-it is found in 
the literature as far back as 1908. 
In 1920 Rutherford's formal proposal 
of the name proton was accepted 
by the British Association for the 
Advancement of Science. 



SG 23.3 



multiples of the a-particle mass. For example, the nucleus of an 
atom of the lightest element, hydrogen, with an atomic mass of one 
unit (two units in the case of the heavy isotope), is too light to 
contain an a particle. So is the light isotope of helium, 2He^ 

A positively charged particle with mass of one unit would seem 
to be more satisfactory as a nuclear buOding block. Such a 
particle does indeed exist: the nucleus of the common isotope of 
hydrogen. This particle has been named the proton. According to 
the Rutherford- Bohr theory of atomic structure, the hydrogen atom 
consists of a proton with a single electron revolving around it. 

In the preceding chapter (Sec. 22.4), we discussed Aston's 
whole-number rule, which expressed the experimental result that 
the atomic masses of the nuclides are very close to whole numbers. 
This rule, together with the properties of the proton — for example, 
its single positive charge — made it appear possible that all atomic 
nuclei are made up of protons. Could a nucleus of mass number A 
consist of A protons? If this were the case, the charge of the nucleus 
would be A units; but, except for hydrogen, the nuclear charge Z 
is found to be always less than A — usually less than 2'A. To get 
around this difficulty, it was assumed that in addition to the 
protons, atomic nuclei contain just enough electrons to cancel the 
charge of the extra protons; that is, they were supposed to contain 
A — Z electrons. These electrons would contribute only a small 
amount to the mass of the nucleus, but together with the protons 
they would make the net charge equal to +Z units, as required. It 
seemed thus plausible to consider the atom as consisting of a 
nucleus made up of A protons and A— Z electrons, with A additional 
electrons outside the nucleus to make the entire atom electrically 
neutral. For example, an atom of (,0'" would have a nucleus with 
16 protons and 8 electrons, with 8 additional electrons outside the 
nucleus. This model of the nucleus is known as the proton-electron 
hypothesis of nuclear composition. 

The proton-electron hypothesis seemed to be consistent with 
the emission of a and /3 particles by atoms of radioactive substances. 
Since it was assumed that the nucleus contained electrons, 
explanation of beta decay was no problem: when the nucleus is in 
an appropriate state it may simply eject one of its electrons. It also 
seemed reasonable that an a particle could be formed, in the 
nucleus, by the combination of four protons and two electrons. 
(An a particle might exist already formed in the nucleus, or it might 
be formed at the instant of emission.) 

The proton-electron hypothesis is similar to an earlier idea 
suggested by English physician William Prout in 1815. On the basis 
of the small number of atomic masses then known, he proposed 
that all atomic masses are multiples of the atomic mass of 
hydrogen, and that therefore all the elements might be built up of 
hydrogen. Prout's hypothesis was discarded when, later in the 
nineteenth century, the atomic masses of some elements were 
found to be fractional, in particular, those of chlorine (35.46 units) 
and copper (63.54 units). With the discovery of isotopes, however, 
it was realized that the fractional atomic masses of chlorine and 



Section 23.3 



51 



copper, like that of neon, arise because these elements are mixtures 
of isotopes, with each separate isotope having an atomic mass close 
to a whole number. 

Although the proton-electron hypothesis was satisfactory in 
some respects — as in accounting for the whole number rule for 
isotope masses, and in being consistent with the emission of a and 
)8 particles by radioactive nuclides — it led to serious difficulties and 
had to be given up. The existence of electrons inside the nucleus 
had to be ruled out for a number of reasons, not the least being that 
the more precise the mass measurements became, the further the 
mass of nuclei departed from that predicted by the proton-electron 
hypothesis. 

Q1 Why was the idea of hydrogen atoms being a basic build- 
ing block of all atoms given up in the nineteenth century? 

Q2 On the basis of the proton-electron hypothesis, what would 
a nucleus of gC^^ contain? 

Q3 Does the proton-electron hypothesis work out for, say, jHe^? 



Careful inspection of the modern 
values of nuclide masses (table 22.1) 
shows that nuclides can not be 
considered as simple conglomerates 
of hydrogen and electrons. 



23.3 The discovery of artificial transmutation 



A path which led to a better understanding of nuclear com- 
position was opened, almost by accident, in 1919. In that year 
Rutherford found that when nitrogen gas was bombarded with a 
particles from bismuth 214, swift particles were produced which 
could travel farther in the gas than did the a particles themselves. 
When these particles struck a scintillation screen, they produced 
flashes of light fainter than those produced by a particles, about 
the intensity that would be expected for positive hydrogen ions 
(protons). Measurements of the effect of a magnetic field on the 
paths of the particles suggested that they were indeed protons. 
Rutherford ruled out, by means of careful experiments, the 
possibility that the protons came from hydrogen present as an 
impurity in the nitrogen. Since the nitrogen atoms in the gas were 
the only possible source of protons, Rutherford concluded that an 
a particle, in colliding with a nitrogen nucleus, can occasionally 
knock a small particle — a proton — out of the nitrogen nucleus. In 
other words, Rutherford deduced that an a particle can cause the 
artificial disintegration of a nitrogen nucleus, with one of the 
products of the disintegration being a proton. But this process does 
not happen easily. The experimental results showed that only one 
proton was produced for about one million a particles passing 
through the gas. 

Between 1921 and 1924, Rutherford and Chadwick extended 
the work on nitrogen to other elements and found evidence for 
the artificial disintegration of all the light elements, from boron to 
potassium, with the exception of carbon and oxygen. (These were 
later shown to undergo artificial disintegration.) 

The next step was to determine the nature of the nuclear 



fi/m/m//imy»ni»iiij//f///j///jj/^////jj/yA 9/f///jjj/////) 



f 



>^WM////WWW//WWWW/MWW>77m 



Rutherford's diagram of the appa- 
ratus used to detect the protons from 
disintegrations produced by a par- 
ticles. The a source was on a movable 
stand D. Nitrogen nuclei in the nitro- 
gen gas which filled the box are trans- 
muted by the a particle. At the end of 
the box was a piece of silver foil F 
thick enough to stop a particles, but 
not protons. Behind the foil was a lead 
sulfide screen S which would show 
flashes of light when struck by protons. 
To see the flashes, the screen S had to 
be watched through a microscope 
with a dark-adapted eye. 



52 



Probing the Nucleus 






The Wilson cloud chamber. When the 
piston is moved down rapidly the gas 
in the cylinder cools and becomes 
supersaturated with water vapor. The 
water vapor will condense on the ions 
created along the path of a high- 
energy charged particle, thereby mak- 
ing the track. For his invention of the 
cloud chamber, C. T. R, Wilson (1869- 
1959) of Scotland shared the 1927 
Nobel Prize in physics with Arthur H. 
Compton. (See also page 65 margin) 



a-particle tracks from a source at the 
left, in a cloud chamber filled with 
nitrogen gas. At the far right, one a 
particle has hit a nitrogen nucleus; 
a proton is ejected upward toward the 
left, and the resulting oxygen nucleus 
recoils downward to the right. (From 
P. M. S. Blackett, 1925) 



process leading to the emission of the proton. Two hypotheses were 
suggested for this process: (a) the nucleus of the bombarded atom 
loses a proton, "chipped off" as the result of a collision with a swift 
a particle; or (b) the a particle is captured by the nucleus of the 
atom it hits, forming a new nucleus which, a moment later, emits 
a proton. It was possible to distinguish experimentally between 
these two possible cases by using a device, called a "cloud chamber," 
which reveals the path or track of an individual charged particle. 
The cloud chamber was invented by C. T. R. Wilson and perfected 
by him over a period of years. In 1911 it became a major scientific 
instrument; a simplified diagram is shown at the left, (a) If a proton 
were being chipped off, four tracks should be seen in a photograph 
of a disintegration event: the track of an a particle before the 
collision, the track of the same a particle after collision, and the 
tracks of both the proton and the recoiling nucleus after collision. 
In case (b), on the other hand, the a particle should disappear in the 
collision, and only three tracks would be seen: that of the a particle 
before collision, and the tracks of the proton and recoil nucleus 
after the collision. The choice between the two possibilities was 
settled in 1925 when P. M. S. Blackett studied the tracks produced 
when particles passed through nitrogen gas in a cloud chamber. 
He found, as shown in the photograph below, that the only tracks 
which could be seen for artificial disintegration were those of the 
incident a particle, a proton, and the recoil nucleus. The absence 
of a track corresponding to the presence of an a particle after the 
collision proved that the a particle disappeared completely and that 
case (b) is the correct interpretation of artificial disintegration. 
The process in which an a particle is absorbed by a nitrogen 




Section 23.4 



53 



nucleus and a proton is emitted may be represented by an "equation" 
which is analogous to the representation used near the end of Sec. 
22.6 to represent radioactive decay. The equation expresses the fact 
that the total mass number is the same before and after the 
collision (that is, there is conservation of mass number), and the 
fact that the total charge is the same before and after the collision 
(there is conservation of charge). The atomic number, the mass 
number, and the nuclear charge are known for the target nucleus 
7N", for the incident a particle sHe^, and for the proton ,H^ The 
product nucleus will therefore have the atomic number 7 + 2 - 1=8 
(which is the atomic number for oxygen), and will have the mass 
number 14 + 4-1 = 17. Hence the product nucleus must be 
80*^ an isotope of oxygen. The disintegration process may therefore 
be represented by the nuclear reaction: 



^He' + ^W 



,0>^ + ,H> 



This reaction shows that a transmutation of an atom of one 
chemical element into an atom of another chemical element has 
taken place. The transmutation did not occur spontaneously, as it 
does in the case of natural radioactivity, but was man-made; it 
was produced by exposing target atoms (nuclei) to projectiles 
emitted from a radioactive nuclide. In the paper in which he 
reported this first artificially produced nuclear reaction, Ruther- 
ford said: 



See "The Tracks of Nuclear 
Particles" in Reader 6. 



® 



^ 



* 




0, 



SG 23.4 



The results as a whole suggest that, if a particles — or 
similar projectiles — of still greater energy were available 
for experiment, we might expect to break down the 
nuclear structure of many of the lighter atoms. 



This call for greater energies of 
"projectiles" was soon answered 
by the construction of accelerators. 
(See Sec. 23.7.) 



The further study of reactions involving light nuclei led (as you 
shall see in the next section) to the discovery of a new particle — 
the neutron — and to a better theory of the constitution of the 
nucleus. Many types of reactions have been observed with nuclei 
of all masses, from the lightest to the heaviest, and the possibilities 
indicated by Rutherford have been realized to an extent far beyond 
what he would have imagined in 1919. 

Q4 What evidence showed that the bombarding a particle was 
temporarily absorbed by the nitrogen nucleus, rather than that it 
simply broke up and bounced off? 



23.4 The discovery of the neutron 



In 1920 Rutherford suggested that a proton inside the nucleus 
might have an electron tied to it so closely as to form a neutral 
particle. Rutherford even suggested the name "neutron" for this 
hypothetical particle. Physicists looked for neutrons, but the search 
presented at least two difficulties: (1) they could find no naturally 



54 



Probing the Nucleus 



-^ ? 



Be 



Be 



fartxffii 




James Chadwick (born 1891) received 
the Nobel Prize in Physics in 1935 for 
his discovery of the neutron. 



occurring neutron-emitting materials; and (2) the methods used for 
detecting atomic particles all depended on effects of the electric 
charge of the particles — and so could not be applied directly to 
neutral particles. Until 1932, the search for neutrons was 
unsuccessful. 

The proof of the existence of neutrons came in 1932 as the 
climax of a series of experiments on nuclear reactions made by 
physicists in different countries. The discovery of the neutron is a 
good example of how physicists operate — how they think about 
problems and arrive at solutions; it is an excellent "case history" 
in experimental science. Working in Germany in 1930, W. G. Bothe 
and H. Becker found that when samples of boron or of beryllium 
were bombarded with a particles, they omitted radiations which 
appeared to be of the same kind as y rays, at least insofar as the y 
rays had no electric charge. Beryllium gave a particularly marked 
effect of this kind. Observations by physicists in Germany. France 
and Great Britain showed that the radiation from the beryllium 
penetrated further (through lead, for example) than any y radiation 
found up to that time, and had an energy of about 10 MeV. The 
radiation was thus much more energetic than the y rays (that is, 
high-energy photons) previously observed, and, as a result, aroused 
much interest. 

Among those who investigated this radiation were the French 
physicists Frederic Joliot and his wife Irene Curie, a daughter of 
the discoverers of radium. They studied the absorption of the 
radiation in paraffiin, a material rich in hydrogen. They found in 
the course of their experiments that the radiation from beryllium, 
when it fell on paraffin, ejected large numbers of hydrogen nuclei — 
protons — from the paraffin. The energies of these protons were 
found to be about 5 MeV. Using the principles of conservation of 
momentum and energy, they calculated the energy a y ray would 
need if it were to transfer 5 MeV to a proton in a collision. The 
result was about 50 MeV, a value much greater than the 10 MeV 
that had been measured for the radiation. In addition, the number 
of protons produced was found to be much greater than that 
predicted on the assumption that the radiation consisted of y rays. 

These discrepancies (between the results of two sets of experi- 
ments, and between theory and experiment) left physicists in a 
dilemma. Either they could conclude that the conservation principles 
of momentum and of energy did not apply to the collisions between 
the radiation and the protons in the paraffin, or they could adopt 
another hypothesis about the nature of the radiation. Now, if there 
is any one thing physicists do not want to do it is to give up the 
principles of conservation of momentum and of energy. These 
principles are so basic to scientific thought and have proven so 
useful that physicists tried very hard to find an alternative to giving 
them up. 

The English physicist James Chadwick found similarly perplex- 
ing results for recoiling nuclei from several other light elements, 
including helium, lithium, carbon, nitrogen, and argon. 

In 1932 Chadwick proposed a successful alternative hypothesis 



Section 23.4 



55 



about the nature of the radiation. His first published report of his 
hypothesis is reproduced on the next page. In a later, more complete 
paper. "The Existence of a Neutron." he said: 

If we suppose that the radiation is not a quantum radia- 
tion [y ray], but consists of particles of mass very nearly 
equal to that of the proton, all the difficulties connected 
with the collisions disappear, both with regard to their 
frequency and to the energy transfers to different masses. 
In order to explain the great penetrating power of the 
radiation, we must further assume that the particle has 
no net charge. We must suppose it to consist of a proton 
and electron in close combination, the 'neutron' discussed 
by Rutherford in his Bakerian Lecture of 1920. 

Thus, according to Chadwick's hypothesis, when an element 
such as beryllium is bombarded with a particles, a nuclear reaction 
can take place that produces neutrons: 



,He^ 



.Be« 



.€'•' + „n» 



Here, the symbol on^ represents the neutron postulated by Chadwick, 
with zero charge, and mass number equal to 1. Such neutrons then, 
because they have no electric charge, could penetrate bricks of a 
material as dense as lead without giving up their energy. When 
neutrons go through paraffin, there would occasionally be head-on 
collisions with hydrogen nuclei — protons. The recoiling protons 
could then be observed because of the ionization they produce. 
Thus Chadwick's chargeless particle hypothesis could account in a 
qualitative way for the observed effects of the mysteriously 
penetrating radiation. 

His estimate that the particle's mass must be nearly equal to 
the mass of a proton was made by applying the laws of conservation 
of momentum and energy to the case of perfectly elastic collisions - 
simply applying the laws that worked well for the case of interacting 
billiard balls and other objects treated in "classical" physics. In 
a perfectly elastic head-on collision between two bodies, as you saw 
in Chapter 9. almost all of the kinetic energy of the initially moving 
body will be transferred to the initially stationary body only if the 
bodies have approximately equal masses. In collisions that are not 
precisely head-on, less kinetic energy will be transferred. Therefore, 
on the average, a kinetic energy of about 5 MeV for the recoiling 
protons would be about right for collisions produced by neutrons 
with energies about 10 MeV, if the neutron and proton masses were 
approximately equal. 

Chadwick was able to make a more precise calculation of the 
neutron's mass by applying the conservation laws to data on 
collisions wdth nuclei of different masses; the details of the deriva- 
tion are shown on page 57. 

Chadwick found the mass of the neutron to be 1.16 amu. The 
difficulties of measuring the kinetic energies of the recoiling nuclei 
made this only an approximate value, but it was good enough to 




SG 23.5, 23.6 



oC 



TV 



Se 



^'^ 



.- 



Paraffin wax contains 14 hydro- 
carbon compounds ranging from 
CigHsg to 032^68. 



As explained in Text Sec. 14.8, the 
electron-volt (eV) is a unit of energy. 
1KeV=10'eV 

1MeV=10'«V 

1BeV =10'eV 



SG 23.7, 23.8 



312 



NATURE 



[February 27, 1932 



Letters to the Editor 

[The Editor does not hold himself responsible for 
opinions expressed by his correspondents. Neither 
can he undertake to return, nor to correspond with 
the writers of, rejected manuscripts intended for this 
or any other part of Natxjke. No notice is taken 
of anonymous communications.] 

Possible Existence of a Neutron 

It has been shoMni by Bothe and others that 
beryllium when bombarded by a -particles of polonium 
emits a radiation of great penetrating power, which 
has an absorption coefficient in lead of about 0-3 (cm.)"'. 
Recently Mme. Curie-Joliot and M. Joliot found, 
when measuring the ionisation produced by this 
beryllium radiation in a vessel with a thin window, 
that the ionisation increased when matter containing 
hydrogen was placed in front of the window. The 
effect appeared to be due to the ejection of protons 
with velocities up to a maximum of nearly 3x10* cm. 
per sec. They suggested that the transference of 
energy to the proton v as by a process similar to the 
Compton effect, and estimated that the beryllium radia- 
tion had a quantum energy* of 50 x 10' electron volte. 

I have made some experiments using the valve 
counter to examine the properties of this radiation 
excited in beryllium. The valve counter consists of 
a small ionisation chamber connected to an amplifier, 
and the sudden production of ions by the entry of a 
particle, such as a proton or a-particle, is recorded 
by the deflexion of an oscillograph. These experi- 
ments have shown that the radiation ejects particles 
from hydrogen, helium, lithium, beryUiura, carbon, 
air, and argon. The particles ejected from hydrogen 
behave, as regards range and ionising power, like 
protons with speeds up to about 3-2 x 10» cm. per sec. 
The particles from the other elements have a large 
ionising power, and appear to be in each case xwjoil 
atoms of the elements. 

If we ascribe the ejection of the proton to a Compton 
recoil from a quantum of 52 x 10* electron volts, 
then the nitrogen recoil atom arising by a similar 
process should have an energy not greater than about 
400,000 volts, should produce not more than about 
10,000 ions, and have a range in air at N.T.P. of 
about 1-3 nun. Actually, some of the recoil atoms 
in nitrogen produce at least 30,000 ions. In col- 
laboration with Dr. Feather, I have observed the 
recoil atoms in an expansion chamber, and their 
range, estimated visually, was sometimes £t3 much 
as 3 nun. at N.T.P. 

These results, and others I have obtained in the 
course of the v/ork, are very difficult to explain on 
the assumption that the rauliation from beryllium 
is a quantum radiation, if energy and momentum 
are to be conserved in the collisions. The difficulties 
disappear, however, if it be assumed that the rcklia- 
tion consists of particles of mass I and charge 0, or 
neutrons. The capture of the a-particle by the 
Be» nucleus may be supposed to result in the 
formation of a C* nucleus and the emission of the 
neutron. From the energy relations of this process 
the velocity of the neutron emitted in the forward 
direction may well be about 3 x 10* cm. per sec. 
The collisions of this neutron with the atoms through 
which it passes give rise to the recoil atoms, and the 
observed energies of the recoil atoms are in fair 
agreement with this view. Moreover, I have ob- 
served that the protons ejected from hydrogen by the 
radiation emitted in the opposite direction to that of 
the exciting a-particle appear to have a much smaller 
range than those ejected by the forward radiation. 

No. 3252, Vol. 129] 



This eigain receives a simple explanation on the 
neutron hypothesis. 

If it be suppxjsed that the radiation consists of 
quanta, then the capture of the o-particle by the 
Be* nucleus will form a C* nucleus. The maaa 
defect of C* ia known with sufficient accuracy to 
show that the energy of the quantum emitted in this 

frocess cannot be greater than about 14 x 10* volts, 
t is difficult to make such a quantum responsible 
for the effects observed. 

It is to be expected that many of the effects of a 
neutron in passing through matter should resemble 
those of a quantum of high energy, and it is not easy 
to reach the final decision between the two hypo- 
theses. Up to the present, all the evidence is in 
favour of the neutron, while the quantum hypothesis 
can only be upheld if the conservation of energy and 
momentum be relinquished at some point. 

J. Chadwick. 
Cavendish Laboratory, 
Cambridge, Feb. 17. 



Chadwick's first publication of the 
"neutron hypothesis" to explain the 
Joliot-Curie experimental results. 



Determining the Neutron's Mass 



0-^:^ 




n. 



•patacf/k; 



(a) The sketch above represents an elastic 
collision of a neutron (n) and a proton (p). If it 
were a head-on collision, the neutron would 
rebound straight back and the proton would 
be seen to ennerge along the same line. To 
determine the nnass of the neutron, /n^, we 
return to the principles of conservation of 
kinetic energy and conservation of momentum, 
which provide two algebraic equations that must 
both hold. The case is particularly simple if we 
consider a perfectly elastic head-on collision. 
As shown at the right, an expression for the 
proton's recoil speed v'^ can be derived by 
combining the equations algebraically (solving 
the momentum equation for v„, substituting the 
resulting expression for v^ in the energy 
equation, expanding, collecting terms, and 
solving for v'^). However, this expression 
includes the term v„, the neutron's initial speed, 
which cannot be measured directly. We can 
eliminate v^ from the equation by analyzing 
another collision and combining the results with 
what we already have. 




(b) The sketch above represents a perfectly 
elastic collision between a neutron (n) and a 
nitrogen nucleus (A/). When the collision is head- 
on, we can write energy and momentum equa- 
tions similar to what we wrote before, but this 
time leading to an expression for the recoil speed 
of the nitrogen nucleus, v'^. This expression 
also includes the unmeasurable quantity v„. 










I tw. \/^ - m, \ii 













\^ fKj, Z-*^ 



in„ = 






(c) The i/p equation and i/^ equation are 
then combined algebraically (eliminating v„), 
and solved for m^. The expression for m^ now 
contains only terms which can be measured — 
so the mass of the neutron, at?,,, can be 
calculated. Note that we use here nothing but 
the ideas developed for ordinary elastic 
collisions. (See SG 23.7 and 23.8). 



58 



Probing the Nucleus 



The best methods now available 
for determining the neutron mass 
give 1.008665 amu (based on the 
scale C'^ = 12 exactly). 



show that the neutron has a mass very close to that of the proton; 
thus Chadwick's hypothesis did indeed offer a satisfactory solution 
to the problem of the "radiation" emitted when beryllium or boron 
was bombarded with particles. 

Much research has been done since 1932 on the properties of 
neutrons and on the interactions between neutrons and atoms. An 
entire branch of study called neutron physics has been developed. 
Neutron physics deals with the production of neutrons, their 
detection and their interaction with atomic nuclei and with matter 
in bulk. This research has led, among other things, to the discovery 
of nuclear fission, to be discussed in Chapter 24. 

Q5 Why could the penetrating radiation from bombarded 
beryllium not be considered y rays? 

Q6 Why did the mass of a neutron have to be found by 
measurements on protons the neutrons ejected in collision? 

Q7 How could the principles of conservation discussed in Unit 
3 be used to find the mass of the neutron? 






ypC 






■f>ro'ton 



OC- 



pat 



•iicle 



See models of the nucleus in Unit 6. 



SG 23.9, 23.10 



23.5 The proton-neutron theory of the composition of atomic nuclei 

The discovery of the neutron, with an atomic mass close to one 
unit and with no electric charge, confirmed Rutherford's suggestion 
that the atomic nucleus is made up of protons and neutrons. This 
hypothesis was soon used as the basis of a detailed theory of the 
nucleus by Heisenberg in 1932, and is still the basis of attempts 
to describe the properties and structure of the nucleus. According 
to the proton-neutron hypothesis, the nucleus of an atom having 
atomic number Z and mass number A consists of Z protons and 
A — Z neutrons. The nuclei of the isotopes of a given element differ 
only in the number of neutrons they contain. Thus the nucleus of 
the hydrogen isotope of mass number 1 contains one proton; the 
nucleus of the hydrogen isotope of mass number 2 contains one 
proton and one neutron (that nucleus is called a deuteron). The 
nucleus of the neon isotope Ne-" contains 10 protons and 10 
neutrons, while that of Ne^^ contains 10 protons and 12 neutrons. 
The atomic number Z identified with the charge in the nucleus, 
is the number of protons in the nucleus. The mass number A is 
the total number of protons and neutrons. If we use the term 
nucleons to refer to both kinds of nuclear particles, then A is 
simply the number of nucleons. 

Is the proton-neutron hypothesis for the structure of nuclei fully 
consistent with the facts of radioactivity, such as a and /3 emission 
and the transformation rules? If two protons and two neutrons 
could combine, the resulting particle would have Z = 2 and A = 4, 
just the properties of the a particle. The emission of two protons 
and two neutrons (in the combined form of an a particle) would be 
consistent with the first transformation rule of radioactivity. (The 
a particle might exist as such in the nucleus, or it might be formed 
at the instant of emission; the latter possibility is now considered 



Section 23.6 59 

more likely.) But if the nucleus consists of protons and neutrons, 
where could a (3 particle come from? This question is more difficult 
to answer than that of the origin of an a particle. The second 
transformation rule of radioactivity provides a clue: when a nucleus 
emits a fi particle, its charge Z increases by one unit while its mass 
number A remains unchanged. This would happen, if a neutron 
were to change into a proton and a /3 particle. 

This idea was not a return to the proton-electron hypothesis 
discussed in Sec. 23.2. Physicists had already come to the conclusion 
that electrons are not present in the nucleus, so jS decay was not 
considered to be a simple separation of a proton and electron; it 
would have to be a transformation of a neutron that created a 
proton and electron. However, there were additional experimental 
data that raised difficulties for such a simple transformation idea. 

Q8 According to the proton-neutron theory of the nucleus, 
what is in the nucleus of yN'"*? 

Q9 Describe an ordinary helium atom in terms of the three 
elementary particles: the proton, the neutron, and (outside the 
nucleus) the electron. 

Q1 If nuclei do not contain /3 particles, how can /3 emission 
be explained? 



23.6 The neutrino 

The description of jS decay in terms of the transformation of a 
neutron in the nucleus is part of one of the most fascinating stories 
in modem physics: the prediction and eventual discovery of the 
particles called the neutrino and the antineutrino. Quantitative 
studies of the energy relations in /3 decay during the 1920's and 
1930's raised a difficult and serious question. Methods were devised 
for determining the energy change in a nucleus during f3 decay. 
According to the principle of conservation of energy, the energy lost 
by the nucleus should be equal to the energy carried off by the /3 
particle. But, the kinetic energy of the (3 particles had a whole range 
of measured values, all smaller than the amount of energy lost by 
the nucleus: some of the energy lost by the nucleus seemed to have 
disappeared. Measurements made on a large number of /3-emitters 
indicated that on the average about two-thirds of the energy lost by 
the /3-decaying nuclei seemed to disappear. Attempts to find the 
missing energy failed. For example, some physicists thought that 
the missing energy might be carried off by y rays; but no such y 
rays could be detected experimentally. The principle of conservation 
of energy seemed to be violated in ^3 decay. Similar discrepancies 
were found in measurements of the momentum of the emitted 
electron and the recoiling nucleus. 

As in the case of the experiments that led to the discovery of 
the neutron, physicists tried very hard to find an alternative to 
accepting the failure of the principles of conservation of energy and 



60 



Probing the Nucleus 






® 



® 



— Y .1 

P2 



We now know that a free neutron — 
a neutron separated from an atom — 
sooner or later decays into a proton, 
an electron, and a neutrino. (The 
half-life of a beam of free neutrons 
has been measured to be 12 
minutes.) 




The first detection of neutrinos was 
in this tank. Reactions provoked by 
neutrinos cause flashes of light in 
the liquid with which the tank is filled. 
The flashes are detected by the photo- 
electric tubes which stud the tank wall. 
This work was done by two American 
physicists, Clyde Cowan and Fred- 
erick Reines. 



momentum. The Austrian physicist Wolfgang Pauli suggested in 
1933 that another, hitherto unnoticed particle, is emitted in /3 decay 
along with the electron, and that this particle carries off the missing 
energy and momentum. This hypothetical particle could have no 
electric charge, because the positive charge of the proton and the 
negative charge of the ft particle together are equal to the zero 
charge of the original neutron. The mass-energy balance in the 
decay of the neutron indicated that the rest mass of the hypothetical 
particle should be very small — much smaller than the mass of an 
electron, and possibly even zero. The combination of zero electric 
charge, and zero or nearly zero mass, would make the particle 
extremely hard to detect. 

The Italian physicist Enrico Fermi called the suggested particle 
the neutrino ("little neutral-one" in Italian). In 1934 Fermi 
constructed a theory of fi decay based on Pauli's suggestion. This 
theory has been successful in describing all the known facts of /3 
decay. From 1934 on, the neutrino was accepted as a "real" particle 
for two reasons, both theoretical: it saved the principle of conserva- 
tion of energy in /3 decay, and it could be used successfully both 
to describe the results of experiments in ^3 decay and to predict the 
results of new experiments. (See "Conservation Laws" in Reader 6.) 

Many unsuccessful attempts were made to capture neutrinos 
over a period of 25 years. Finally, in 1956, neutrinos were detected 
in an experiment using the extremely large flow of neutrinos that 
comes out of a nuclear reactor (see Chapter 24). The detection of 
neutrinos is an indirect process that involves detecting the products 
of a reaction provoked by a neutrino. The reaction used was a 
reverse /3 decay — the production of a proton from a neutron. Because 
the proper meeting of a proton, an electron, and a neutrino at the 
same place and same time is an exceedingly unlikely event — and 
the resulting neutron difficult to detect — "catching" the neutrinos 
required a very elaborate and sensitive trap. (See photo at the left.) 
Again the faith of physicists in the principle of conservation of 
energy was justified. 

There is one more complication: it is now known that there are 
several kinds of neutrinos. The one involved in p decay (as 
discussed so far) is now referred to as an anti-neutrino, and is 
denoted by the symbol T> (Greek letter "nu" with a bar over it). The 
transformation of a neutron during jS-emission is then written: 

,n" » ,p' + _,e» + P 



Q1 1 Why was an almost undetectable particle invented to 
patch up the theory of /3 decay? 



23.7 The need for particle accelerators 

Up to 1932 the study of nuclear reactions was limited by the 
kind of projectile that could be used to bombard nuclei: only a 
particles from the naturally radioactive nuclides could bring about 



Section 23.7 



61 



reactions. Progress was limited because a particles could be 
obtained only in beams of low intensity and with fairly low kinetic 
energies. These relatively low-energy particles could produce 
transmutations only in light elements. When heavier elements are 
bombarded with a particles, the repulsive electric force exerted by 
the greater charge of the heavy nucleus on an a particle makes it 
difficult for the a particle to reach the nucleus. The probability of a 
nuclear reaction taking place becomes very small or zero. But 
because the interest in nuclear reactions was great, physicists in 
many countries sought methods of increasing the energy of charged 
particles to be used as projectiles. 

There were advantages to be gained in working with particles 
that have only one positive charge — the proton or the deuteron (the 
nucleus of the deuterium or heavy hydrogen atom). Having but a 
single charge, these particles would experience smaller repulsive 
electric forces than would a particles in the neighborhood of a 
nucleus, and thus would be more successful in getting close enough 
to produce transmutations — even of heavy (and therefore high- 
charge) target nuclei. Protons or deuterons could be obtained from 
positive-ray tubes, but their energies were rather low. Some device 
was needed to accelerate these particles to higher energies, as 
Rutherford was among the first to ask (see p. 57). Such devices 
might also offer other advantages: the speed (and energy) of the 
bombarding particles could be controlled by the experimenter; and 
very intense projectile beams might be obtained. It would then be 
possible to find how nuclear reactions depend on the energy of the 
bombarding particles. 

Since 1930, many devices for accelerating charged particles 
have been invented and developed. In each case, the particles used 
(electrons, protons, deuterons, a particles or heavy ions) are 
accelerated by an electric field. In some cases a magnetic field is 
used to control the path of particles, that is, to steer them. The 
simplest type (hke the Van de Graaff machine shown at the right) 
has a single high- voltage step — these cannot be practically operated 
above about 10 million volts, so they cannot be used to increase 
electron or proton energies above about 10 MeV. 

Another type (like the Linac on p. 62) has a long series of low 
voltage steps — some of these produce electron energies up to 20 
BeV. A third general type uses magnetic fields to hold the particles 
in a circular path, returning them over and over to the same low- 
voltage accelerating fields. The first machine of this type was the 
cyclotron (see the photograph on p. 48). Other circular types are 
illustrated on pp. 62 and 63. The most recent of these will produce 
7 BeV electrons or 500 BeV protons! Accelerators have become 
basic tools for research in nuclear and high-energy physics; their 
operation, and the way a typical recent experiment was actually 
done, are the subject of the two Project Physics films, Synchrotron, 
and People and Particles. Also, accelerators are used in the 
production of radioactive isotopes, and serve as radiation sources 
for medical and industrial purposes. 




First stage of a 750-kilovolt proton 
accelerator. 




A Van de Graaff generator, built on a 
vertical axis. 



SG 23.16 



See "The Evolution of the Cyclo- 
tron" and "The Cyclotron as Seen 
by . . ." in Reader 6. 





a and b: outside and inside the Stanford "Linac" (linear 
accelerator). 



c and d: outside and inside the CERN proton-synchrotron 
at Gene va. (See "CERN" in Reader 6.) The evacuated ring 
in which the protons are accelerated is at the upper left of 
photograph d. 



e: the Brookhaven Cosmotron, in operation from 1952 
to 1967, and now superceded by larger accelerators at 
Brookhaven. 



TYPE 



Major Types of Particle Accelerators 

PRINCIPLE OF OPERATION MAXIMUM ENERGY PARTICLES 



NOTES AND EXAMPLES OF USE 



ONCE-THROUGH ACCELERATION 



Cockcroft- 


direct high voltage 


= 4 MeV 


various 


Walton 


potential 






Van de Graaff 


high voltage by transport 


-3 MeV 


electrons 


generator 


of charges on moving belt 


- 14 MeV 


protons 


Linear 


successive application of 


- 10 MeV 


heavy ions 


accelerator 


high frequency voltages 


per particle 




Linear 


pulsed high frequency 


- 20 BeV 


electrons 


accelerator 


wave 







commercially available 



commercially available 



Lawrence Radiation Laboratory 
and Yale University 

Stanford University, 
two miles long 



CYCLIC ACCELERATION 



Betatron 



Proton 
synchrotron 



magnetic induction 
(electrons in an evacuated 
tube accelerated by variable 
field of electromagnet) 



= 300 MeV 



orbiting in variable mag- 
netic field 

synchronized voltage of 
high frequency applied to 
particles orbiting in variable 
magnetic field 



12 BeV 



electrons 



Cyclotron 


voltage of constant fre- 
quency applied to particles 
in fixed magnetic field 


- 12 MeV 

- 24 MeV 
= 48 MeV 


protons 

deuterons 

He-nuclei 


Synchro- 
cyclotron 


voltage of variable fre- 
quency applied to particles 
in fixed magnetic field 


- 750 MeV 


protons 


Electron 
synchrotron 


voltage of constant fre- 
quency applied to particles 


-7 BeV 


electrons 



protons 



largest machine is at 
University of Illinois 



commercially available; 
numerous installations, includ- 
ing some built by students at 
high schools 

184-inch unit at Lawrence 
Radiation Laboratory, Berkeley 



Hamburg, Germany (7.5 BeV); 
Cambridge Electron Accelerator 
(6 BeV) operated by Harvard 
and M.I.T. 

6.2 BeV "Bevatron" at Lawrence 
Radiation Laboratory; 3 BeV 
Cosmotron at Brookhaven; 3 BeV 
at Princeton: and 12.5 BeV syn- 
chrotron at Argonne National 
Laboratory 



Alternating 
gradient 
synchrotron 



Strong-focusing 
synchrotron 



same as synchrotron 
except successive seg- 
ments of magnetic field 
have opposite curvature 



= 30 BeV 



= 76 BeV 



500 BeV 



protons Brookhaven National Laboratory 

(Long Island), and CERN, 
Switzerland (where a 300 BeV 
accelerator is in design stage) 

protons Serpukhov, U.S.S.R. (Also a 

1000 BeV accelerator in design 
stage) 

protons Enrico Fermi Laboratory, Bata- 

via, Illinois (in construction) 



Section 23.7 



65 



The table on p. 64 summarizes the major types of particle 
accelerators now being used or planned. One of the latter is a 200 
to 500 BeV particle accelerator being built for completion in about 
1973 or 1974. It is being paid for with approximately $240 million 
appropriated from public funds through the Atomic Energy 
Commission. Such "machines" are among the most complex and 
grandiose structures ever built by man. Indeed, they are monuments 
to his imagination and ingenuity, his ability to reason and to 
collaborate in groups on peaceful projects that further the under- 
standing of nature. Basically, the "machines" are tools to help us 
find out as much as we can about the structure of nuclear particles 
and the forces holding them together. 

With the discovery of the neutron in 1932 it was believed that 
three "elementary" particles act as the building blocks of matter: 
the proton, the neutron, and the electron. We have mentioned the 
existence of new particles, such as neutrinos and antineutrinos. As 
high-energy accelerators became available, additional "elementary" 
particles were discovered, one after another. On page 175 is a 
list of some of these particles; they are grouped into "families" 
according to their properties. Most of these particles exist only 
briefly — typical lifetimes are of the order of 10~^ second or less. 
A whole new field, high-energy physics, has evolved, and the aim 
of the high-energy physicist of today is to discern the order and 
structure behind the large number of "elementary" particles that 
have been discovered. 

How do we detect these particles? We have already mentioned a 
number of methods by which we can observe and measure radio- 
active emissions. They include the electroscope and the electrometer 
employed since the early days of radioactivity, the Geiger counter 
(see Text Sec. 19.3), and the Wilson cloud chamber. In addition we 
now have various types of ionization chambers, scintillation 
counters, photographic emulsions (see "The Tracks of Nuclear 
Particles" in Reader 6), semiconductor devices, spark chambers 
(see "The Spark Chamber" in Reader 6), and bubble chambers 
(some of which are displayed on the next two pages). One of the 
supplemental units in the Project Physics Course, entitled 
Elementary Particles, further describes in detail the devices, 
and the discoveries made with them. 

Q12 Why can low-energy a particles cause transmutations only 
in nuclei of relatively small atomic number? 

Q1 3 Why are protons more effective projectiles for producing 
nuclear reactions than are a particles or heavy ions? 

Q14 What are some of the devices for producing high-energy 
particles to be used as projectiles? What are some devices for 
detecting nuclear reactions induced by such projectiles? 

The top photograph shows C. T. R. Wilson's cloud chamber. (See also p. 52.) 
The middle photograph shows particle tracks in a cloud chamber. (The posi- 
tively and negatively charged ions had separated before the cloud was formed, 
so the track shows up as two vertical streaks.) In the bottom photograph high 
voltages between the plates in a spark chamber cause sparks to jump along 
the ionized trails left by high-energy charged particles. 






Above: The tiny bubble chamber, 3 cm long, 
invented by D. A. Glaser in 1952. (Note the 
particle track.) Glaser was 26 at the time, 
and later was awarded the Nobel Prize for 
his invention. 

Below: the 200-cm Bubble Chamber Assem- 
bly at the Brookhaven National Laboratory. 
Right: The viewing of a projected, enlarged 
photograph made of particle tracks in a 
bubble chamber. 






The bubble chamber photo at the left illustrates 
one of the major discoveries of modern physics, 
the interconversion of energy and matter (to be 
discussed in Chapter 20.) The diagram at the 
right shows the significant tracks recorded in 
the photo. In the upper left, an electron-positron 
pair is formed by a gamma ray (not visible in 
bubble chamber pictures) interacting with a 
hydrogen nucleus. (The discovery of positrons 
is described briefly on p. 70.) An applied mag- 
netic field causes the electron and the positron 
to be deflected in opposite directions. (In what 
direction was the magnetic field?) 
In the lower left of the same photo a gamma ray 
forms another electron-positron pair; the ad- 
ditional electron (third track, upward) was 
knocked out of a hydrogen atom during this 
process. 

The bubble chamber photo was taken in a 10" 
liquid-hydrogen bubble chamber at the Law- 
rence Radiation Laboratory of the University 
of California. The chamber is shown below at 
the left, with the liquid nitrogen shield removed. 
The accompanying diagram at the right gives 
some of the details of the bubble chamber and 
its auxiliary equipment. 





EXPANSION TANK [-1^ EXPANSION VALVE 



i VENT 




COiN^PRESSOR 
RECOMPR"iSSlON' 

TANK - LNj 
TO VACUUM PUMP_ 

LIQUID Nj JACKET 

VACUUM TANK — 

LIQUID Hj FLASK 

EXPANSION LINE 

HEAT LEAK 

RADIATION SHIELD 

AT LIQUID Nj 

TEMPERATURE 

HEATERS 
SH UTTER 

LIGHTS 



BEAM 



68 



Probing the Nucleus 



23.8 Nuclear reactions 



We discuss the transmutation into 
gold only as an example of a nuclear 
reaction; a more. useful reaction is 
the transmutation of gold into some- 
thing else— for example: 



7,^u'"' + „n' 



„Hg"« + _,e" 



This reaction can be used to obtain 
pure samples of a single mercury 
isotope. (It's alchemy turned 
upside down.) 



@ 




The development of the cyclotron and other particle accelerators 
led to great advances in the study of nuclear reactions. Nearly all 
of the stable nuclides have now been bombarded with protons, 
deuterons, a particles, neutrons and y rays, and hundreds of nuclear 
reactions have been examined. Examples of reactions induced by 
a particles and protons have already been discussed. 

Since the first known alchemical writings during the third or 
fourth centuries a.d., and throughout the historical development 
of chemistry, the dream of transmuting materials (usually into gold) 
has always haunted some people. In most nuclear reactions one 
element is indeed changed into another: so in a sense the ancient 
dream of the alchemist has come true. But it is unhkely to make 
a fortune for anyone. It is possible to transmute various elements 
into gold, but such transformations are of course completely 
different, both in method and purpose, from the attempts of the 
ancient alchemists. (Moreover, they are all entirely uneconomical 
methods for "making gold.") 

Gold has only one stable isotope found in nature — ygAu'^"; other 
gold isotopes can be made, but are radioactive. We can also 
illustrate two types of nuclear reactions induced by deuterons, 
both resulting in the stable isotope of gold: 



,W + «oHg' 



,H2 + ,«Pt' 



»Au' 



,He^ 



9Au'«^ + on^ 



In both cases we need an accelerator to produce high-energy 
deuterons; in bombarding a mercury isotope we produce a particles 
besides our desired gold. In bombarding platinum we produce 
neutrons in addition to the gold. 

The last reaction, in which a neutron was produced, is an 
example of reactions which have become especially important 
because of the usefulness of the neutrons. Neutrons can be 
produced when nuclei are bombarded with protons, deuterons, or 
a particles, as in the reactions: 



,Ni= 



.H> 



,Cu= 



,C'^ + .H^ 



7N'3 + on' 



4Be» + zHe^ 



X' 



The neutrons produced by such bombardment can, in turn, be 
used to induce other nuclear reactions. As we noted before, neutrons 
are especially effective as "bullets," because they have no electric 
charge. They are not subject to repulsive electrostatic forces in the 
neighborhood of a positively charged nucleus, and are therefore 
more likely to penetrate nuclei than are protons, deuterons, or 
a particles. 



Section 23.8 



69 



Because of the neutron's lack of electrical charge, many more 
reactions have been induced by neutrons than by any other kind of 
particle. Enrico Fermi was the first to undertake a systematic 
program of research involving the use of neutrons as projectiles 
in nuclear reactions. Starting in 1934, he and his group bombarded 
many elements, from the lightest to the heaviest, with neutrons, 
and studied the properties of the nuclides produced. The research 
described in the Prologue to Unit 1 was done as part of this program. 

A typical neutron-induced reaction, again one resulting in 
gold, is: 



oil -r soiig 



gAu'^^ + ,H2 



In another, a very common type of neutron-induced reaction, 
the neutron is captured and a y ray is emitted, as in the following 
example: 



,Pt' 



^Pt'97 + y 



Note that since there is no change in the atomic number, the 
element here remains the same. An isotope of the target nucleus is 
produced with a mass number greater by one unit than that of the 
target nucleus. The new nucleus so produced has more energy than 
it needs to be stable, and is said to be produced in an "excited state." 
It returns to its lowest energy state by emitting one or more y rays. 
Some nuclei can also undergo reactions when bombarded with 
y rays; an example, for illustration's sake once again resulting in 
gold, is the reaction: 



y 



oHg' 



,Au'«^ + ,H' 



In this case, the energy of the y ray excites the mercury target 
nucleus which becomes unstable, ejects a proton, and thereby 
becomes a gold nucleus. 

The amount of gold that can be produced by the above reaction 
is very small; we have simply tried to illustrate some typical 
artificial transmutations. The examples we have given barely 
suggest the rich variety of such reactions that have been observed. 
The products of these reactions may change as the energy of the 
bombarding particles changes. Nuclear reactions are important, 
not only because they indicate our ability to produce new nuclides, 
but also because they provide important data about nuclear 
structure. A model of nuclear structure, to be successful, must 
enable us to predict the results of these nuclear reactions, just as 
a successful model of atomic structure must allow us to predict 
the results of chemical reactions. 

What property of neutrons makes them particularly useful 
for producing nuclear reactions? 

Q16 Complete the following equation for a nuclear reaction: 

13AI" + ,H2 > on' + , Si^ 





■w ' 




\\ 




^ W 


\ 
• 


. \^ 


\ 1 

\ 

\ 


\ 


^\^ '' ■^T 



In this bubble chamber picture, a 
neutron is produced at the bottom, 
at the end of the 2" long track, near 
the -I- mark. This neutron in turn causes 
a reaction near the center of the plate. 
(Neutral particles do not leave tracks 
in bubble chambers.) 




SG 23.11 
SG 23.12 



70 



Probing the Nucleus 



23.9 Artificially induced radioactivity 




One of the earliest records of a 
"shower" of electrons and positrons; 
it shows their tracks curving in op- 
posite directions in a strong magnetic 
field. The shower was caused by 
cosmic rays, and was recorded in a 
Wilson cloud chamber, taken to an 
altitude of 4.3 km. 



In the discussion of nuclear reactions so far we have only 
hinted at an interesting discovery. We have shown in the last section 
that the capture of a neutron by platinum 196 results in platinum 
197 and the emission of a y ray. As is listed in the table on p. 42, 
six different isotopes of platinum are found in nature — but platinum 
197 is not among these. The question arises: is platinum 197, 
produced by neutron capture, stable? The answer is no; it is radio- 
active and decays by the emission of a )3 particle to gold 197 (the 
only stable gold isotope): 



«Pt> 



9Au'^^ + _,e« + i^ 



The half life of platinum 197 is 20 hours. 

The production of radioactive platinum 197 in a nuclear 
reaction is an example of artificially induced radioactivity. This 
phenomenon was discovered in 1934 by Irene Curie and F. Joliot. 
They were studying the effects of a particles on the nuclei of light 
elements. When they bombarded boron, magnesium, and aluminum 
with a particles from polonium, they observed the immediate 
ejection of protons and neutrons from the bombarded nuclei, as 
expected. But, in addition to these particles, positive electrons, or 
positrons, also were observed to be emitted. The positron is a 
particle whose mass is the same as that of the electron, and whose 
charge has the same magnitude but opposite sign to that of the 
electron. 

The positron had been discovered earlier by the American 
physicist C. D. Anderson in 1932 while studying cosmic rays. 
(Cosmic rays are highly penetrating radiations which originate 
outside the earth and consist of protons, electrons, neutrons, photons, 
and other particles.) Employing a cloud chamber situated in a 
magnetic field, Anderson observed some tracks which, judged by 
the density of ionization along the track, could have been produced 
only by high-speed particles having the same mass and magnitude 
of charge as an electron; but the curvature was opposite in direction 
to that of high-speed electron tracks. Anderson concluded that the 
particles producing them must have been positively charged 
electrons, to which the name positron was given (symbol jS*, or iC"). 

In the Joliot-Curie experiment, the production of positrons along 
with neutrons as a result of the bombardment of a light element 
with (X particles seemed to indicate that a new type of nuclear 
reaction was occuring. Further experiments by this couple showed 
that the light-element targets continued to emit positrons, even 
after the source of the a particles had been removed. When the rate 
of emission of the positrons was plotted against time elapsed since 
removal of the a particle source, curves were obtained, for each 
target, similar to the curves obtained in natural /8 radioactivity. 
(The half-life of the emitter was found to be 2.5 min). The results 
seemed to show that an initially stable nuclide had been changed 
into a radioactive one. In the case of the bombardment of 13AI" 
by a particles, which produced neutrons as well as a new radio- 



Section 23.9 



71 



active material, a nuclear reaction would produce a nuclide of 
mass number 30 (= 27 + 4 - 1) and atomic number 15 (^ 13 + 2 - 0) 
— hence an isotope of phosphorus. The reaction would be: 



oAV' + Me' 



„1 _L. p30 



Curie and Joliot ran chemical separations similar to those 
made in the study of the naturally radioactive elements, and 
showed that the target, after bombardment, indeed contained a 
small amount of phosphorus, and an isotope that was radioactive. 
Now, phosphorus occurs in nature only as isP^^ no isotope of 
phosphorus with mass number 30 had ever been found to occur 
naturally. It was reasonable to suppose that if P^*' were made in a 
nuclear reaction, it would not be stable but radioactive. If it decayed 
by emission of a positron, that reaction would be expressed in 
the following manner: 

i5P3« > i.Si^o + ,e^+v 




Irene Curie and F. Joliot in their lab- 
oratory. They were married in 1926. 
In 1935 they shared the Nobel Prize 
for chemistry. 



where nSi^" is a known isotope of silicon, ie° represents a positron 
and i^ is a neutrino. 

This kind of decay implies that a proton in the nucleus may be 
transformed into a neutron that remains in the nucleus, a positron 
that is emitted, and a neutrino: 



iP' 



nn' + ,e«+ V 



In sum, after the discovery that the bombardment of light 
nuclides by a particles can lead to radioactive products, it was 
found that nuclear reactions induced by protons, deuterons, 
neutrons and photons can also result in radioactive products. As in 
the case of the natural radionuclides, an artificial radionuclide can 
be characterized by its half-life and the type of radiation it emits. 
When the products of nuclear reactions are radioactive they can be 
traced in chemical separations by means of their characteristic 
half-lives or decay products. (They can not be traced chemically 
because very small amounts are involved — often less than a 
millionth of a gram.) The special branch of chemistry that deals 
with the separation and identification of the radioactive products 
of nuclear reactions is called radiochemistry, and has become an 
important part of nuclear science. The breadth of this field is 
indicated by the fact that since 1935 about 1200 artificially radio- 
active nuclides have been made and identified, many of which are 
in use in research and industry. 



Among the various modes of decay 
of artificial radioactive nuclides are 
tt, /i", (3*, y emissions and capture 
of an orbital electron by the nucleus. 



SG 23.13-23.16 



Q17 Complete the following equation for a positive /3-decay: 

^Ni3 . ,e»+??- 

How many neutrons and protons were there in the nitrogen 
nucleus before decay? How many in the resulting product nucleus 
afterward? 



23.1 The Project Physics learning materials 
particularly appropriate for Chapter 23 include 
the following: 

Activity 

Neutron Detection Problem Analogue 

Film Loop 

Collisions With an Object of Unknown Mass 

Films 

People and Particles 

Synchrotron 

Reader Articles 

Some Personal Notes on the Search for the 

Neutron 
Antiprotons 

The Tracks of Nuclear Particles 
The Spark Chamber 
The Evolution of the Cyclotron 
The Cyclotron As Seen By . . . 
CERN 

Conservation Laws 
The Fall of Parity 
Can Time Go Backward? 
Particle Accelerators 

23.2 Why would it be difficult to explain the 
nucleus of 92U-^'' as a mixture of alpha particles 
and electrons? 

23.3 On the basis of the proton-electron hypothesis 
of nuclear composition, how many protons would 
you expect to find in the 92U^'" nucleus? How 
many electrons? 

23.4 Complete the following nuclear equations: 

(a) sB'" +.,He' » ( ) + ,H' 

(b) iiNa^'-' + ^He^ >{ ) + ,H' 

(c) ,3AP^ +,He^ >( ) + ,H' 

(d) ( ) + ,He' > ,-CF +,H' 

(e) ( ) + ,He' ^,„Ca^^+,H' 

23.5 Complete the following nuclear equations: 

(a) 3Li« +,H' ^^He^ +( ) 

(b) ^Be" +,H' >.,He^ +( ) 

(c) ,Be» +,H' >( ) + ,W 

(d) ,B" +,He' ^jN" +( ) 

23.6 Complete the following nuclear equations 
(consult periodic table of elements for atomic 
numbers of indicated nuclides): 

(a) Al" + „n' * AP +( ) 

(b) AF + ,H-^ * ,H' +( ) 

(c) A1" + ,H' »,He^ + ( ) 

(d) AF + ,H^ ^^He-i + C ) 

What aspect of nuclear reactions do equations 
(b) and (d) illustrate? 



23.7(a) Explain briefly why the maximum speed 
gained by nitrogen nuclei in collisions with 
neutrons is roughly 10 times less than that gained 
by hydrogen nuclei in collisions with neutrons? 

(b) Where in this course was the physics 
needed for this problem first developed? 

23.8 One major disadvantage of indirect methods 
of measurement is that the experimental un- 
certainty is often larger. If Chadwick had 
measured a maximum speed of 3.2 x 10" cm/sec 
for hydrogen nuclei (a change of only 3%), and 
4.7 X 10** cm/sec for nitrogen nuclei (no change), 
what would be the calculated mass of the neutron? 
By what percentage would the calculated mass of 
the neutron change due to the 3% shift in the 
speed measurement. 

23.9 Indicate the mass number A, the atomic 
number Z, the number of protons and the number 
of neutrons for each of the following nuclei: 
(Make a similar table in your notebook if you may 
not write in this book.) 









number of 


number of 


A Z protons 


neutrons 


H' 










H^ 










He^ 










Li^ 










C13 










TJ238 










Th-^-"' 










Th""' 










pb2H 










Pb206 











23.10 How many electrons are there in a neutral 
atom of 

(a) platinum 196? 

(b) gold 198? 

(c) mercury 198? 

(d) mercury 199? 

23.11 Complete the following nuclear reaction 
equations: 

(a) ,,Na-^=' + ,H- * ,H' +( ) 

(b) ,,Na--'+„n' > y +( ) 

(c) ,.,Mg^-' + „n' >,H' +( ) 

(d) ,.,Mg^'« + ,H- > .He' + ( ) 

What aspect of nuclear reactions do these 
equations illustrate? 

23.12 Describe the following reactions in luords: 
,3AF + on' *,2Mg-^^ + ,H'. 

i^Mg-^' > ,3A1-" + _,e« +u + y(,Ti = 9.5 min) 



72 



23.13 It is often necessary to infer information 
in the absence of direct evidence. Thus when a 
hunter following the tracks of a rabbit in the 
snow finds that the tracks suddenly stop with no 
evidence of other tracks or of hiding places, he 
may infer something about the possible presence 
of owls or eagles. 

The bubble chamber photograph at the right 
shows, among other things, the tracks of two 
nuclear particles that originate or terminate at a 
point in the lower center. Describe interactions 
that might occur at that point in terms of your 
knowledge of the law of conservation of 
momentum. 

23.14 How may the discovery of artificially 
radioactive nuclides have helped the development 
of theories of nuclear structure? 

23.15 If you have seen one or more of the films 
Synchrotron, People and Particles, and The 
World of Enrico Fermi, write an essay on either 

(a) the way research teams work together in 
modern high-energy physics, or 

(b) the reasons why some parts of modern 
experimental physics require large "machines" 
to do research, or 

(c) why in many major countries millions of 
dollars of public money are appropriated to buOd 
and run these machines. 



\ - 


■, ' 

\\ \ 




\ 


\\\ •■ 


1 1 \/ 


\ 

1 >. 


1 , » 1 

w \ 




• 




\ 

d - 


^B 




V 


1 


■ \ \ \\\ 


, -.iA 


. • >- \ \ \\ \ 1 \ 



23.16 Compare the mass of a neutral hehum 
atom with the sum of the masses of four hydrogen 
nuclei plus two electrons outside (to get a neutral 
helium atom). What conclusions do you draw? 



73 



24.1 Conservation of energy in nuclear reactions 75 

24.2 The energy of nuclear binding 76 

24.3 Nuclear binding energy and stability 77 

24.4 The mass-energy balance in nuclear reactions 79 

24.5 Nuclear fission: discovery 81 

24.6 Nuclear fission: controlling chain reactions 84 

24.7 Nuclear fission: large-scale energy release and some 

of its consequences 88 

24.8 Nuclear fusion 95 

24.9 Fusion reactions in stars 97 

24.10 The strength of nuclear forces 99 

24.11 The liquid-drop nuclear model 100 

24.12 The shell model 102 

24.13 Biological and medical applications of nuclear physics 103 




CHAPTER TWENTY-FOUR 



Nuclear Energy; Nuclear Forces 



24.1 Conservation of energy in nuclear reactions 



In the discussion of nuclear reactions in the last chapter, the 
emphasis was on the transformations of nuclei and on the properties 
of the nuclides formed. But there is another property of these 
reactions that is important — the absorption or release of energy. 

You know that in some chemical reactions energy must be 
supplied from the outside to keep the reaction going, while in others 
energy is liberated. The formation of water from oxygen and 
hydrogen is an example of a reaction in which energy is liberated; 
the reaction between these two gases is usually violent, and heat is 
given off. We may conclude that the water which is formed has less 
energy than did the substances of which the water is made. On the 
other hand, when water is decomposed by electrolysis, electrical 
energy must be supplied by passing a current through the water, 
and the products of the reaction — the oxygen and hydrogen liberated 
— have more energy than the water. 

Nuclear reactions too may absorb energy, or liberate energy. 
One main reason for the interest in nuclear reactions is the fact 
that the amount of energy absorbed or liberated per nucleus 
involved can be greater by a factor of a million or more than the 
amount involved per atom in a chemical reaction. Nuclear fission 
and nuclear fusion (discussed later in this chapter) are two special 
kinds of nuclear reactions in which the energy release is excep- 
tionally large; hence these types of reactions have made them 
important in industrial and military applications. 

Since there is an equivalence between mass and energy, a large 
release of energy in a nuclear reaction will be accompanied by 
corresponding changes in the total rest mass of the interacting 

In this nuclear-electric power plant, a controlled 
fission reaction inside the domed housing sup- 
plies heat energy for operation of a steam tur- 
bine which drives an electrical generator. 

75 



SG 24.1 



In both kinds of chemical reactions, 
we neglect the small amount of 
energy that may be required to 
trigger the reaction. 



It would be a good idea to reread 
Sec. 20.1 in Unit 5, to review the 
relativistic relationship of mass and 
energy. Two important ideas for this 
chapter are: (a) the mass of a 
moving body is greater than the rest 
mass by KE/c-, and (b) a body at 
rest has an energy of m„c-. 



76 



Nuclear Energy, Nuclear Forces 



nuclei. Therefore the relation of £ = mc- plays an important part in 
interpreting nuclear reactions. 

In this chapter we shall examine the mass and energy relations 
in nuclear reactions. This study will show how some of the ideas 
and experimental information of the last three chapters are linked 
together. 

Q1 Is energy always liberated in a nuclear reaction? 



As early as 1927 Aston concluded 
from his measurements with a mass 
spectrograph that when two light 
nuclei combine to form a heavier 
one, the new nucleus weighs less 
than the sum of the original ones. 



The energy equivalent of 1 atomic 
mass unit: 

1 amu = 1.66 X 10 -"kg 
A£ = Amc2 

= (1.66 X lO-"kg) X (3 X lO'^m/sec)- 

= 14.9 X 10-" joules 

But 1 MeV = 1.60 X lO"'- joules 



.-_ 14.9 X 10" joules 

1.6 X 10 '^ joules/MeV 
= 931 MeV 



SG 24.2 



24.2 The energy of nuclear binding 

Our concepts of atomic and nuclear structure — that an atom 
consists of a nucleus surrounded by electrons and that the nucleus 
is made up of protons and neutrons — led to a fundamental question: 
is the mass of a neutral atom equal to the sum of the masses of the 
protons, neutrons, and electrons that make up the neutral atom? 
This question can be answered precisely because the masses of the 
proton, the neutron, and the electron are known, as are the masses 
of nearly all the atomic species. A survey of the known atomic 
masses shows that, for each kind of atom, the atomic mass is always 
less than the sum of the masses of the constituent particles in their 
free states. The simplest atom containing at least one proton, one 
neutron, and one electron is deuterium, ,H-; in this case we have 
for the masses: 

rest mass of one proton = 1.007276 amu 

rest mass of one neutron = 1.008665 

rest mass of one (orbiting) electron = 0.000549 

total rest mass of constituent 
particles in free state 

rest mass of deuterium atom 
difference (Am) 



= 2.016490 amu 

= 2.014102 amu 
= 0.002388 amu 

Although the difference in rest mass. Am, may appear small, it 
corresponds to a significant energy difference, because of the factor 
c^ in the relation E = mc^. The difference Am in mass corresponds to 
the difference AE in energy according to the relation: IE = Amc-. A 
convenient conversion factor from atomic mass (expressed in amu) 
to energy (expressed in MeV) is, as shown in the margin. 1 amu = 
931 MeV. If we therefore think of a deuterium atom being made 
with a proton and a neutron coinbine (and are joined by a tiny 
electron), then an amount of mass 0.002388 amu will have to be 
"lost" in the process. This means that an amount of energy equal 
to 0.002388 amu x 931 MeV/amu = 2.22 MeV has to be somehow 
radiated away from this system of combining particles, before they 
settle down as a deuterium atom. 

The expected energy loss calculated from the difference in rest 
mass can be compared with the result of a direct experiment. When 
hydrogen is bombarded with neutrons, a neutron can be captured 
in the reaction: 

on' + ,H' -^ .H^-h-y 



Section 24.3 



77 



This reaction produces no particle fragments having large kinetic 
energy, so the mass of 0.002388 amu by which iH- is hghter than 
qU^ + jH* must be carried away by the y ray. The energy of the y ray 
has been determined experimentally, and is found to be 2.22 MeV, 
just as predicted! The inverse reaction, in which deuterium is 
bombarded with y rays, has also been studied: 

iH^ + y ^ iH' + on' 

When the energy of the y rays is less than 2.22 MeV, this reaction 
cannot occur. But if we use y rays of energy 2.22 MeV or greater, 
the reaction does occur: the proton and neutron separate and can be 
detected. 

Following the "capture" of a neutron by the nucleus iH\ energy 
is liberated in a y ray. The energy 2.22 MeV is called the binding 
energy of the deuteron. It can be thought of as the energy released 
when a proton and -neutron combine to form a nucleus. To get the 
inverse reaction (when ,H- is bombarded with y rays), energy must 
be absorbed. So one can think of the binding energy as the amount 
of energy needed to break the nucleus up into its constituent 
nuclear particles. 

The concept of binding energy was, of course, already implied 
in earlier parts of the course, though not applied to nuclear physics. 
For example, the earth is held in orbit around the sun and would 
need to be given a certain additional amount of kinetic energy to 
escape from the sun. which binds it by gravitational attraction. In a 
hydrogen atom, the electron needs 13 eV before it can escape from 
the nucleus that binds it by an electric attraction. And conversely, 
when a bare jH' nucleus captures an electron and becomes a stable, 
ordinary neutral atom of hydrogen, the system must give up an 
amount of energy equal to 13 eV by radiation -exactly the observed 
energy of the photon emitted in this process of electron capture. 



Q2 When energy is "liberated" during a nuclear reaction, what 
becomes of it? 

Q3 What is the definition of binding energy for the case of the 
deuteron nucleus? 



24.3 Nuclear binding energy and stability 

The calculation of nuclear binding energy made for deuterium 
can be extended to all other nuclear species. But it is first necessary 
to explain a convention: in practice, physicists make such calcula- 
tions for neutral atoms rather than for bare atomic nuclei. 
(Experimental values of masses found from mass-spectrographic 
measurements are for atoms that are missing only one or two 
electrons.) Since an atom contains electrons orbiting around the 
nucleus as well as the protons and neutrons inside the nucleus, the 
mass of one electron outside the nucleus must be included for every 
proton inside the nucleus in the calculations. 



78 



Nuclear Energy, Nuclear Forces 






I 



/ 



/ 



E 



rf» /OO 'so 20D 

Nuclear binding energy as a function 
of the number of particles in tiie 
nucleus. 



Notice the unusually high position 
(above the curve) of the dot near 7.1 
MeV, compared to its neighbors. 
The point is for He'. The relatively 
high value of the binding energy of 
their nucleus is related to its 
unusually great stability. 



Average nuclear binding energy per 
particle as a function of the number 
of particles in the nucleus. 



The following example illustrates the calculations that allow 
finding the nuclear binding energy of an atom. Let us compare the 
actual mass of a carbon- 12 atom with the sum of the masses of its 
component particles: 



rest mass of 6 hydrogen atoms 
(includes 6 protons and 
6 electrons) 

rest mass of 6 neutrons 

total rest mass of particles 

rest mass of carbon- 12 atom 

difference in rest mass (Atti) 

corresponding energy = 



6 X 1.007825 = 6.04695 amu 
6 X 1.008665 - 6.05199 
= 12.09894 
= 12.00000 
- 0.09894 



0.09894 amu x 931 MeV/amu= 92.1 MeV 

In the same manner one can calculate the nuclear binding 
energy of any stable atom. The figure in the margin shows in 
graphic form how the nuclear binding energy for stable nuclides 
actually increases with increasing atomic mass, as more particles 
are added to form the nucleus. The term nucleons refers to both 
protons and neutrons, so we can say that the binding energy of the 
nucleus increases with the number of nucleons. But as you see, the 
answer is not a straight line. Such experimental data have 
important implications. 

The implications can be seen more clearly if we calculate the 
average binding energy per particle. In the case of the carbon- 12 
example, we found the total binding energy to be 92.1 MeV. Since 
we are deahng with 12 particles inside the nucleus (6 protons and 
6 neutrons), the average binding energy per particle in 92.1 MeV/12 
or 7.68 MeV. In the graph at the bottom of the page, the values 
of average binding energy per particle (in MeV) are plotted 





/CO 



Wo 



/6o 



MASS/^i^M8£R(A) 



/to 2oo 220 24o 



Section 24.4 



79 



against the number of particles in the nucleus (mass number, A). 
The significance of the graph lies in its striking shape. 

Note that the binding energy per particle starts with a low 
value for deuterium (the first point), and then increases rapidly. 
Some nuclei in the early part of the curve, for example He^, C^^, 
and 0^^ have exceptionally high values as compared with their 
neighbors. More energy would have to be supplied to remove a 
particle from one of them than from one of their neighbors. We 
would therefore expect He^, C'^ and O'*' to be exceptionally stable. 
There is evidence in favor of this conclusion: for example, the fact 
that the four particles making up the He* nucleus are emitted as a 
single unit, the oc particle, in radioactivity. The curve has a broad 
maximum, extending from approximately A = 50 to A = 90 and then 
drops off for the heavy elements. Thus 29Cu'^^ near the maximum is 
found to have a binding energy per particle of about 8.75 MeV, 
while gzU^^^, near the high-A end of the curve, has a value of 7.61 
MeV. It follows that the nuclei in the neighborhood of the maximum 
of the curve, like those of copper, should be more difficult to break 
up than those of uranium. 

The idea of binding energy should now make it clear why 
atomic masses, when precisely measured, turn out not to be exactly 
whole-number multiples of the mass of a hydrogen atom, even 
though nuclei are just collections of identical protons and neutrons. 
When those particles combined to make a nucleus, their total rest 
mass was reduced by an amount corresponding to the binding 
energy — and the average binding energy varies from nuclide to 
nuclide, as shown in the lower graph on p. 78. 

With the information we now have about the nuclear binding 
energy, we shall be able to calculate and predict the energy needed 
for or released in nuclear reactions. (The average binding energy 
curve has other important imphcations which we shall mention 
later.) 



SG 24.3 

Remember: high binding energy per 
particle means lots of energy 
needed per particle to take the 
nucleus apart into its constituent 
nucleons. 



Q4 Which would be more stable, a nuclide with a high total 
binding energy, or a nuclide with a high average binding energy per 
nucleon? 



24.4 The mass-energy balance in nuclear reactions 

In the previous section we used a very simple nuclear reaction 
to introduce the concept of binding energy. In this section we shall 
use a more complicated reaction to show an important relation 
between the binding energy and the energy liberated in a nuclear 
reaction. 

We shall analyze the mass-energy balance in the reaction of a 
proton with lithium 7: 



.H' + aLi^ 



,He'' + .,He* 



This reaction has historical interest: it was the first case of a 
nuclear disintegration brought about by artifically accelerated 
particles; and the analysis of the reaction provided one of the 



80 



Nuclear Energy, Nuclear Forces 





REST MASSES 






before 


after 




Li' 


7.016005 


amu He' 4.002604 


amu 


H' 


1.007825 


amu He' 4.002604 


amu 




8.023830 


amu 8.005208 

difference 

8.023830 amu 
- 8.005208 amu 


amu 



Am = 0.018622 amu 

0.018622 amu x 931 MeV/amu 

= 17.3 MeV 



SG 24.4 



SG 24.5-24.7 



earliest quantitative tests of Einstein's mass-energy relation. The 
reaction was a good one to analyze because the masses of the 
proton, the a particle and the lithium atom were known, and the 
kinetic energies of the incoming proton and the two resulting 
a particles could be measured accurately (by their ionizing effects). 

rest mass of Li" atom = 7.016005 amu 
rest mass of H' atom = 1.007825 amu 
rest mass of He^ atom = 4.002604 amu 

The energy we expect to be released in the reaction may be 
calculated by finding the difference in rest masses before and after 
the nuclear reaction takes place. The rest mass of the products is 
less by 0.018622 amu compared with the rest mass of the initial 
atoms, corresponding to a deficit of 17.3 MeV. The corresponding 
deficit in energy, 17.3 MeV, appears as the kinetic energy of the two 
a particles emitted. (In fact the incident proton also has kinetic 
energy, so that the 17.3 MeV represents the difference between the 
kinetic energies of the two emitted a particles and the kinetic 
energy of the incident proton.) 

When the experiment is made, one finds full agreement between 
the expected kinetic energy deficit calculated from the data for 
the rest masses and the experimental value found for the kinetic 
energies. This agreement shows that the mass-energy relation is 
valid. There is a release of energy when the lithium atom is broken 
up, and this release shows up at the expense of some of the rest 
mass of its fragments. This experiment was first done in 1932; 
since then, hundreds of nuclear transformations have been studied, 
and the results have invariably agreed with the mass-energy 
relationships calculated by means of the equation AE = Amc^. 

The balance of rest mass and kinetic energy can be related to the 
idea of binding energy. In the lower graph on page 78, the average 
binding energy per nucleon of the lithium-7 nucleus is given as 5.6. 
MeV. Since lithium 7 has seven particles in the nucleus, the total 
nuclear binding energy is 7 x 5.6 MeV = 39.2 MeV. The incident 
proton has no binding energy. The nuclear binding energy of each 
a particle (He^ nucleus) is 28.3 MeV making a total of 56.6 MeV for 
the two a particles. The difference between the binding energies 
before and after shows how much more tightly the nucleons in the 
product fragments are bound: 56.6 MeV -39.2 MeV = 17.4 MeV: 
consequently there have to be 17.4 MeV of energy released in the 
reaction, appearing as kinetic energy of the fragments. This checks 
closely with the experimentally found kinetic energies. 

Analysis of many nuclear reactions verifies this general rule: 
When the total binding energy of the products exceeds that of the 
reactants, energy is liberated. We can express this also as when 
the products of a nuclear reaction have greater average binding 
energy per particle than the reactants do, energy is liberated. This 
rule is a summary of the fact that energy will be liberated in a 
nuclear reaction when the products lie higher on the average 
binding energy curve than the reactants do. 



Section 24.5 



81 



The shape of the average binding energy curve, which drops off 
at both ends, indicates therefore that there are two general nuclear 
reaction processes by which one can hope to release energy from 
nuclei: combining light nuclei into a more massive nucleus, or 
splitting up heavy nuclei into nuclei of medium mass. In either 
process the products would have greater average binding energy, 
so energy would be released. A process in which two nuclei join 
together to form a heavier nucleus is called nuclear fusion. A 
process in which a heavy nucleus splits into fragments of 
intermediate mass is called nuclear fission. Both fusion and fission 
have been shown to occur, and the technology of fission has been 
simplified and exploited in many countries. Fission reactions can 
be made to take place slowly (as in a nuclear power plant) or very 
rapidly (as in a nuclear explosion). 

Q5 Would breaking up a heavy nucleus into very many light 
nuclei result in the liberation of energy? 



24.5 Nuclear fission: discovery 



The discovery of nuclear fission is an example of an unexpected 
result of great practical importance, obtained during the course 
of research carried on for reasons having nothing to do with the 
possible usefulness of the discovery. It is also an excellent example 
of the combined use of physical and chemical methods in nuclear 
research, and of the effectiveness of team work. After Joliot and 
Curie showed that some products of nuclear reactions are 
radioactive (Sec. 23.9), Fermi and his colleagues in Italy undertook 
a systematic study of nuclear reactions induced by neutrons. One 
of the purposes of this research was to produce new nuclides. As a 
result, many new radioactive nuclides were made and their half- 
lives determined. One nuclear reaction used successfully in this 
study was the capture of a neutron followed at once by the emission 
of a y ray. For example, when aluminum is bombarded with 
neutrons, the following reaction occurs: 



,AP 



3AP« + y 



Aluminum 28 is radioactive, with a half-life of 2.3 minutes, decaying 
by /3 emission into silicon: 



,3AP 



1401 



+ _,e°+ V 



As a result of these two reactions, a nuclide (nSi^*) is produced with 
values of Z and A each greater by one unit than those of the initial 
nucleus. Fermi thought that if neutrons bombarded uranium -the 
atomic species having the largest value of Z known then -an 
entirely new element might be formed by the ^ decay of the heavier 
uranium isotope: 



A few of the problems encountered 
by Fermi in his work on these 
reactions were described in the 
Prologue to Unit 1. The supplemental 
Project Physics Unit "Discoveries 
in Physics" goes into more detail 
on the discovery of fission. 




Enrico Fermi. 



82 



Nuclear Energy, Nuclear Forces 



zU^ 



^U239 + y 



SG 24.8 



^(9)239 _ 




Starting about six years after Fermi's 
speculation of 1934, it was found 
possible, by a variety of methods, 
to create transuranium elements. The 
new elements up to Z = 1 03, are listed 
below. A tiny sample of one of them, 
curium 244-dissolved in a test tube 
of water, is shown in the 5-minute 
exposure above (by light produced 
when the radiation interacts with the 
surrounding matter). 



92 U 


Uranium 


9.,Np 


Neptunium 


94 PU 


Plutonium 


^Am 


Americium 


9«Cm 


Curium 


97 Bk 


Berkelium 


9HCf 


Californium 


99 ES 


Einsteinium 


100 Fm 


Fermium 


■o.Md 


Mendelevium 


.02 No 


Nobelium 


.0.-.1-W 


Lawrencium 



He also speculated that the new nuclide denoted by gsC?)^^^ in turn 
might also undergo ^3 decay: 



m 



^(9)239 + _^gO + j7 



In this way, two new elements might be produced (one with Z = 93, 
one with Z = 94). If these reactions could really be made to occur, 
the result would be the man-made production of an element, or 
elements, not previously known to exist — trawsuraniuTn elements. 

Fermi found in 1934 that the bombardment of uranium with 
neutrons actually produced new radioactive elements in the target 
as shown by the emission of rays and a decay activity that defined 
new, relatively short half-lives. The new elements were at first 
assumed to be the hypothesized transuranium elements. 

The results aroused much interest, and in the next five years a 
number of workers experimented with the neutron bombardment of 
uranium. Many different radioactive half-lives were found for the 
radiation from the target, but attempts to identify these half-lives 
with particular elements led to great confusion. The methods used 
were similar to those used in the study of the natural radioactive 
elements (Sec. 21.7). But the difficulty was even greater because a 
radioactive nuclide formed in a nuclear reaction is usually present 
in the target area only in an extremely small amount, possibly as 
little as 10"'^ grams; special techniques to separate these small 
quantities had to be developed. 

The reason for the confusion was found early in 1939 when 
Otto Hahn and Fritz Strassmann, two German chemists, showed 
definitely that one of the supposed transuranium elements was 
actually an isotope of barium (seBa*''**), identified by its half-life of 
86 minutes and its chemical behavior. Another nuclide resulting 
from the neutron bombardment of uranium was identified as 
lanthanum (j^La'^"), with a half-life of 40 hours. 

The production of the nuclides agBa'^** and s^La'^" from uranium, 
a nuclide with the atomic number 92 and an atomic mass of nearly 
240, required an unknown kind of nucleai' reaction, one in which 
the heavy nucleus is split almost in half. Nothing like it had been 
known to exist before. If such a process really occurred, it would 
also have to be possible to find "the other half," that is, to find 
nuclides with mass between 90 and 100 and atomic numbers of 
about 35. Indeed, Hahn and Strassmann were able to find in the 
target material a radioactive isotope of strontium (Z = 38) and one 
of yttrium (Z = 39) which fulfilled these conditions, as well as 
isotopes of krypton (Z = 36) and xenon (Z — 54). It was clear from 
the chemical evidence that the uranium nucleus, when bombarded 
with neutrons, can indeed split into two nuclei of intermediate 
atomic mass. 

Although Hahn and Strassmann showed that isotopes of 
intermediate mass did appear, they hesitated to state the conclusion 



Section 24.5 



83 



that the uranium nucleus could be split. In their historic report, 
dated January 9, 1939, they said: 

On the basis of these briefly presented experiments, we 
must, as chemists, really rename the previously offered 
scheme and set the symbols Ba, La, Ce in place of Ra, Ac, 
Th. As "nuclear chemists" with close ties to physics, we 
cannot decide to make a step so contrary to all existing 
experience of nuclear physics. After all, a series of strange 
coincidences may, perhaps, have led to these results. 

The step which Hahn and Strassmann could not bring 
themselves to take was taken on January 16, 1939 by two Austrian 
physicists, Lise Meitner and Otto R. Frisch. They suggested that 
the neutron provoked a disintegration of the uranium nucleus into 
"two nuclei of roughly equal size," a process which they called 



o- 



N 





Schematic diagram representing uranium fission. 

"nuclear fission" by analogy to the biological division, or fission, of 
a living cell into two parts. On the basis of comparison of the low 
average binding energy per nucleon of uranium with the higher 
average binding energy per nucleon of the products, they predicted 
that the fragments would have high kinetic energy. This was soon 
verified experimentally. Shortly afterward, it was found that 
transuranium elements may, after all, also be formed when 
uranium is bombarded with neutrons. In other words the capture 
of a neutron by uranium sometimes leads to fission, and sometimes 
leads to /3 decay. The /3 decay results in the formation of isotopes 
of elements of atomic number 93 and 94 — later, named neptunium 
and plutonium. The presence of both types of reaction — fission, and 
neutron capture followed by /3 decay — was responsible for the 
difficulty and confusion in the analysis of the effects of neutrons 
on the uranium target. Now, the interpretation of the experiments 
opened two new fields of scientific endeavor: the physics and 
chemistry of the transuranium elements, and the study of nuclear 
fission. 

The discovery of nuclear fission inspired research workers all 
over the world, and much new information was obtained within a 




Lise Meitner and Otto Hahn 

Lise Meitner, born in Austria, joined 
Otto Hahn in 1908 in a research col- 
laboration that lasted thirty years. In 
1938, Miss Meitner was forced to leave 
Germany by the Hitler regime. She was 
in Sweden when she published the 
first report on fission with her nephew, 
O. R. Frisch. 




Otto R. Frisch 



84 



Nuclear Energy, Nuclear Forces 



SG 24.9, 24.10 

Similarly, (fiKr'- is transformed into 
,nZr-'- by four successive 13 decays. 
See SG 24.11. 



short time. It was found that the uranium nucleus, after capturing 
a neutron, can spHt into one of more than 40 different pairs of 
fragments. Radio-chemical analysis showed that nuclides resulting 
from fission have atomic numbers between 30 and 63 and mass 
numbers between 72 and 158. 

Yet nuclides of medium mass are not the only fission products. 
Neutrons also are emitted in fission; the average number of 
neutrons emitted is usually between 2 and 3. The following reaction 
indicates only one of the many ways in which a uranium nucleus 
can split: 



.n> + ,„U^ 



,Ba'^' + ,«Kr«=^ + 3nn' 



ggBa*^* and ggKr^^ are not "natural" nuclides, and are not stable; they 
are radioactive and decay by /3 emission. For example, sgBa*^' can 
decay into sciPr'^' by successive emission of three /3 particles, as 
shown by the following scheme (the numbers in parentheses are 
the half-lives): 



(18 min) 



(3.6 hr) 



(32 days) 



Plutonium 239 (.,|Pu-'') is produced 
by the capture of a neutron by .cU-'" 
and the subsequent emission of two 
/i particles, as was discussed on 
p. 82. 



It has been found that only certain nuclides can undergo fission. 
For those which can, the probability that a nucleus will split when 
bombarded depends on the energy of the neutrons used in the 
bombardment. The nuclides gzU"^ and 94Pu^^^ can undergo fission 
when bombarded with neutrons of any energy even 0.01 eV or less. 
On the other hand, U"^ and Th"^ undergo fission only when 
bombarded with neutrons having kinetic energies of 1 MeV or more. 

The energy released in the fission of a nucleus is about 200 
MeV. This value can be calculated either by comparing atomic rest 
masses of reactants and products, or from the average binding 
energy curve of the graph on p. 78. The energy release in fission is 
more than 20 times larger than in the more common nuclear 
reactions where it is usually less than 10 MeV, and more than a 
million times larger than in chemical reactions. 

Under appropriate conditions the neutrons released in fission 
can, in turn, cause fission in neighboring uranium atoms, and a 
process known as a chain reaction can develop in a sample of 
uranium. The combination of the large energy release in fission 
and the possibility of a chain reaction is the basis of the large- 
scale use of nuclear energy. 

Q6 What two successive reactions can result in the appearance 
of a transuranium element? 

Q7 What product of the fission process makes a chain reaction 
possible? 

24.6 Nuclear fission: controlling chain reactions 

For a chain reaction in a sample of uranium to continue at an 
even rate, there must be a favorable balance between the net 



Section 24.6 



85 



production of neutrons by fissions, and the loss of neutrons due to 
the following three processes: 

1. capture of neutrons by uranium without fission resulting; 

2. capture of neutrons by other materials in the sample or the 
structure containing the sample; 

3. escape of neutrons from the sample without being captured. 
If too many neutrons escape from or are absorbed in the structure 
or assembly (called a "reactor") there will not be enough to sustain 
the chain reaction. If too few neutrons escape or are absorbed, the 
reaction will continue to build up more and more. The design of 
nuclear reactors as energy sources involves finding proper sizes, 
shapes, and materials to maintain or control a balance between 
neutron production and neutron loss. 

Since the nucleus occupies only a tiny fraction of an atom's 
volume, the chance of a neutron colliding with a uranium nucleus 
is small, and a neutron can go past the nuclei of billions of uranium 
(or other) atoms while moving a few inches. If the reactor assembly 
is small, a significant percentage of the fission neutrons can escape 
from the assembly without causing further fissions. The "leakage" 
of neutrons can be so large that a chain reaction cannot be 
sustained. The number of neutrons produced is proportional to 
the volume, but the number of neutrons that escape is proportional 
to the surface area. As the linear size L of the assembly is 
increased, the volume and area increase in proportion to L^ and L-; 
so neutron production increases with size more rapidly than neutron 
escape does. For a given combination of materials — uranium and 
other structural materials which may be needed — there is a size of 
the reactor, called the critical size, for which the net production of 
neutrons by fission is just equal to the loss of neutrons by non- 
fission capture and escape. If the size of the reactor assembly is 
smaller than this critical size, a chain reaction cannot be sustained. 
The design of a reactor of reasonable dimensions with given 
materials which will correspond to critical size is an important part 
of research in the field of "nuclear engineering." 

Another important consideration in the design of nuclear 
reactors is the fact that fission is much more probable when U"^ is 
bombarded with slow neutrons than when it is bombarded with 
fast neutrons. The neutrons released in fission generally come out 
at very high speeds having kinetic energies from about 0.01 MeV 
to nearly 20 MeV, with an average kinetic energy of about 2 MeV. 
But the fast neutrons can be slowed down in the reactor by the 
addition of material to which the neutrons can lose energy in 
collisions. The material should be relatively low in atomic mass so 
that the neutrons will transfer a significant fraction of their energy 
in elastic collision; but the material should not also capture and 
absorb many neutrons. Pure carbon in the form of graphite, and 
also water and beryllium meet these requirements. These 
substances are called moderators because they slow down — 
moderate — the newly produced neutrons to lower speeds at which 
the probability of causing additional fission is high. 



Q 




4 

Ox ©X / 

/ © f 

Q I 

A schematic diagram of the beginning 
of a chain reaction. The nucleus in the 
center has fissioned into 2 parts, re- 
leasing also gamma rays and neu- 
trons. Some of the neutrons are 
captured by other nuclei, promoting 
further fissioning with the accom- 
panying release of more neutrons. . . 
and so on. 




SG 24.12 



Although nuclear reactors can be 
built in which the fissions are 
induced by fast neutrons, it has 
been easier to build reactors with 
materials in which the fissions are 
induced by slow neutrons. 



86 



Nuclear Energy, Nuclear Forces 



We have described (Sec. 23.4) how 
neutrons lose nearly all their kinetic 
energy in a headon collision with a 
hydrogen nucleus -but most colli- 
sions will not be head-on. 



Heavy water: (H%0, or D,0. 

(low probability) 

,H2 + „n' > ,H^' + 7 



Hydrogen atoms in water are very effective in slowing down 
neutrons because the mass of a hydrogen nucleus is nearly the 
same as that of a neutron and because the number of hydrogen 
atoms per unit volume is high. A neutron can lose a large fraction 
of its energy in a collision with a hydrogen nucleus and only about 
20 collisions are needed, on the average, to slow down the fast 
neutron to energies under 1 eV. However, neutrons can also be 
captured by the hydrogen nucleus in the reaction: 



,H> + on' 



iH^ 



The probability of this reaction occurring instead of an elastic 
collision is high enough so that it has been found impossible to 
achieve a chain reaction with natural uranium and ordinary 
water. 

But there are other ways to make reactors. We note, for 
example, that the absorption of a neutron by a deuterium nucleus — 
such as the nucleus of the heavy isotope of hydrogen, found in 
heavy water — has an extremely small probability. Neutrons do not 
lose as much energy per collision with H^ nuclei, but this disadvant- 
age is overbalanced by the much lower absorption rate — so a chain 
reaction can be achieved easily with natural uranium and heavy 
water. Reactors with natural uranium as the fuel and heavy water 
as the moderator have been built in the United States, Canada, 
France, Sweden, Norway and other countries. 

The contrast between the nuclear properties of hydrogen ,H' 
and deuterium dH^ or ,D'^) has important implications for the 
development of nuclear reactors. Heavy water is much more 
expensive than ordinary water, but when it is used with natural 
uranium (mostly U^^**), a chain reaction can be achieved efficiently. 
Ordinary water can be used, if uranium enriched in the isotope 
U"^ is used instead of natural uranium. Many reactors "fueled" 
with enriched uranium and moderated with ordinary water have 
been built in the United States. In fact, this general reactor type 
has been used in nearly all the large nuclear power plants built 
so far, and in the reactors used in nuclear-powered ships. 

Carbon in the form of graphite has been used as a moderator 



Schematic diagram of three types of 
functions fulfilled by parts of a nuclear 
reactor. 






• • • 




Section 24.6 



87 



in many reactors, including the earliest ones. It is not as good a 
slowing-down agent as water or heavy water; about 120 collisions 
with carbon atoms are needed to slow down a fast neutron with an 
initial energy of 2 MeV to the energy of about 0.025 eV desired; 
in heavy water only about 25 colhsions are needed. Although carbon 
in the form of graphite is not the best moderator and absorbs some 
neutrons, it does permit a chain reaction to occur when lumps of 
natural uranium (cylindrical rods, for example) are arranged in a 
large mass of graphite. The determination of just how this could 
be done was one of the main problems that had to be solved before 
the world's first chain reaction was achieved by a team under 
Enrico Fermi in December 1942 at the University of Chicago. (It 
was a crucial experiment because until its success it was by no 
means certain that a chain reaction was really possible.) Many 
graphite-moderated reactors are now in operation throughout the 
world. Their chief purpose will be discussed in the next section. 

The control of a reactor is relatively simple. If fission is occur- 
ring too frequently, a few "control" rods are inserted into the 
reactor. The rods consist of a material (such as cadmium or boron) 
that absorbs slow neutrons, thereby reducing the number of 
neutrons in the moderator. Removal of the control rods wHl allow 
the rate of the reactor to go up. The sketch at the bottom of the 
opposite page illustrates the basic reactions that occur in a nuclear 
reactor in which uranium is the fissionable material. 

Q8 What is a "moderator"? 

Q9 What is an advantage and a disadvantage of using water 
as a moderator in nuclear reactors? 

Q10 How can the rate of reaction be controlled in a reactor? 







The west wall of the football stands of 
Stagg Field, University of Chicago. 
Squash courts under these stands 
were used as the construction site of 
the first nuclear reactor. Below is 
an artist's sketch of that graphite- 
moderated reactor during the experi- 
mental run on December 2, 1942, 
when it first became self-sustaining. 




88 



Nuclear Energy, Nuclear Forces 



Fission occurs less than one billionth 
of a second after the neutron is 
captured. 



Recall that fission of U- '"' can occur 
with neutrons of any speed, but 
fission of U-"' requires high-speed 
neutrons. 



From the beginning, scientists have 
been prominently involved in activi- 
ties to alert their government and 
fellow citizens to the moral and 
practical problems raised by the 
nuclear weapons race. See Reader 6. 
"Report to the Secretary of War" 
by Jameis Franck and colleagues. 



24.7 Nuclear fission: large-scale energy release and some of its 
consequences 

The large-scale use of nuclear energy in chain reactions was 
accomplished in the United States between 1939 and 1945. The 
work was done under the pressure of World War II, as a result of 
the cooperative efforts of large numbers of scientists and engineers. 
The workers in the United States included Americans, Britons, and 
European refugees from fascist-controlled countries. 

The aim was to produce a so-called atomic (more properly. 
nuclear) bomb, essentially an uncontrolled nuclear reactor in which 
an extensive chain reaction occurs throughout the material in a few 
millionths of a second. This differs therefore from the controlled 
nuclear reactor, in which the operating conditions are so arranged 
that the energy from fission is released at a much slower and 
essentially constant rate. In the controlled reactor the fissionable 
material is mixed with other materials in such a way that, on the 
average, only one of the neutrons emitted in fission causes the 
fission of another nucleus; in this way the chain reaction just 
sustains itself. In a nuclear bomb the fissionable material is pure 
(that is, not mixed with a moderator) and the device is designed 
so that nearly all of the neutrons emitted in each fission can cause 
fissions in other nuclei. 

Nuclear reactors were used during World War II to produce raw 
materials for one kind of nuclear bomb, namely to manufacture 
Py239 fj-ojn U^^^ These reactors were designed in such a way that 
some of the neutrons from the fission of U^^^ were slowed down 
sufficiently not to cause fission in U--^** atoms. (In natural uranium 
only about j % of the atoms are U"^^.) Instead, the neutrons were 
absorbed by U"* nuclei to form Pu-^^ through the reactions described 
in the previous section. 

Pu"** acts similar to U-^"^; both materials can sustain a rapid, 
uncontrolled chain reaction. Nuclear bombs have been made of 
both materials; a single nuclear bomb, using U-'-^. destroyed the city 
of Hiroshima, Japan, on August 6, 1945; another bomb, using 
94Pu"^, destroyed the city of Nagasaki three days later. Since 
the end of World War II in 1945, the technology of fission has 
been further developed in two different directions. One direction 
has been military. Other countries besides the United States have 
made nuclear weapons, including (as of 1970) the United Kingdom, 
the Soviet Union, France, and China. The enormous death-dealing 
capability of these weapons, and the ever-larger numbers of bombs 
of many varieties that have been accumulating all over the globe, 
have increased and made more dangerous the tensions existing 
throughout the world and have emphasized critically the need for 
the peaceful settlement of international disputes. 

One incidental problem has been that of the radioactive /a//oMt 
from bomb tests. In the explosion of a nuclear bomb, large 
amounts of radioactive fission products are scattered. These 
materials can be blown by winds from one part of the world to 
another and carried down from the atmosphere by rain or snow. 
Some of the radioactive materials are long-lived; they may be 



Section 24.7 



89 



absorbed in growing foodstuffs and eaten by animals and people. It 
is known that such radioactive materials can cause harmful 
genetic effects as well as somatic effects. One of the most abundant 
and long-lived products of the fission of either U"' or Pu"^^^ is 
strontium 90 CgSr^"). This isotope of strontium is similar to 2oCa^*' in 
its chemical properties. Hence when Sr^" from radioactive fallout 
enters the body, it finds its way into bone material. It decays by 
emission of 0.54-MeV 13 particles (half-hfe = 28 years), which 
can injure cells and cause leukemia, bone tumor, and possibly other 
forms of damage, particularly in growing children. 

There has been much research and discussion concerning 
possible harm to present and future generations. Partly as the result 
of petitions and protests organized by scientists, the United States, the 
United Kingdom, the Soviet Union and most other nations (but not 
France and China) agreed in 1963 to a moratorium on further 
bomb tests in the atmosphere. Though it allowed continuation of 
tests underground, the atmospheric test ban treaty was rightly 
considered a great step forward in simultaneously curbing radio- 
active pollution and increasing somewhat the chances for further 
arms control treaties. For example, it is said to have helped pave 
the way to the treaty, in effect since 1970, by which most nations 
agreed not to disseminate nuclear weapons to "non-nuclear" 
nations. 

The second direction in which the use of nuclear energy has 
been pushed on a large scale has been in the production of electrical 
power from the energy released in fission. The increasing need for 
electrical energy is an important aspect of modem life. The amount 
of electricity used in an advanced industrial country, such as the 
United States, has been doubling approximately every ten years 
since about 1900. Although there are still large supplies of coal, oil, 
and natural gas. it is evident that additional sources of energy will 
be needed, and nuclear energy from fission can fill this need. More- 
over, such energy plants avoid the chemical pollution of their 
environment, since this method of energy release does not involve 
combustion. 

In almost all present systems of nuclear power production, the 
reactor is a source of heat for running steam turbines; the turbines 
drive electrical generators just as they do in conventional power 
stations. 




Genetic effects of radiation: effects 

producing changes in cells which 

will affect offspring of exposed 

individual. 

Somatic effects: all effects caused 

by radiation to an exposed individual 

during his lifetime. 




A grain of radioactive dust from the 
atmosphere caused these a-particie 
tracks in a photographic emulsion 
(enlarged 2000 times). 



See "The Nuclear Energy 
Revolution" in Reader 6. 



If proper controls are seriously 
applied, two remaining sources of 
pollution can also be avoided in 
such plants: thermal pollution by 
heating the water of streams or 
lakes used for cooling the reactor, 
and leakage of small quantities of 
radioactive materials from the 
reactor. 



Heat produced in a reactor (by the 
flying fission fragments) does not 
directly turn water to steam. As this 
simplified diagram indicates, the 
water is heated in a "heat exchanger" 
by a fluid that circulates through the 
reactor core. 



Hb-Aoivk. 



^EAT £.KCi/AU!}£^ 



The photograph at the left illustrates one type 
of commercial installation for converting the 
heat energy from a fission chain reaction into 
electrical energy. This steel "drywell" is the 
housing for the nuclear reactor at the Nine Mile 
Point generating station, near Oswego on Lake 
Ontario. The cutaway drawing below shows the 
reactor, turbine-generator and other compo- 
nents of a similar installation at the Dresden 
nuclear power station at Joliet, Illinois. 




CONTICH lOOM 



PIISJUII SUmiSSION SVSIiM 



^VH<i»- ' < ! !. ' 




Above is a small research reactor at M.I.T. in 
Cambridge, Mass. 

At the right, technicians load "fuel" slugs con- 
taining fissionable materials into the A.E.C.'s 
graphite-moderated reactor at Oak Ridge, 
Tennessee. 




92 



Nuclear Energy, Nuclear Forces 



See "Twentieth Birthday of the 
Atomic Age" and "Calling all Stars' 
in Reader 6. 



"Manhattan District" was the code 
name given to the bomb-develop- 
ment project during World War II. 



Below is shown a model of a plant for 
producing both nuclear power and 
desalted water, designed to be built 
on a man-made island off the coast of 
southern California. It will generate 
electricity at the rate of 1.8 million 
kilowatts and also produce, by distil- 
lation, 150 million gallons of fresh 
water daily for use in cities, industries, 
and agriculture. 



For a variety of reasons, some administrative and some 
technical, but mostly connected with the "Cold War" with the 
Soviet Union that started after World War II and intensified during 
the early fifties, the U.S. Atomic Energy Commission (AEC) did not 
emphasize applied research on nuclear-electric power systems until 
President Eisenhower so directed in 1953. By that time America's 
first experimental breeder reactor (EBR-1) had demonstrated for 
two years in Idaho that electric power could be produced in 
significant amounts while simultaneously producing (or "breeding") 
Plutonium in a U-^** blanket around the neutron-and-energy- 
producing core of U^^^ and moderator. 

Not until fully twenty years after the Manhattan project 
reached its goals could one say that the age of nuclear-electric 
generation of power had arrived. Nuclear energy sources became 
economically competitive with hydroelectric and fossil-fuel sources 
(coal, oil, natural gas) in the early 1960's when costs per kilowatt- 
hour from nuclear energy sources became as low as one-half cent. 
More than half of the total new electric power plant construction in 
the United States is now committed to nuclear sources. The United 
Kingdom and France also successfully used reactors to generate 
commercial electric power. Thus there finally are strong reasons 
for optimism concerning the new source of energy through nuclear 
fission. 

Such a new source was clearly needed, for along with the 
population explosion and the depletion of fossil fuels, an energy 




Section 24.7 



93 



shortage threatened to Hmit mankind's future development. Nuclear 
power reactors, now entering a third generation of development, 
also show promise of being able to furnish energy economically for 
desalting sea water, to convert atmospheric nitrogen into powdered 
fertilizers, and to make fluid fuels from hydrocarbons in low-grade 
coal. If all this can be done cheaply enough with breeder reactors 
that produce at least as much fissionable material as they "bum," 
then indeed the war-born nuclear technology at last can have the 
beneficial impact on all human society that is desperately 
needed. 

In the meantime, the social costs of the nuclear energy 
revolution have already been very high — in human lives, in money, 
and in the anxiety of life under the threat of nuclear war. In some 
ways these are analogous problems to the human price of industrial- 
ization after the development of the steam engine (Unit 3). At the 
same time, the potential benefit to man is great. As in the past, the 
decisions that will be necessary in the future development of 
nuclear power cannot be made on the basis of physics alone. 
Science can help to illuminate alternatives on which essentially 
political decisions can be based, but it cannot and should not be 
used by itself to choose among them. Responsible scientific opinion 
must be supplemented by political insight and a broad humanistic 
view of society. But at the very least, responsible citizens must have 
some understanding of the scientific principles that will underlie 
the alternatives among which they must choose. 



ir^.- :• 








t 












^ '^xp^l^^^^^^^^^^^^^^^^^^^^^^^^^B^^^k. 




l^> 




1 












V 








A blast of exhaust (above) from an 
experimental nuclear rocket engine 
(below). 




Among the many problems for public 
policy raised by developments in 
nuclear power is the Plowshare Pro- 
gram of the AEC. The crater at the left 
was part of Plowshares research into 
the possibility of creating lakes, har- 
bors and sea-level canals between 
oceans by exploding nuclear devices. 
The problems raised include those of 
pollution, the dangers of diversion of 
such devices for war purposes, and 
the wisdom of engaging on some 
large-scale projects that may end up 
moving mountains to serve the pur- 
poses of relatively small groups rather 
than all who will be affected by such 
transformations. 



Chronology of Some Developments in Nuclear Science and Technology 



1896 Becquerel discovers unstable 
(radioactive) atoms. 

1899 Isolation of radium by Curies. 

1905 Einstein's statement of equiva- 
lence of mass and energy. 

1911 Rutlierford discovers nucleus. 



1952 First detonation of a hydrogen 
bomb. Eniwetok Atoll, Pacific 
Ocean. 

1953 President Eisenhower an- 
nounces U.S. Atoms-for-Peace 
program and proposes estab- 
lishment of an international 
atomic energy agency. 



1919 Rutherford achieves trans- 
mutation of one stable chemi- 
ical element into another. 

1920- Improved mass spectrographs 
1925 show that changes in mass per 
nuclear particle accompanying 
nuclear reactions account for 
energy released by nucleus. 

1931 Lawrence and Livingston con- 
struct first cyclotron. 

1932 Chadwick identifies neutrons. 

1934 Fermi's group in Rome finds 

radioactivity induced by neutrons. 

1939 Evidence of uranium fission 
by Hahn and Strassmann, 
identification of fission 
products by Meitner and Frisch. 

1940 Discovery of neptunium and 
Plutonium at the University 
of California. 

1942 Achievement of first self- 
sustaining nuclear reaction, 
University of Chicago. 

1945 First test of a nuclear device, 
at Alamagordo, New Mexico, 
followed by the dropping of 
nuclear bombs in Hiroshima 
and Nagasaki, at the end of 
World War II. 

1946 President Truman signs the 
bill creating the U.S. Atomic 
Energy Commission. 

First shipment of radioactive 
isotopes from Oak Ridge 
to hospital in St. Louis, Mo. 

1951 First significant amount of 
electricity (100 kilowatts) 
produced from nuclear energy 
at testing station in Idaho. 



1954 First nuclear-powered subm- 
rine, Nautilus, commissioned. 

1955 First United Nations Interna- 
tional Conference on Peaceful 
Uses of Atomic Energy held in 
Geneva, Switzerland. 

1956 First commercial power plant 
begins operation at Calder 
Hall, England. 

1957 Shippingport Atomic Power 
Plant in Pennsylvania reaches 
full power of 60,000 kilowatts. 

International Atomic Energy 
Agency formally established. 

1959 First nuclear-powered mer- 
chant ship, the Savannah, 
launched at Camden, New 
Jersey. 

1961 A radioactive isotope-ppwered 
electric generator placed in 
orbit, the first use of nuclear 
power in space. 

1963 President Kennedy signs the 
Limited Test Ban Treaty for 
the United States 

1964 President Johnson signs law 
permitting private ownership 
of certain nuclear materials. 

1966 Beginning of the rapid de- 
velopment of nuclear power 
plants in the U.S. 

1968 "Non-proliferation" agreement, 
signed by the United States, 
the Soviet Union and other 
countries, limiting the number 
of countries possessing 
nuclear weapons. 

1970 "Non-proliferation" agreement 
ratified. 



Section 24.8 



95 



24.8 Nuclear fusion 

Fusion reactions have been produced in the laboratory by 
bombarding appropriate Ught target materials with, for example, 
high-energy deuterons from a particle accelerator. In these reactions 
nuclei result which are heavier than the nuclei of either the 
"projectiles" or the targets; there are usually also additional 
particles released — and energy. Some typical examples effusion 
reactions, together with the energy liberated in each reaction, are: 

,H2 + ,H2 -^ ,H3 + ,Hi + 4MeV 






iHe^ + on' + 3.3 MeV 
2He^ + on' + 17.6 MeV 



iH2 + 2He3 -^ 2He^ + jH' + 1 8.3 MeV 
In the first of the above equations, the heavier product nucleus is 
an isotope of hydrogen, called tritium, with mass number A = 3; it 
has been found in small traces in nature, is radioactive with half- 
life of about 12 years, and it decays by beta emission into 2He^ an 
isotope of helium. 

When a target containing tritium is bombarded with deuterons, 
aHe* can be formed, as in the third equation above, liberating 17.6 
MeV of energy. Of this energy. 14.1 MeV appears as kinetic energy 
of the neutron and 3.5 MeV as kinetic energy of the product 
nucleus. 

The fusion of tritium and deuterium offers the possibility of 
providing large sources of energy, for example, in electric power 
plants. Deuterium occurs in water with an abundance of about one 
part in seven thousand hydrogen atoms, and can be separated from 
the lighter isotope. One gallon of water contains about one-eighth of 
a gram of deuterium which can now be separated at a cost of about 
4 cents. If this small amount of deuterium could be made to react 
under appropriate conditions with tritium (perhaps produced by the 
reaction discussed above), the energy output would be equivalent 
to that from about 300 gallons of gasoline. The total amount of 
deuterium in the oceans is estimated to be about 10'' kilograms, 
and its energy content would be about 10^° kilowatt-years. If 
deuterium and tritium could be used to produce energy, they would 
provide an enormous source of energy. 

There are, however, some difficult problems to be solved before 
fusion reactions are likely to be useful as steady sources of energy; 
some of these should be discussed at least briefly. The nuclei which 
react in the fusion processes are positively charged and repel one 
another because of the repulsive electric force. The nuclei must, 
therefore, be made to collide with a high relative speed to overcome 
the repulsive force tending to keep them apart. Experiments have 
shown that this can occur when the particles have kinetic energies 
of about 0.1 MeV or more. The nuclei must also be confined in a 
region where they can undergo many collisions without escaping, 
or being absorbed by the walls bounding the region, or losing energy 
by collisions with too many "cooler" (less energetic) molecules. 



Although the energy liberated in a 
single fusion is less than in a single 
fission, the energy released per unit 
mass is much greater. The mass of 
about 50 helium atoms is approxi- 
mately equal the mass of one 
uranium atom; 50 x 17.6 IWeV is 
1040 MeV-compared to 200 MeV 
for a typical fission. 



SG 24.13, 24.14 



96 



Nuclear Energy, Nuclear Forces 



A plasma is an ionized gas in which 
positively and negatively charged 
particles move about freely. 



There must be enough coUisions per unit time so that fusion can 
occur at a rate that will yield more energy than that needed to cause 
the collisions. The combination of these requirements means that 
the nuclei must be contained at a temperature of the order of 100 
million degrees. 

At the temperature required for fusion, the atoms have been 
stripped of their electrons, and the resulting nuclei and separated 
electrons are said to form a plasma. No wall made of ordinary 
material can contain a hot plasma at 10** °K (the wall would be 
vaporized instantly!). But the charged particles of a plasma could, 
in theory, be contained in an appropriately designed magnetic 
field. The first problem to be solved, therefore, is to contain the 
plasma of deuterium and tritium nuclei in a magnetic field, while 
accelerating the nuclei by means of an electric field to the required 
kinetic energy (or temperature). The behavior of the charged 
particles in a plasma is complicated; there are many kinds of 
instabilities that make the plasma difficult to contain properly and 
long enough. These problems of the release of energy to form a 
controlled and sustained fusion reaction have not yet been solved on 
a practical scale, but research on them is being carried on in many 
countries. There is considerable international cooperation in this 
research, including visits of research teams between the United 
States, Britain, France, and the U.S.S.R. Although the effort and 
expense are great, the possible pay-off in terms of future power 
resources is enormous. 



Q11 Why are very high temperatures required to cause fusion 
reactions? 

Q12 How could extremely hot gases be kept from contacting 
the wall of a container? 



A demonstration model of a "Stellara- 
tor." The figure-eight shape enables 
strong magnetic fields to contain a 
continuous plasma stream in which, 
it is hoped, a controlled fusion re- 
action might be made to occur. 




Section 24.9 



97 




Pen drawing by Vincent van Gogh. 



24.9 Fusion reactions in stars 



One of the most fascinating aspects of nuclear physics is the 
study of the sources of the energy of different types of stars. The 
sun is an example. In the sun. the fusion process results in the 
production of a helium nucleus from four protons. The net results 
of the reactions can be written as: 



4 iH' 



.He^ + 2+ie« + 26 MeV 



The reaction does not take place in a single step but can proceed 
through different sets of reactions whose net results are summarized 
in the above equation; in each case, the overall amount of energy 
released is 26 MeV. 

The fusion of four protons into a helium nucleus is the main 
source of the energy of the sun. Chemical reactions cannot provide 
energy at large enough rates (or for long enough duration!) to 
account for energy production in the sun. but nuclear fusion re- 
actions can. Hydrogen and helium together make up about 99 
percent of the sun's mass, with approximately twice as much H as 
He. There is plenty of hydrogen to supply the sun's energy for many 
millions of years to come. 

But by which of the several possible sets of reactions does the 
transformation of hydrogen into helium take place? The direct 
process of four protons colliding to form a helium nucleus has been 
ruled out because the probability for such a reaction under solar 
conditions is too low. It may happen, but not often enough for the 
amount of energy released. A more likely set of reactions is the 
process represented in the sketch on the next page. When the 
temperature is about 10' °K, the kinetic energies are large enough to 
overcome the electric repulsion between protons, and fusion of two 



SG 24.15 



For details see SG 24.16, 24.17, and 
24.18. 



98 



Nuclear Energy, Nuclear Forces 



protons dH') takes place. The nuclear reaction results in a deuteron 
(iH^), a positron (+,e"), and a neutrino. As soon as a deuteron is 
formed, it reacts with another proton resulting in helium 3 (^He^) 
and a y ray. The helium-3 nuclei fuse with each other, forming a. 
particles and two protons. In each of these reactions energy is 
released, resulting in 26 MeV for the complete cycle of four protons 
forming a helium nucleus. 



One form of proton-proton fusion 
chain which releases energy in stars: 

• protons 

O neutrons 

• positrons 
— *■ y-rays 



o 



y 



\^, 



9 



'• o 






/ 



.^ 



o ^- 



See "Power from the Stars" 
Reader 6. 



The lack of an upper limit on the 
destructiveness of fusion bombs is 
one of the reasons why scientists 
such as Oppenheimer. Fermi, and 
Rabi advised against making such 
weapons, at least as long as there 
was any reasonable hope for inter- 
national arms control agreements. 



The rates of the reaction depend on the number of nuclei per 
unit volume and on the temperature; the higher the temperature, 
the faster the thermal motion of the particles and the more frequent 
and energetic the collisions. At the temperature of the sun's interior, 
which has been estimated to be 10 to 20 million degrees, the kinetic 
energies resulting from the thermal motion are in the neighborhood 
of 1 KeV. 

The release of large amounts of energy by means of fusion 
processes on earth has so far been possible only in thermonuclear 
explosions, such as hydrogen bombs. A hydrogen bomb consists of 
a mixture of light elements with a fission bomb. The high particle 
energies produced by the fission reaction serve to initiate the fusion 
reaction. The explosion of a fission bomb produces a temperature of 
about 5 X 10^ °K, which is sufficiently high to make fusion possible. 
The fusion reactions then release additional large amounts of 
energy. The total energy release is much greater than would be 
liberated by the fission bomb alone. Moreover, while there is a sort 
of upper limit beyond which fission bombs become not much more 
destructive (because they disperse the extra fissionable material 
before it can undergo fission), there seems to be no such upper limit 
to the size — and hence the destructive power — of fusion weapons. 

Q13 Is the ratio of the amount of hydrogen to the amount of 
helium in the sun increasing or decreasing? 



Section 24.10 



24.10 The strength of nuclear forces 

The large energies involved in nuclear reactions, a million or 
more times larger than the energies involved in chemical (molecu- 
lar) reactions, indicate that the forces holding the nucleus together 
are very much stronger than the forces that hold molecules together. 
Another clue to the magnitude of nuclear forces is the density of a 
typical nucleus. The work of Rutherford and his colleagues on the 
scattering of a. particles showed that atomic nuclei have radii in 
the neighborhood of 10"*^ cm to 10~*^ cm; this means that the 
volume of an atomic nucleus may be as small as lO"^** to 10~^^ cm^. 
Now, the mass of one of the lighter atoms is of the order of 10"^^ 
gram, and this mass is almost all concentrated in the nucleus, with 
the result that the density of the nucleus may be as high as 10'^ to 
10'^ grams per cubic centimeter. Densities of such magnitude are 
thousands of billions of times beyond the limits of our ordinary 
experience, since the greatest densities of ordinary material are in 
the neighborhood of 20 grams per cubic centimeter (uranium, gold, 
lead). It is evident that the forces that hold the atomic nucleus 
together must be very different from any forces we have considered 
so far. The search for understanding of these forces is one of the 
most important problems of modem physics. Although a good deal 
has been learned about nuclear forces, the problem is far from 
solved. 

Information about nuclear forces has been obtained in several 
ways. It is possible to deduce some of the properties of nuclear 
forces from the known properties of atomic nuclei, for example, 
from the binding-energy curve of the graph on p. 78. That curve 
shows that the average binding energy per nucleon has nearly the 
same value for all but the lightest nuclei — about 8 MeV per nucleon. 
In other words, the total binding energy of a nucleus is roughly 
proportional to the number of nucleons. Now, if every particle in 
the nucleus were to exert a force on every other particle, it would be 
expected that the energy of the interactions, and therefore the 
binding energy, would be approximately proportional to the number 
of interacting pairs. But the number of pairs of nucleons goes up 
nearly in proportion to the square of the number of nucleons, so the 
binding energy calculated by assuming such interacting pairs is 
very different from the experimental results. To deal with this 
contradiction it is necessary to assume that a nuclear particle does 
not interact with all other nuclear particles, but only with a limited 
number of them, that is, only with its nearest neighbors. For this to 
be the case the nuclear forces must have a short range: the nuclear 
forces must fall off very rapidly as the distance between two 
nucleons increases. This decrease must be more rapid than the 1/r'- 
decrease of the gravitational force between two particles, or the 
1/r^ decrease of the Coulomb electric force between two charges. 

The presence of protons in the nucleus also tells us something 
about nuclear forces. Since there are only positively charged and 
neutral particles in the nucleus, the electric forces must be 
repulsive. The nucleus is very small, of the order of 10"'^ cm in 



The chief problem studied by the 
team of physicists in the docu- 
mentary film People and Particles 
is whether the electric force between 
charged particles at very small 
distances varies inversely as the 
square of the distance. (It does.) 



100 Nuclear Energy, Nuclear Forces 

diameter; therefore these repulsive forces must be enormous. Why 
then do the pieces that make up the nucleus not fly apart? It seems 
reasonable to assume that the electric repulsion is overcome at 
very small distances by very strong attractive forces between the 
nuclear particles. Information about such specifically nuclear forces 
can be obtained by studying the scattering of protons or neutrons by 
materials containing protons. Scattering experiments and the theory 
needed to account for their results form an important branch of 
nuclear physics. They show that such attractive nuclear forces do 
indeed exist. Many of the properties of these forces are now known. 
But the problems of nuclear forces and how they hold the nucleus 
together lie at the frontier of nuclear research. 

In the absence of a complete theory of nuclear forces and 
See "Models of the Nucleus' in structure, models of the nucleus have been developed. Several 

Reader 6. models are in use, each for a specific aspect of nuclear phenomena, 

because no one model adequately describes the whole wide range 
of phenomena, from particle emission in radioactive decay to 
nuclear reactions and fission. Two of the most prominent of these 
models are described briefly in the next two sections: the liquid 
drop model and the shell model. 



Q14 Why is it assumed that there are special nuclear forces to 
hold the nucleus together? 

Q1 5 Why is it assumed that the nuclear force is very short-range? 



24.11 The liquid-drop nuclear model 

In the liquid-drop model the nucleus is regarded as analogous 
to a charged drop of liquid. This model was suggested because the 
molecules in a liquid drop are held together by short-range forces, 
as the nucleons in a nucleus appear to be. According to this model. 
the particles in the nucleus, like the molecules in a drop of liquid, 
are in continual random motion. In analogy with the evaporation of 
molecules from the surface of a liquid drop, a group of nuclear 
particles may thus pick up enough energy through chance collisions 
with other nucleons to overcome the attractive nuclear forces and 
escape from the nucleus; this process would conespond to spon- 
taneous a emissions. 

This model has been especially useful in describing nuclear 
reactions: a particle may enter the nucleus from outside and impart 
enough additional kinetic energy to the protons and neutrons to 
permit the escape of a proton or a neutron, or a combination such 
as a deuteron or an a particle. A detailed quantitative theory of 
nuclear reactions based on this idea has been developed. 

The usefulness of the liquid-drop model is well shown in its 
ability to account for fission. As we know, when a sample of U-^ 
is bombarded with slow neutrons, that is, neutrons whose kinetic 
energy is very small, a U"^ nucleus may capture a neutron to form 
a U-'" nucleus. We can calculate the energy made available inside 
the nucleus by the captured neutron: 



Section 24.11 



101 



mass of U-^'^ nucleus 
mass of neutron 
total mass 

mass of (unexcited) U'^^ nucleus 
difference in mass 



= 235.04393 amu 

1.00867 amu 

= 236.05260 amu 

= 236.04573 amu 



= 0.00687 amu 
corresponding excess energy = 0.00687 amu x 931 MeV/amu 

= 6.4 MeV 

Therefore, at the instant when the neutron is captured, the U"^ 
nucleus formed has this additional energy, 6.4 MeV, which is called 
the excitation energy due to the neutron capture. This energy is 
several MeV, even though the kinetic energy of the neutron (less 
than 1 eV) is relatively so small that it can be neglected in this 
calculation. 

What happens to the excited U^^** nucleus? This problem was 
studied theoretically in 1939 by Niels Bohr, who had come to the 
U.S., and John A. Wheeler, an American physicist. They showed 
that, according to the liquid-drop model, the U^^^ should be able to 
act like a drop of water when the latter is "excited" by being given 
mechanical energy. The nucleus can be deformed into an elongated 
or dumbell-like shape whose two (charged) parts may be beyond the 
range of the nuclear forces of attraction. The electric force of 
repulsion between the two parts of the deformed nucleus can over- 
come the short-range attractive forces, causing the nucleus to split, 
that is, to undergo fission, and causing the fragments to separate 
with high speeds. Each of the fragments will then quickly assume 
a spherical (or nearly sperical) form because within it the attractive 
nuclear forces again predominate. A schematic picture of a possible 
sequence of stages is sketched below. 




The liquid-drop model gives a simple answer to the question: 
why do some nuclides (U-'^'^ and Pu-'^^) undergo fission with slow 
neutrons while others (Th^^^ and U^'''*) undergo fission only with fast 
neutrons? The answer is that a certain minimum amount of energy 
must be available to a nucleus to deform it enough so that the 
repulsive electric forces can overcome the attractive nuclear forces. 
This amount, called the activation energy, can be calculated with 
the aid of the mathematical theory of the liquid-drop model. When 
U-'^^ captures a neutron to make U-•^^ the excitation energy of the 
U"^ nucleus is greater than the energy required for fission, even if 
the exciting neutron has very low kinetic energy. This calculation 
was made by Bohr and Wheeler in 1939; they found that their model 



Fission sometimes occurs sponta- 
neously-but so rarely that we can 
neglect it for our treatment. 



102 Nuclear Energy, Nuclear Forces 

predicted, correctly, that U^*^ undergoes fission with slow neutrons. 
The theory also predicted that when U^^^ captures a slow neutron to 
form U^^** the excitation energy is smaller than the activation 
energy by 0.9 MeV. Hence U^^** should not undergo fission unless 
SG 24.19, 24.20 bombarded with neutrons with kinetic energies of 0.9 MeV or more. 
The correctness of this prediction was verified by experiment. 

Q16 According to the liquid-drop model, what kind of force is 
responsible for fission of a nucleus? 

Q17 Why does U'^^^ require /ast neutrons to provoke fission? 
Why does fission occur in U^^^ with slow neutrons? 



24.12 The shell model 

Another nuclear model is required to account for other properties 
of the nucleus — properties that could not be accounted for by the 
liquid-drop model. We mentioned in Sec. 22.7 that nuclides with 
even numbers of neutrons and protons are more stable than 
nuclides that contain odd numbers of either protons or neutrons. 
Detailed experimental studies of nuclear stability have shown that 
nuclei having 2, 8, 20, 50 or 82 protons, or 2, 8, 20, 50, 82 or 126 
neutrons are unusually numerous and stable. These nuclei have 
greater binding energies than closely similar nuclei. When the 
exceptional properties of nuclei with these numbers of protons 
and neutrons became clear, in 1948, no available theory or model 
of the nucleus could account for this situation. The numbers 2. 8, 
20, 50, 82 and 126 were referred to as "magic numbers." 

It was known from the study of chemical properties that atoms 
with atomic numbers 2, 10, 18, 36, 54, and 86 -gases helium to 
radon — have special chemical stability. This property was explained 
in the Bohr-Rutherford model of the atom by the idea that the 
electrons around each nucleus tend to arrange themselves in 
concentric shells, with each shell able to contain only a certain 
maximum number of electrons: 2 for the innermost shell, 8 for the 
next, and so on. An especially stable atom is one with a full electron 
shell on the outside. Although the Bohr-Rutherford model has been 
replaced by a more successful one based on quantum mechanics, 
the idea of shells still provides a useful picture, and a nuclear 
model — the nuclear-shell model — has been developed to deal with 
the observation that some nuclei are particularly stable. 

In the nuclear shell model it is assumed that protons can, in a 
rough way of speaking, arrange themselves in shells, and that 
neutrons can, independently, do likewise; in the "magic-number" 
nuclei the shells are filled. The model has been worked out in great 
detail on the basis of quantum mechanics, and has been successful 
in correlating the properties of nuclides that emit a or /3 particles 
and y photons, and in describing the electric and magnetic fields 
around nuclei. But the nuclear-shell model does not help us under- 
stand fission, and there are fundamental differences between this 
model and the liquid-drop model. For example, the shell model 



Section 24.13 



103 



emphasized definite patterns in which nucleons are arranged, while 
the hquid-drop model pictures the nuclear material in random 
motion. Each model is successful in accounting for some nuclear 
phenomena, but fails for others. 

When two seemingly contradictory theories or models must be 
used in a field of physics, a strong effort is put into trying to develop 
a more general viewpoint, or theory, which can include the two as 
special cases. Such a nuclear theory is being developed; it is called 
the collective model, and one of the physicists who has worked on 
this model is the Danish physicist Aage Bohr, the son of Neils Bohr. 
This model represents an advance beyond the shell and hquid-drop 
models in correlating nuclear data. It also has limits; thus, it does 
not answer fundamental questions about nuclear forces, which are 
still among the chief problems in the physics of our times. 

Q18 According to the shell model, what gives nuclei having a 
"magic number" of protons and neutrons their special properties? 

Q19 Which is better, the liquid-drop or the shell model of the 
nucleus? 



24.13 Biological and medical applications of nuclear physics 

In Sec. 24.7 we mentioned military applications of nuclear 
energy, and the use of nuclear energy as a source of electric power 
for cities, industries, and agriculture. There are many other applica- 
tions which may, in the long run, turn out to be more important 
than some of those. These may be included under the general 
heading of radiation biology and radiation medicine. The fields of 
science indicated by these names are broad and we can only 
indicate, by means of a few examples, some of the problems that 
are being worked on. In this work, radiations are used in the study 
of biological phenomena, in the diagnosis and treatment of disease, 
and in the improvement of agriculture. 

The physical and chemical effects of various kinds of radiations 
on biological materials are being studied to find out, for example, 
how radiation produces genetic changes. Since it has been dis- 
covered that many of the key chemical processes in cells are 
organized by single chains of molecules, it is clear that a single 
particle of radiation can, by breaking a chemical bond in such a 
chain, cause a permanent and perhaps disastrous change in the cell. 

The metabolism of plants and animals is being studied with 
the aid of extremely small amounts of radioactive nuclides called 
isotopic tracers, or "tagged atoms." A radioactive isotope (for 
example, C'*) acts chemically (and therefore physiologically) like a 
stable isotope (C^). Hence a radioactive tracer can be followed with 
counters as they go through various metabolic processes. The role 
of micronutrients (elements that are essential, in extremely small 
amounts, for the well-being of plants and animals) can be studied 
in this way. Agricultural experiments with fertilizers containing 
radioactive isotopes have shown at what point in the growth of a 
plant the fertilizer is essential. In chemistry, radioactive isotopes 





The upper portion of the photo above 
shows normal plant cell chromosomes 
divided into 2 groups. Below that the 
same cell is shown after x-ray ex- 
posure. Fragments and bridges be- 
tween groups are typical radiation- 
induced abnormalities. 




An autoradiograph of a fern frond 
made after the plant had taken 
in a solution containing radioactive 
sulfur (.eS^^). 




Damaged trees surround a radio- 
active cesium 137 capsule which had 
been kept there for nearly 6 months in 
an experiment to study the effects of 
ionizing radiation on biological sys- 
tems. 



The Medical Research Center of 
Brookhaven National Laboratory on 
Long Island, New York. The research 
reactor is housed in the cylindrical 
structure at the rear; beside it is a 
stack which exhausts the air used to 
cool the reactor. 




M.*f ^£ gS 



Section 24.13 105 

help in the determination of the details of chemical reactions and 
of the structure of complex molecules, such as proteins, vitamins 
and enzymes. 

Perhaps the most rewarding uses of radioisotopes have been in 
medical research, diagnosis, and therapy. For example, tracers can 
help to determine the rate of flow of blood through the heart 
and to the limbs, thus aiding in the diagnosis of abnormal conditions. 
Intense doses of radiation can do serious damage to all living cells, 
but diseased cells are often more easily damaged than normal cells. 
Radiation can, therefore, be used to treat some diseases, such as 
cancer. Some parts of the body take up particular elements 
preferentially. For example, the thyroid gland absorbs iodine 
easily. Specially prepared radioisotopes of such elements can be 
administered to the victims of certain diseases, thus supplying 
desired radiation right at the site of the disease. This method has 
been used in the treatment of cancer of the thyroid gland, blood 
diseases and brain tumors and in the diagnosis of thyroid, liver 
and kidney ailments. 

Some Typical Isotope Applications 



ISOTOPE 


HALF-LIFE 


IMPORTANT USES 


,H« 


11 years 


Used as a tag in organic sub- 
stances. 


eC" 


4700 years 


Used as a tag in studying the 
synthesis of many organic 
substances When ^0'*' is in- 
corporated in food material, 
its presence can be traced in 
the metabolic products 


„Na2'» 


15 hours 


Useful in a wide variety of 
biochemical investigations 
because of its solubility 
and chemical properties. 


P32 


14 days 


For the study of bone metab- 
olism, the treatment of blood 
diseases and the specific 
uptake in tumor tissue. 


reS"" 


87 days 


Has numerous chemical and 
industrial applications. 


,,Co- 


5.3 years 


Because of its intense y 
emission, may be used as a 
low-cost substitute for 
radium in radiography and 
therapy. 


^l''' 


8 days 


For the study of thyroid 
metabolism and the treatment 
of thyroid diseases. 



The table above summarizes the use of a few radioisotopes, 
most of which are produced by neutron bombardment in nuclear 
reactors. Such uses suggest the promise that nuclear physics holds 
for the future. Indeed, they symboHze the meaning of science at its 
best: research in science lays open to our understanding the 
secrets of nature — and from the application of his knowledge to 
human needs, all mankind can benefit. 



SG 24.21 




106 The Nucleus 

EPILOGUE In this unit we have traced the development of nuclear 
physics from the discovery of radioactivity to current work in nuclear 
fission and fusion. Radioactivity provided the starting place and 
tools to work with. In radioactivity we found the naturally occurring 
transmutation of elements, and so were led to achieve artificial trans- 
mutations. The naturally occurring radioactive series pointed to the 
existence of isotopes, both radioactive and stable. Artificial 
transmutation has increased by many hundreds the number of nuclear 
species available for study and use. 

Nuclear physicists and chemists study the reactions of the stable 
and radioactive nuclides. The collection and correlation of a vast body 
of experimental data now available remind us of the work of the 
nineteenth-century chemists and spectroscopists. Nuclear models are 
built, changed, and replaced by newer and, perhaps, better models. But 
the detailed nature of nuclear forces is still the subject of much 
research, especially in the field of high-energy physics. 

Yet that is only one of the fields that remains to be explored. The 
nucleus also has magnetic properties which affect the behavior of 
atoms. Sometimes it helps to study these properties when the atoms of 
matter are at very low temperatures, as close to absolute zero as we 
can get them. Nuclear physics overlaps with solid-state physics and 
with low-temperature physics; at low temperatures wonderful things 
happen-and quanta again help us to understand them. 

The study of light through the development of devices such as the 
laser attracts many physicists. These devices are made possible by, 
and contribute to, our increasing understanding of how complex atomic 
systems jump from one energy to another- and how they can be made 
to change where and when we want them to. 



I 



Epilogue 



107 



The properties of liquids are still only imperfectly understood. 
Thales of Miletus was perhaps the first man on record to make a large- 
scale scientific speculation when he proposed, over twenty-six centuries 
ago, that maybe everything in the world is basically made of water in 
combinations of its various states. Thales was wrong, but even today we 
are trying to develop an adequate theory of the behavior of water 
molecules. 

All the subjects we have mentioned touch on engineering, where 
physics and other disciplines are put to use to fashion the "man-made 
world". All of the engineering fields involve physics. Nuclear engineer- 
ing and space engineering are the most recent and, at the moment, 
perhaps the most glamorous. But today the chemical engineer, the 
mechanical engineer and the metallurgist all use the physicist's way of 
understanding the properties of atoms and atomic nuclei, because it is 
no longer enough to know only the properties of matter in bulk. 

The radiations we have talked about- a. /3. and y rays- are tools 
for industry, biology and medicine. They help to cure, preserve, study, 
understand. Neutrons are not only constituents of the nucleus, they are 
also probes for studies in science and in industry. 

So our study of atoms and nuclei, indeed our whole course, has 
been an introduction not only to physics but also to the many fields 
with which physics is closely linked. !t has been an introduction to an 
ever-expanding world in which much is known and understood; where 
much more — and perhaps the most wonderful part— is waiting to be 
discovered. 




J^Mi. 


/ ^'^^^1 




mk^M 


m ^VL~~ 


^mm 




M^NalAfit 


■:> ■ • - y.^MM^^^^^^B 


1^ ''nII^^bB^^^H 








24.1 The Project Physics learning materials 
particularly appropriate for Chapter 24 in- 
clude: 

Film 

The World of Enrico Fermi 

Transparency 

Binding Energy Curves 

Reader Articles 

New World of Nuclear Power 

Models of the Nucleus 

Power from the Stars 

Success 

The Nuclear Energy Revolution 

A Report to the Secretary of War 

Calling All Stars 

Tasks for a World Without War 

24.2 Suppose that a nucleus of ^C'^ is formed by 
adding a neutron to a gC'^ atom. Neglecting any 
kinetic energy the neutron may have, calculate 
the energy that becomes available to the nucleus 
due to the absorption of that neutron to make 
gC'^; the atomic masses of C'^ and C" (in an 
unexcited state) are 12.000000 and 13.003354 
amu. 

24.3 The atomic mass of He< is 4.00260 amu; 
what is the average binding energy per particle? 

24.4 Suppose that a proton with relatively small 
kinetic energy induces the following reaction: 



24.7 Calculate the amount of energy (in MeV) 
liberated in the following nuclear reaction: 



.Li^ 



,H' 



.,He^ + 2He^ 



If the lithium nucleus were initially at rest, what 
would be the relative directions of the two a 
particles? What would be the kinetic energy of 
each a particle? 

24.5 The first nuclear transmutation (obtained 
by Rutherford in 1919) was the reaction: 

^N'^ + aHe^ -» 80'' + ,H' 

The atomic masses involved are: 

N": 14.003074 amu 

O"': 16.999134 amu 

He": 4.002604 amu 

H': 1.007825 amu 

Is energy absorbed or released in this reaction? 
How much energy (in MeV) is absorbed or 
released? 

24.6 In an experiment on the reaction given in 
SG 24.5, the a particles used had a kinetic energy 
of 7.68 MeV, and the energy of the protons was 
5.93 MeV. What was the energy of the "recoiling" 
O'' nucleus? 



-N'^ + .H^ 
The atomic masses are: 



7N' 



iH' 



N'<: 14.003074 amu 
H^ : 2.014102 amu 
N'^: 15.000108 amu 
H' : 1.007825 amu 

24.8 Appreciable amounts of the uranium isotope 
gaU^^'' do not occur outside the laborator>'; y^U-" 

is formed after the thorium nucleus gf,Th-^'- has 
captured a neutron. Give the probable steps 
leading from <,(,Th-^'- to gaU^^^. 

24.9 Use the graph at the top left hand corner 
of p. 78 to find the binding energies for U'-'^, Ba'"' 
and Kr^-. Use these values to show that the energy 
released in the fission of U-^^ is approximately 
200 MeV. 

24.10 Possible end-products of U"* fission, when 
provoked by capture of slow neutrons, are sjLa''^ 
and ^jMo'l This reaction may be described by the 
equation: 

<,2U"^ + on' -^ s7La'3« + ^^Mo"^ + 2on' + 7(_,e<') 



The mass of 5,La'3« is 138.8061 amu; that of 
^.,Mo^^ is 94.9057 amu. How much energy is 
released per atom in this particular fission? (The 
mass of the seven electrons may be neglected.) 

24.11 Write a set of equations that describe the 
decay of the fission product agKr*- into joZr**"- 

24.12 Loss of neutrons from a structure contain- 
ing fissionable material depends on its shape as 
well as its size. For some shapes, it is impossible 
to reach a critical size because the neutron loss 
through the surface is too great. With what shape 
would a mass of fissionable material suffer the 
least loss of neutrons by passage through the 
surface? The most? 

24.13 Why are the high temperatures produced 
by the explosion of a fission bomb necessary to 
initiate fusion in a thermonuclear device? 

24.14 It is generally agreed that stars are formed 
when vast clouds of hydrogen gas collapse under 
the mutual gravitational attraction of their 
particles. How might this process lead to fusion 
reactions beginning in such stars? (Hint: The 
cloud has gravitational potential energy.) 



108 



UDY QUID 



24.15 One of the energy sources in the sun is 
the production of helium nuclei by four protons 
as described in Sec. 24.9: 4,H' -> 2He^ + 2+,e". 
Show that about 27 MeV of energy are released in 
each cycle. 

24.16 Fusion reactions in the sun convert a vast 
amount of hydrogen into radiant energy each 
second. 

(a) Knowing that the energy output of the sun 
is 3.90 X lO^" joules/sec, calculate the rate 
at which the sun is losing mass. 

(b) Convert the value 3.90 x 10^* joules/sec to 
horsepower. (Recall that 1 horsepower is 
equivalent to 746 watts.) 

24.17 A source of energy in the sun may be the 
"carbon cycle," proposed by Hans Bethe, which is 
outlined below. 

(a) Complete the six steps of the cycle. 

(b) After a cycle has been completed, which 
nuclides used in the cycle have been 
changed (and in what ways), and which 
have come out the same as they entered 

the cycle? 



24.20 Bombardment of 94Pu^^' with slow neutrons 
sometimes leads to the reaction: 



4Pu2'" + on' 



^PU242 + y 



The atomic masses of Pu^*' and Pu^" are 
241.056711 amu and 242.058710 amu. The 
activation energy of Pu'^"" is 5.0 MeV. Is Pu^*' 
fissionable with slow neutrons? 

24.21 The chemical structural formula for the 
energy carrying adenosine triphosphate (ATP) 
molecule in living cell is 



.e-N -C ^-' - 

c=c' 





C— c-o-p-o-p-o-p=o 
V /<-?-" A i i i 

C-H " ** 0-M 



^"\ 



Energy is provided to some other molecule when 



O 
the end phosphate group ( — p=0 ) is transferred 



eC'^ + .H' ^ 
( ) - 

6C'=' + iH> ^ 
( ) + ,H' 

sO'* - ( 
( ) + .H' 



( ) + y 

8C'3 + +,e»+i' 

( ) + y 

-^ «0'5 + y 

) + +16" + V 

-> fiC'^ + .He" 



to it, changing the ATP to adenosine diphosphate 
(ADP). Energy from the oxidation of food is used 
to attach new phosphate groups to the ADP, 
changing it once again to ATP. Suggest a proce- 
dure by which you could determine the rate at 
which new molecules of ATP are formed. 



24.18 Another reaction which may take place in 
the sun is: 



He^ + He* 



Be^ 



y 



The atomic mass of He'' is 3.016030 amu, and 
that of Be' is 7.016929. Is energy absorbed or 
released? How much energy? 

24.19 The atomic masses of gjU^^^ and gaU^^"* are 
233.039498 and 234.040900 amu. The activation 
energy for the fission of the nucleus saU^^'' is 4.6 
MeV. Is U^^^ fissionable by slow neutrons? 



24.22 Write an essay on one of the following 
topics: 

(a) The various ways a citizen can help assure 
that technological innovations will be made 
and used in a manner benefiting society as 
a whole. 

(b) The differences between technology and 
basic science. 

(c) The responsibilities of scientists to society. 

(d) The responsibilities of society to further 
science. 

(e) The fields of physics or related sciences in 
which you may want to do further study. 




A perspective on the Project Physics Course: 
a letter from the Directors. 



Harvard Project Physics 




Harvard University 
Cambridge, Massachusetts 



Dear Student, 

While taking this introductory course in physics you have worked 
through a great deal of the content and development of the physical 
sciences. You now have a good headstart for further study of physics 
as well as other fields such as astronomy, chemistry, engineering, 
and the history of science. You are now no longer an "outsider, " but 
are knowledgeable about many of the main currents of scientific 
advance over the past centuries. 

Even if you cannot yet solve the detailed problems that a profes- 
sional physicist may be working on, you do now share with him much of 
the cultural heritage of modern physical science. Therefore you can, 
if you wish, make an important decision: if you found yourself 
intrigued or even just curious about any part of the material in this 
course, you should consider going more deeply into these fields as 
part of your further schooling — whether or not science will be your 
eventual career. 

But in addition to physics, and in addition to the way men and women 
make discoveries in science, you have also learned something about the 
place of science in society. By now you should have some answers if 
anyone should ask "Why physics?" or "What is the relevance of science?" 

It would have been impossible to do justice to these important 
questions when you started this course. Now you have first-hand know- 
ledge on which to base your own answers. We, who have worked for years 
together with literally hundreds of colleagues and students in our 
participating try-out schools, to fashion these books, lab experiments, 
film, etc., would like to share with you some of our own answers to 
these questions, as a kind of epilogue to the whole Project Physics 
Course. We hope you may agree with at least some of our opinions. 

What special reasons are there for thinking that physics, among all 
the sciences, is of basic importance? What is the relevance of science 
today? We believe there are at least five parts to a complete answer, 
and for each part there were examples in the course materials you 
have now studied. The fact that the questions about "relevance" have 
in the last few years almost become cliches does not change the need 
to be clear about the subject. So let us attack it head-on. 



Relevance 1: The intellectual excitement of physics 



At some points during the year — often, we hope — you yourself have 
felt the intellectual excitement that accompanies understanding human 
achievements of the kind that have been chronicled here. This sort 
of excitement can be derived from the explanation of the motion of 
planets in our solar system, just as it can from the discovery of the 
internal structure in Shakespeare's King Lear . You may have felt it, 
keenly and suddenly, when a theory showed the connection between 
apparently separate parts of experience, or when a lab experiment 
succeeded after many tries, or when the computed planetary orbit 
closed, or when a long derivation that seemed to ramble on and on 
came suddenly to a resolution like a Bach fugue. 

At such a moment, one catches a glimpse that the sort of knowledge 
which physics leads to can crystallize the confused world of phenomena. 
Here is a way to see nature's clarity, here is the place to find the 
necessity which guides all things. Remember how lyrical Kepler became 
when he found the law that (T^/R^) is a constant? One must not dismiss 
such a moment of emotion. It does belong in science, too. It is 
a real and profound experience, an intellectual excitement that every 
scientist has when he discovers something new, or even when he just 
reads for the first time of a beautiful piece of work done by someone 
else. If we did not treasure such experiences, life would grow dull 
indeed. The joy of intellectual engagement in the deepest phenomena of 
the material world, and the joy of discovering therein the success of 
one's own rational and intuitive faculties — these are among the most 
relevant and enobling activities one can pursue. 

In the Text and in the Reader, you have often encountered remarks by 
scientists praising the simplicity of physics, the fact that there 
are only a few really deep laws but that they suffice to deal with the 
myriad of apparently different observations. From the very beginning, 
from Chapter 1 where we quickly abandoned the gyrations of a falling 
leaf as a useful beginning for the study of motion, we learned to look 
for simple commonalities in all behavior. We have been seeking overall 
principles that will unify many diverse cases, whether it be a falling 
leaf in one's backyard or the turning of an unseen solar system at 
the edge of the universe. Nothing is more astonishing than that it is^ 
possible to have such a universal physics! The most distant hydrogen 
atom is built on exactly the same principle as the one nearest you — as 
seen by the fact that both emit the same wavelengths of light. All 
the laws of physics that govern the structure of matter and its behav- 
ior in space and time have that universality. 

Einstein once expressed these thoughts in a memorable way. Physical 
theory, he said, has two ardent desires: To gather up as far as pos- 
sible all pertinent phenomena and their connections; and to help us 

not only to know how nature is and how her transactions are 
carried through, but also to reach as far as possible the 
Utopian and seemingly arrogant aim of knowing why nature is 



thus and not otherwise Thereby one experiences, so to 

speak, that God Himself could not have arranged those con- 
nections in any other way than that which factually exists, 
anymore that it would be in His power to make the nvimber 
4 into a prime number. This is the Promethean element of the 
scientific experience. .. .Here has always been for me the 
particular magic of scientific effort. 

Three and a half centuries earlier, Johannes Kepler had used almost 
the same words. In the preface of his first book he announced that he 
wanted to find out, with respect to the number, positions, and motions 
of the planets, "Why they are as they are, and not otherwise." To 
a friend he wrote at about the same time that with regard to numbers 
and quantity "our knowledge is of the same kind as God's, at least 
insofar as we can understand something of it in this mortal life." 

These were by no means sacrilegious thoughts. On the contrary, it 
was a pious man who wrote this. As Kepler often stated — and many 
scientists since that day have agreed with him — the world that God 
made stands before our minds as a kind of puzzle, for us to solve in 
order that we may prove we are worthy of the mind given to us for that 
very purpose. 

We hope to have shown that physics is neither an isolated, bloodless 
body of facts and theories with mere vocational usefulness, nor a 
glorious entertainment for an elite of mathematical wizards. (As 
a matter of fact, some of the best physicists, including several whose 
accomplishments are detailed in this course, were themselves not par- 
ticularly good at mathematics.)" Physics is the study of what makes the 
whole world go, and we think it is too beautiful to be kept secret 
from anyone, no matter what his eventual career plans may be. To live 
with more joy and intelligence, one has to know the world in which 
one lives, and this surely includes the majestic yet simple order 
physicists have found in our universe. Without such a study, as Galileo 
said, one may be lost in a labyrinth and not even know it. To be 
ignorant of physics may leave one unprepared for living in one's own 
time — as an intelligent spectator in the human adventures of our time 
no less than as an effective wage-earner and citizen. 

Relevance 2; Immediate practical benefits to society 

A second, very different way of seeing the relevance of science is 
in terms of the effect science sometimes has in helping to prepare the 
base for technological advance. We speak here not of the long-range, 
slower effects of which more will be said later, but the quick "spin- 
off, " the intentional use of basic science "for the relief of man's 
estate, " in the phrase of the seventeenth-century philosopher 
Francis Bacon. 

Many students and critics of science seem to have only this particu- 
lar aspect in mind when they use the word "relevance." However, useful 
though science can be in this sense, it would be quite wrong to settle 
merely for the assistance physics can give, say, to the study of such 



problems as pollution. We say this for two reasons: First of all 
there really is, and need be relatively little connection between 
today's basic physics research and current technological advance. The 
gadgets and devices being produced today by industry, even if they are 
as sophisticated as those used for space exploration, rely very 
little on new research in basic physics or on the discovery of new 
laws. They are mostly based on applications of well-known laws and of 
techniques developed long ago. On the contrary, people who do basic 
research in physics find themselves nowadays much more often in the 
position of having to oppose new plans for large-scale technological 
"advance" (whether it be a widely deployed ABM system, or excavation by 
use of nuclear devices, or supersonic transport planes, all of them 
gadgets that in the opinion of the majority of physicists have more 
long-range dangers than benefits) . 

In fact, contrary to folklore, the connection between basic physics 
and technical advance is generally indirect or roundabout. Only rarely 
is a basic advance made consciously as a prelude to a major technical 
improvement. The physicist H.B.G. Casimir illustrated this proposition 
by giving examples of progress made as a result of the work of 
scientists who did not set out to work for specific well-defined 
practical aims : 

One might ask whether basic circuits in computers might 
have been found by people who wanted to build computers. As 
it happens, they were discovered in the 1930 's by physicists 
dealing with the counting of nuclear particles because they 
were interested in nuclear physics.... 

One might ask whether there would be nuclear power because 
people wanted new power sources, or whether the urge to 
have new power would have led to the discovery of the 
nucleus. Only it didn't happen that way, and there were the 
Curies, and Rutherford, and Fermi, and a few others.... 

One might ask whether induction coils in motorcars might 
have been made by enterprises which wanted to make motor 
transport, and whether then they would have stumbled on the 
laws of induction. But the laws of induction had been found 
by Faraday many decades before that.... 

Or whether, in an urge to provide better communication, 
one might have found electromagnetic waves. They weren't 
found that way. They were found by Hertz who emphasized the 
beauty of physics and who based his work on the theoretical 
considerations of Maxwell. I think there is hardly any 
example of twentieth-century innovation which is not 
indebted in this way to basic scientific thought. 

There is also another reason why it would be quite wrong to seek 
relevance for science merely in the rare immediate benefits to 
technology. Technological advance all too often brings with it major 
social problems that arise as unforeseen by-products, and these 
problems cannot be cured or even properly understood through existing 



scientific or technological or political means alone. Rather, such 
cures depend to a large extent on making new, basic scientific ad - 
vances . To put it differently, at the heart of social problems created 
by technological advance is the absence of some specific basic 
scientific knowledge. This fact gives a whole new mandate and a new 
range of expectations for basic scientific research. 

Examples come readily to mind. Thus, it is quite customary to say 
that the population explosion is in part caused by the advance of 
medical science (owing to better sanitation, innoculation, antibiotics, 
etc.). But one can equally well claim that the population explosion 
is bound to overwhelm us precisely because we do not yet have at hand 
sufficient knowledge in pure science. That is to say, the complex 
problem of over-population is due in a large degree to our current 
ignorance of the basic process of conception — its biophysics, biochemi- 
stry, physiology. No wonder that attempts at controlling population 
are so halting. What is astonishing, rather, is that the first medical 
school laboratory in the United States specifically designed to study 
the whole range of scientific problems in the process of reproduction 
is only now being built. 

Similarly, it is sometimes said that progress in physics is "respon- 
sible" for the threatening arms race. But it is more accurate to say 
that arms control treaties were difficult to achieve in good part 
because of insufficient knowledge of geophysics that made inspection 
through seismographs of suspected illegal weapons tests difficult and 
uncertain. A better understanding of geophysics, it turned out, was 
needed before different nations would consider it safe to enter in 
arms control treaties that outlaw weapons tests. 

The problem of bringing food to hungry people in arid lands that are 
near the sea, as in Peru or India or Egypt, is to a large extent 
political, as are most of the problems mentioned above. But it is also 
a problem of basic science: Before it is possible to design much more 
economical desalination plants, a more fundamental understanding of the 
structure of liquids — one of the much-neglected problem areas in 
current physics and chemistry — and of the phenomena of materials moving 
through membranes will be needed. And turning to pollution, that is 
of course also the result of greed, stupidity, apathy, and the conse- 
quent lack of law enforcement; but to clean up smog-ridden areas more 
effectively will require greater basic knowledge than we have today of 
the physics and chemistry of combustion and of meteorology. And in 
the meantime, to this day the most effective and insufficiently used 
device for getting rid of pollution due to solid particles is the 
electrostatic precipitator, working on the scientific principles we 
discussed in Unit 4, and known since 1600. 

These remarks should serve to oppose two widely current but errone- 
ous notions: one, that basic science is an unnecessary luxury, and 
should be supported only if it is directed to immediate practical 
applicability ( — as the quotation bv Casimir above indicates, things 
just don't happen that way) 7 and second, that one way of stopping the 
abuses that come as by-products of technical innovation is to stop 
science ( — whereas in fact curing the abuses depends on scientific 
advances yet to be made) . 



I 



Relevance 3; Long-range social benefits 

Turning from the immediate to the long-range effects of science that 
give it relevance, we have seen ample evidence that every person alive 
today, whether or not he or she has studied science, is intellectually 
a child of Copernicus and Galileo, Newton and Faraday, Einstein and 
Bohr. Our imagination and intellectual tools were indeed shaped to 
a large degree by the advances in the knowledge of physics they and 
their contemporaries made, long before we were born. Thus the material 
in the Unit 2 Text and Reader showed how the Copernican and Newtonian 
world view triumphed in the West, and indeed how the recognition that 
a uniform law holds sway over all matter everywhere helped to overcome 
hierarchical thinking, thereby preparing the mind for self-reliant 
democracy. And again, in Unit 3, we saw that the successes of statis- 
tics and of the concepts of energy prepared the ground for the moderni- 
zation of the Newtonian worldview. 

In addition to the long-range influence of science upon the mind — 
the kind of influence that Newton's work had on the imagination of the 
poets and theologians from the eighteenth century onward — there are 
also the more material long-range effects we studied in connection with 
the advances made by James Watt, Michael Faraday, and Enrico Fermi. 
From an understanding of how the steam engine works flowed a century- 
long transformation of society which now is studied under the name 
of the Industrial Revolution. From Faraday's "toys" came electric 
motors and generators and, in time, the electric-powered elevators, 
trains and subways that facilitated the upward and sideways growth of 
cities. Similarly, the experiments of Fermi's group on neutron-induced 
artificial radioactivity prepared for the study of nuclear fission, 
and this in turn led to the design of new sources of energy that will 
turn out to be the only means for meeting the frantically growing 
energy needs of our society. 

Even more than is true for the immediate practical influences, it 
usually is impossible to foresee ahead of time the long-range effects 
of science upon social change. To avoid possible negative effects 
and to capitalize on positive ones, there is only one policy available: 
to exert uncompromising watchfulness, as citizens and scientists — 
calling attention to current flagrant abuses of scientific knowledge 
or skills, and keeping up-to-date on scientific advance so as to be 
ready to keep it from being derailed and abused in the future. 

Relevance 4; Science as a study that is connected to all other 
fields 

The fourth meaning of the word "relevance" refers to science not as 
merely a technical study but as one part of the general humanistic 
development of mankind. We agree fully with the Nobel Prize physicist 
I.I. Rabi, quoted in the Preface to the Text ; 

Science should be taught at whatever level, from the lowest 
to the highest, in the humanistic way. By which I mean it 




should be taught with a certain historical 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. 

We can illustrate the need for this sense of humanistic interconnect- 
edness by means of a simple diagram. The physics course as tradition- 
ally given in many high schools and colleges is like a string of beads. 
One subject follows another, from Galileo's kinematics to the most 
recent advances in nuclear physics — the usual sequence that more or 
less parallels the historical development of the science, whether this 
is made explicit or not. But few if any connections are shown with 
other achievements of human beings who are not physicists, with scien- 
ces other than physics, and with studies and activities other than 
science. And all too often the materials studied in the other courses — 
in chemistry, in biology, in literature, etc. — also hang there by 
themselves like so many separate strings of beads. 



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There are some advantages in such a string-of-beads presentation of 
a course. For example, it is convenient to teach. But ignoring connec- 
tions that do exist among all these fields does not do justice to 
the actual state of affairs. A research project in experimental 
physics, for example, sooner or later draws on material not only from 
almost every part of a physics course, but also from mathematics, 
metallurgy, chemical thermodynamics, electronic engineering, computer 
technology, and many other fields of science — not to speak of group 
psychology, accounting, and skill in writing a good article about the 
work. Moreover, nobody who has engaged in actual scientific work 



can fail to see the influence that advances made in science can have 
in terms of social and practical consequences. "Pure" physics is an 
invention that exists only in the most old-fashioned classrooms. If 
you pick up a real problem in physics (or any other science) there 
extends from it connections to a number of expected and unexpected 
problems in fields that at first glance seem to "belong" to other 
professions . 

In this course you have seen many evidences of these connections to 
subject matter of the kind not usually referred to in physics courses. 
Think back, for example, to our case study in Unit 2 of Newtonian 
mechanics as applied to planetary motion, a subject that is one of the 
"beads" on the physics chain. Newton had studied theology and philos- 
ophy and those ideas echoed in the Principia in his sections on the 
nature of time and space (in the Figure below, link A to philosophy) . 
Within physics itself, Newton brought to a culmination the work of 
Kepler and Galileo (link B) . Much of the established mathematics in 
Newton's work came from the Greeks (link C) . New mathematics, parti- 
cularly the basic ideas of calculus, were invented by Newton to aid his 
own progress, thereby advancing the progress of mathematics (link D) . 



1600 A.D, 



TODAY 



*v 



MATHEMATICS . . • PHYSICS CHEMISTRY 



PHILOSOPHY LITERATURE 




Within physics, all who follow Newton will use his laws and approach 
(link E) . His effects on the philosophy of the deist theologians 
(link F) , on Dalton's atomic models in chemistry (link G) , and on the 
artistic sensibilities of the 18th century in which Newton swayed 
the muses (link H) , were docximented in the Text and in the Reader 
articles . 

The same kind of web extends around every one of the chief topics we 

have discussed in this course. Think of the link from philosophy to 



the work of Oersted, Ampere, and Faraday in electricity (through 
their interest in Nature Philosophy) . Think of the link reaching 
from nuclear physics back along the chain to the classical physics 
of three centuries earlier (as in the discussion of how the mass of 
the neutron was determined), and the links sideways, to biology, engi- 
neering, and politics, through the various applications and by-products 
of nuclear reactors. 

Such links exist between all fields. No doubt you found that some of 
the topics and persons discussed in our course came up also in other 
courses you have been taking. If we drew all links between fields on 
the intellectual map, we would see that instead of the separate strings 
of beads there really exists a coherent crystal, or, if you will, 
a tapestry, a fabric of ideas. This view of the relevance of science 
has deeply penetrated our course: Science is now seen to be in dynamic 
interaction with the total intellectual activity of an age. In a deep 
sense, science is part of the study of history and of philosophy, and 
it may underlie the work of the artist just as it penetrates into the 
explanation a mother gives to her child of the way things move. 

If we therefore tried to think away the whole string with the heading 
"Physics, " the history of Western thought would be almost incomprehen- 
sible. We could not understand — and in fact would not have had — much 
of the work of a John Locke and a Voltaire and an Alexander Pope who, 
among many others, were frankly inspired by the work of the physicists 
of their time. Conversely, philosophy, mathematics, and other fields 
would be far emptier studies without their fulfillment and extension 
through the work of philosopher-scientists such as Mach, Einstein, and 
Bohr. Eliminating physics would of course also make nonsense of the 
history of industrial development following upon Watt's steam engine, 
Volta's battery, Faraday's motors and generators, etc. A neighboring 
science such as chemistry could not have developed without models 
of gases and theories of atomic structure that were largely the work 
of physicists. In short, if you pull out the thread marked "Physics" 
from the tapestry, the fabric would unravel like an old sweater; 
and the same would be true if any of the other threads were pulled out. 
On this view, therefore, the relevance of any field of knowledge, 
including science, is that it is an integral part of the total growth 
of thought. 

All too often students have to discover the existence of the fabric 
of ideas for themselves. For it is a bad habit of some academics to 
teach their own subject as if it had nothing to do with others. But it 
is precisely by seeing these connections between fields that one 
becomes educated rather than only trained. We have made these links 
explicit in our course in the hope of providing an educational experi- 
ence that, in a similar manner, you can and should obtain in all your 
courses. 

Relevance 5; Science as a style of life 

Modern science is not an elite enterprise for only a self-educated 
few; nowadays there are literally millions of men and women engaged in 



it. In the United States alone there are nearly 50,000 people who 
contribute to physics, and each does so in an individual way. Some 
prefer to follow their thoughts entirely alone, some are surrounded by 
students or collaborate with groups of colleagues. Some are in small 
university laboratories, some in large industrial enterprises. Some 
accentuate the sober rationality and objectivity which it is possible 
to achieve in scientific work, others pursue their work with a passion 
and a daring that makes one dizzy to follow them. Some have no academic 
degree at all, others are laden with diplomas. But they all share 
gives a style or way of looking at the world and of life, and this 
fact science a relevance in addition to the four we have mentioned 
above. This style has a number of earmarks or components; in concluding 
this letter, let us list just four: 

A. By and large, these people feel at home in the world of nature. 
It makes sense to them, and they are comfortable with it while knowing 
full well that the most surprising and important findings in their field 
are still to be made in the future. To them the world is not a succes- 
sion of incoherent, unique events. Knowledge about nature gives them 

a sense of the relations of things — how the world hangs together 
in an ecological manner. But such knowledge does not "explain away" 
the phenomena or dull the excitement about them, any more than 
knowing the rules of baseball makes you less involved in watching the 
game than you would be if you were ignorant of them. Of course nobody 
knows all there is to know even about a single one of the sciences. 
But still, you can feel quite at home in a city even if you have per- 
sonally walked through only a few percent of all the streets there; if 
you know the pattern in outline, plus the crucial details of some 
regions within it, you no longer feel a stranger. 

B. Under Relevance 1 above we stressed the intellectual interest in 
science for society as a whole, but there is also a personal aspect 
for every scientist or student: Here is a chance to devote one's 
professional life to something one loves to do. Those who have selected 
a science for their career, and who are at all good at it, are on 

a road through a changing landscape along which each can select his own 
problems to work on. (If only this were possible for people everywhere, 
so many of whom are trapped in dull routines others have decided for 
them!) We speak here of science as doing , not just what is contained 
in books, any more than art is only what is contained in museums and 
libraries. Being a scientist can be a way of spending one's profes- 
sional life, day by day, in what one likes to do and does well. It's 
not like reading a play, or watching it, but like writing it and 
acting in it. And much of the same satisfaction goes to those who 
spend most of their lives not as research scientists but as teachers, 
in high school or college — those who have found that their chief 
satisfaction is helping young people to realize what role science can 
play in their lives. 

C. Each professional group has its own values, and the values of 
day-by-day life in science were illustrated in the course also. No- 
where more than in science is intellectual merit and skill honored. 
No matter who he is, the scientist is taken seriously by his peers for 



what he can do. Consequently, some minority groups have broken through 
the unjust social obstacles first by showing their excellence in 
scientific work. Ihere is in science a great amount of room at the 
top, as well as an atmosphere of belonging to an international and 
cosmopolitan community. 

One "minority" group that has been of particular concern to scien- 
tists is that made up of young people. A whole set of social inventions 
and devices operates in the life of science in order to recognize and 
reward talent as early as possible. As you saw again and again (in the 
Text and in the biographical remarks, in the documentary films People 
and Particles and The World of Enrico Fermi ) , the young scientist 
is welcome and is brought as quickly as possible to participate at the 
growing edge of new science. As a member of a team he may in some sub- 
ject be the expert or teacher for others who are his seniors. And 
unlike the situation in many other fields, it is widely recognized in 
science that a person is at his best in terms of imaginative contri- 
butions while still young. 

D. More and more, scientists have recognized that discovery of new 
knowledge and the teaching of established knowledge do not fulfill all 
their responsibilities. Rather, scientists are prominent among those 
who take part in the process of examining the immediate social 
consequences of scientific and technical advance; their knowledge of 
science adds to their obligations of citizenship. Most of them, and 
particularly the young, therefore feel that there is a happy comple- 
mentarity between taking part in developing the human values of 
a democratic society and taking part in the growth of science. 



The five meanings of relevance we have now set forth are of course 
closely related to one another in many ways. They can all be present 
in the actual lives of actual people. In preparing the materials 
of this course we have tried to catch our own excitement about physics, 
its relevance, and its relations to the rest of the world of thought 
and action — and we hope you have shared some of that excitement 
with us. 



With all good wishes. 







staff and Consultants 



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, 
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 Polytfechnic Institute, 

Mass. / 

Kenneth J. Jones, Harvard University 
LeRoy Kallemeyn, Benson Hign 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, Nation&l Film Board of Canada, 

Montreal / 

Merritt E. Kimball, Oapuchino High School, San 

Bruno, Calif. ' 

Walter D. Knight, Uidiversity 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 





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, 

Cahf. 
Noel C. Little, Bowdoin College, Brunswick. Me. 
Arthur L. Loeb. Ledgemont Laboratory. Lexington, 

Mass. /^ . 

Richard T. Mara, Gettysbijtg Cgfllege, 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, WhQ4t Ridge High School, 

Colo. / 

Priya N. Mehta, Harvara University 
Glen Mervyn, West Va/couver Secondary' School, 

B.C., Canada / 

Franklin Miller, JrVKenyon College, Gambier, 

Ohio / 

Jack C. Miller, Bomona College, Claremont, Calif. 
Kent D. Miller.a:iaremont High School, Cahf. 
James A. Mintstrell, Mercer Island High School, 

Washington 
James F. Moore, Canton High School, Mass. 
Robert Hy Mosteller, Princeton High School, 

Cinciryhati, Ohio 
WUlian/ Naison, Jamaica High School, N.Y. 
Henry^ Nelson, Berkeley High School, Calif. 
Josepi D. Novak, Purdue University, Lafayette, 

Iiyd. 
Tlyjrir Olafsson, Menntaskolinn Ad, Laugarvatni, 
celand 
ay Orear, Cornell University, Ithaca, N.Y. 

aul OToole, 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. 
(Continued on page 182) 




The Project Physics Course 



Handbook 



6 



The Nucleus 




Contents 



HANDBOOK SECTION 



Chapter 21 Radioactivity 

Experiments 

45. Random Events 126 

46. Range of a and /3 Particles 131 

47. Half -life— I 134 

Part A. Twenty-sided Dice 134 
Part B. Electric Circuit 134 

48. Half -life— II 138 

49. Radioactive Tracers 140 
Part A. Autoradiography 142 

Part B. Chemical Reactions and Separations 142 
Activities 

Magnetic Deflection of p Rays 144 
Measuring the Energy of /3 Radiation 144 
A Sweet Demonstration 146 
Ionization by Radioactivity 146 
Exponential Decay in Concentration 146 

Chapter 23 The Nucleus 

Activity 

Neutron Detection Problem Analogue (Chadwick's Problem) 147 
Film Loop 

Film Loop 49 : Collisions with an Object of Unknown Mass 148 

Chapter 24 Nuclear Energy; Nuclear Forces 

Activities 

Two Models of a Chain Reaction 149 

More Information on Nuclear Fission and Fusion 

Peaceful Uses of Radioactivity 149 I \J 





V 



Chapter 



21 



Radioactivity 



EXPERIMENT 45 RANDOM EVENTS 

In Unit 6, after having explored the random 
behavior of gas molecules in Unit 3, you are 
learning that some atomic and nuclear events 
occur in a random manner. The purpose of this 
experiment is to give you some firsthand ex- 
perience with random events. 

What is a random event? 

Dice are useful for studying random behavior. 
You cannot predict with certainty how many 
spots will show on a single throw. But you are 
about to discover that you can make useful 
predictions about a large number of throws. 
If the behavior of the dice is truly random, you 
can use probability theory to make predictions. 
When, for example, you shake a box of 100 
dice, you can predict with some confidence 
how many will fall with one spot up, how many 
with two spots up, and so on. Probability theory 
has many applications. For example, it is used 
in the study of automobile traffic flow, the in- 
terpretation of faint radar echoes from the 
planets, the prediction of birth, death, and acci- 
dent rates, and the study of the breakup of 
nuclei. An interesting discussion of the rules 
and uses of probability theory is found in 
George Gamow's article, "The Law of Dis- 
order," in Reader 3. 

The theory of probability provides ways to 
determine whether a set of events are random. 
An important characteristic of all truly ran- 
dom events is that each event is independent 
of the others. For example, if you throw a legi- 
timate die four times in a row and find that a 
single spot turns up each time, your chance of 
observing a single spot on the fifth throw is no 
greater or smaller than it was on the first 
throw. 

If events are to be independent, the cir- 
cumstances under which the observations are 
made must never favor one outcome over an- 
other. This condition is met in each of the fol- 
lowing three parts of this experiment. You 
are expected to do only one of these parts, (a), 
(b), or (c). The section "Recording your data" 



that follows the three descriptions apphes to all 
parts of the experiment. Read this section in 
preparing to do any part of the experiment. 

(a) Twenty-sided dice 

A tray containing 120 dice is used for this 
experiment. Each die has 20 identical faces 
(the name for a solid with this shape is icosa- 
hedron). One of the 20 faces on each die should 
be marked; if it is not, mark one face on each 
die with a felt-tip pen. 

Ql What is the probability that the marked 
face will appear at the top for any one throw of 
one die? To put it another way, on the average 
how many marked faces would you expect to 
see face up if you roll all 120 dice? 

Now try it. and see how well your predic- 
tion holds. Record as many trials as you can in 
the time available, shaking the dice, pouring 
them out onto the floor or a large tabletop, and 
counting the number of marked faces showing 
face up. (See Fig. 21-1.) 




Fig. 21-1 Icosahedral dice in use. 

The counting will go faster if the floor area 
or tabletop is divided into three or four sec- 
tions, with a different person counting each 
section and another person recording the total 
count. Work rapidly, taking turns with others 
in your group if you get tired, so that you can 
count at least 100 trials. 

(b) Diffusion cloud cfiamber 

A cloud chamber is a device that makes visible 
the trail left by the particles emitted by radio- 



Experiment 45 



127 



active atoms. One version is a transparent box 
filled with supercooled alcohol vapor. When an 
a particle passes through, it leaves a trail of 
ionized air molecules. The alcohol molecules 
are attracted to these ions and they condense 
into tiny droplets which mark the trail. 

Your purpose in this experiment is not to 
learn about the operation of the chamber, but 
simply to study the randomness with which 
the a particles are emitted. A barrier with a 
narrow opening is placed in the chamber near 
a radioactive source that emits a particles. 
Count the number of tracks you observe com- 
ing through the opening in a convenient time 
interval, such as 10 seconds. Continue count- 
ing for as many intervals as you can during the 
class period. 



ro-d I'^o.c'five e'/t'-'^^ 



r' 



L._. 



■fi'irie fntervo-'s 



A convenient method of counting events in successive 
time intervals is to mark them in one slot of the "drag- 
strip" recorder, while marking seconds (or ten second 
intervals) in the other slot. 

(c) Geiger counter 

A Geiger counter is another device that detects 
the passage of invisible particles. A potential 
difference of several hundred volts is main- 
tained between the two electrodes of the 
Geiger tube. When a j8 particle or a y ray ionizes 
the gas in the tube, a short pulse of electricity 
passes through it. The pulse may be heard as 
an audible click in an earphone, seen as a 
"blip" on an oscilloscope screen, or read as a 
change in a number on an electronic scaling 
device. When a radioactive source is brought 
near the tube, the pulse rate goes up rapidly. 
But even without the source, an occasional 
pulse still occurs. These pulses are called 
"background" and are caused by cosmic radi- 
ation and by a slight amount of radioactivity 
always present in objects around the tube. 

Use the Geiger counter to determine the 
rate of background radiation, counting over 



and over again the number of pulses in a con- 
venient time interval, such as 10 seconds. 

Recording your data 

Whichever of the three experiments you do, 
prepare your data record in the following way: 
Down the left-hand edge of your paper 
write a column of numbers from to the high- 
est number you ever expect to observe in one 
count. For example, if your Geiger counts 
seem to range from 3 to 20 counts in each time 
interval, record numbers from to 20 or 25. 



of ei/ent S 
observe cj 



Number of 
evfr\ts obsert/ffd 
in one 
time inteft^^l 


(freciuincij) 


in) 


if) 





1 


1 




X 


1 


3 


-Htr -mi 


4- 


■Hft -kHf III 


5" 
6 


hhH- -Hit 11 

tth i 


7 


.^.f^ 44H444t 1 


8 


Hff mf II 


^ 


nil 


10 


nil 


II 


nil 


liL 


/ 


IS 


/ 



Cn^n 



30 
65 

IISL 

Ao 

13 
623 



Fig. 21-2 A typical data page. 



To record your data, put a tally mark oppo- 
site each number in the column for each time 
this number occurred. Continue making tally 
marks for as many trial observations as you 
can make during the time you have. When you 
are through, add another column in which you 
multiply each number in the first column by 



128 



Experiment 45 



the number of tallies opposite it. Whichever 
experiment you did, your data sheet will look 
something like the sample in Fig. 21-2. The 
third column shows that a total of 623 marked 
faces (or pulses or tracks) were observed in 
the 100 trials. The average is 623 divided by 
100, or about 6. You can see that most of the 
counts cluster around the mean. 

This arrangement of data is called a dis- 
tribution table. The distribution shown was 
obtained by shaking the tray of 20-sided dice 
100 times. Its shape is also typical of Geiger- 
counter and cloud-chamber results. 

A graph of random data 

The pattern of your results is easier to visualize 
if you display your data in the form of a bar 
graph, or histogram, as in Fig. 21-3. 



3lO' 



/bi 



- 10^ 



n 



°: 1 n I I I i : I Ti 

2^ 6 2 10 la. 14 16 

numbar of events (n) 

Fig. 21-3 The results obtained when a tray of 20-sided 
dice (one side marked) were shaken 100 times. 

If you were to shake the dice another set of 
100 times, your distribution would not be ex- 
actly the same as the first one. However, if 
sets of 100 trials were repeated several times, 
the combined results would begin to form a 
smoother histogram. Fig. 21-4 shows the kind 
of result you could expect if you did 1,000 
trials. 

Compare this with the results for only ten 
trials shown in Fig. 21-5. As the number of 
trials increases, the distribution generally be- 
comes smoother and more like the distribution 
in Fig. 21-4. 



zoo- 
tSo- 

r 
J 

. (00- 

30- 
(><y- 



) o- 



>> 






iT 16 



Fig. 21-4 The predicted results of shaking the dice 
1000 times. Notice that the vertical scale is different 
from that in Fig. 21-3. Do you see why? 




6 7 ? 9 10 II 11 13 iH 

O-f c/erts (n) 

Fig. 21-5 Results of shaking the dice ten times. 

Predicting random events 

How can data like these be used to make 
predictions? 

On the basis of Fig. 21-4, the best predic- 
tion of the number of marked faces turning up 
would be 5 or 6 out of 120 rolls. Apparently 
the chance of a die having its marked face up 
is about 1 in 20— that is, the probability is 20- 

But not all trials had 5 or 6 marked faces 
showing. In addition to the average of a dis- 
tribution, you also need to know something 
about how the data spread out around the 
average. Examine the histogram and answer 
the following questions: 

Q2 How many of the trials in Fig. 21-4 had 
from 5 to 7 counts? 



Experiment 45 



129 



Q3 What fraction is this of the total number 
of observations? 

Q4 How far, going equally to the left and 
right of the average, must you go to include 
half of all the observations? to include two- 
thirds? 

For a theoretical distribution like this 
(which your own results will closely approxi- 
mate as you increase the number of trials), it 
turns out that there is a simple rule for express- 
ing the spread: If the average count is A, then 

2 / — 

■3 of the counts will be between A - VA and 
A + VA Putting it another way, about j of the 
values will be in the range of A ± VaI 

Another example may help make this 
clear. For example, suppose you have been 
counting cloud-chamber tracks and find that 
the average of a large number of one-minute 
counts is 100 tracks. Since the square root of 
100 is 10, you would find that about two-thirds 
of your counts would lie between 90 and 1 10. 

Check this prediction in Fig. 21-4. The 
average is 6. The square root of 6 is about 2.4. 
The points along the base of the histogram 
corresponding to 6 it 2.4 are between 3.6 and 
8.4. (Of course, it doesn't really make sense to 
talk about a fraction of a marked side. One 
would need to round off to the nearest whole 
numbers, 4 and 8.) Therefore the chances are 
about two out of three that the number of 
marked sides showing after any shake of the 
tray will be in the range 4 to 8 out of 120. 
Q5 How many of the trials did give results 
in the range 4 to 8? What fraction is this of the 
total number of trials? 

Q6 Whether you rolled dice, counted tracks, 
or used the Geiger counter, inspect your results 



to see if f of your counts do lie in the range 

a±Va. 

If you counted for only a single one-minute 
trial, the chances are about two out of three 
that your single count C will be in the range 
A ± VA, where A is the true average count 
(which you would find over many trials). This 
implies that you can predict the true average 
value fairly well even if you have made only 
a single one-minute count. The chances are 
about two out of three that the single count C 
will be within VXof the true average A. If we 
assume C is a fairly good estimate of A, we can 
use VC^ as an estimate of VaT and conclude 
that the chances are two out of three that the 
value obtained for C is within ±ViC of the 
true average. 

You can decrease the uncertainty in pre- 
dicting a true average like this by counting for 
a longer period. Suppose you continued the 
count for ten minutes. If you counted 1,000 
tracks the expected "two-thirds range" would 
be about 1000 ± VlOOO or 1000 ± 32. The re- 
sult is 1000 ± 32 counts in ten minutes, which 
gives an average of 100 ± 3.2 counts per min- 
ute. If you counted for still longer, say 100 
minutes, the range would be 10,000 ± VlO.OOO 
or 10,000 ± 100 counts in 100 minutes. Your 
estimate of the average count rate would be 
100 ± 1 counts per minute. The table below 
lists these sample results. 
Notice that although the range of uncertainty 
in the total count increases as the count goes 
up, it becomes a smaller fraction of the total 
count. Therefore, the uncertainty in the aver- 
age count rate (number of counts per minute) 
decreases. 



SAMPLE RESULTS AND ESTIMATED "TWO-THIRDS RANGES" 

EXPECTED AVERAGE EXPECTED 



TIME 


TOTAL COUNT 


UNCERTAINTY 


COUNT 


UNCERTAINTY 


min 






per min 


per min 


1 


100 


±10 


100 


±10 


10 


1000 


±32 


100 


±3.2 


100 


10000 


±100 


100 


±1.0 



130 



Experiment 45 



(The percent uncertainty can be expressed 
as "TT", which IS equal to rTTT-- In this expres- 
sion, you can see clearly that the percent un- 
certainty goes down as C increases.) 

You can see from these examples that the 
higher the total count (the longer you count or 
the more dice-rolling trials you do) the more 
precisely you can estimate the true average. 
This becomes important in the measurement 
of the activity of radioactive samples and 
many other kinds of random events. To get a 
precise measure of the activity (the average 
count rate), you must work with large numbers 
of counts. 

Q7 If you have time, take more data to in- 
crease the precision of your estimate of the 
mean. 

Q8 If you count 10 cosmic ray tracks in a 
cloud chamber during one minute, for how 
long would you expect to have to go on count- 
ing to get an estimate of the average with a 



"two-thirds range" that is only 1% of the aver- 
age value. 

This technique of counting over a longer 
period to get better estimates is fine as long as 
the true count rate remains constant. But it 
doesn't always remain constant. If you were 
measuring the half-life of a short-lived radio- 
active isotope, the activity rate would change 
appreciably during a ten-minute period. In 
such a case, the way to increase precision is 
still to increase the number of observations— 
by having a larger sample of material or put- 
ting the Geiger tube closer to it — so that you 
can record a large number of counts during a 
short time. 

Q9 In a small town it is impossible to predict 
whether there will be a fire next week. But in a 
large metropolitan area, firemen know with 
remarkable accuracy how many fires there will 
be. How is this possible? What assumption 
must the firemen make? 



131 



EXPERIMENT 46 

RANGE OF a AND (3 PARTICLES 

An important property of particles from radio- 
active sources is their ability to penetrate 
solid matter. In this experiment you will deter- 
mine the distances a and /3 particles can travel 
in various materials. 

a particles are most easily studied in a 
cloud chamber, a transparent box containing 
super-cooled alcohol vapor. Since the a par- 
ticles are relatively massive and have a double 
positive charge, they leave a thick trail of ion- 
ized air molecules behind them as they move 
along. The ions then serve as centers about 
which alcohol condenses to form tracks of 
visible droplets. 

)8 particles also ionize air molecules as they 
move. But because of their smaller mass and 
smaller charge, they form relatively few ions, 
which are farther apart than those formed by 
a's. As a result, the trail of droplets in the 
chamber is much harder to see. 

A Geiger counter, on the other hand de- 
tects /3 particles better than a particles. This is 
because a particles, in forming a heavy trail, 
lose all their energy long before they get 
through even the thin window of an ordinary 
Geiger tube. /3 particles encounter the atoms in 
the tube window also, but they give up rela- 
tively less energy so that their chances of get- 
ting through the wall are fairly good. 

For these reasons you count a particles 
using a cloud chamber and IB particles with a 
Geiger counter. 

Observing a particles 

Mark off a distance scale on the bottom of the 
cloud chamber so that you will be able to esti- 
mate, at least to the nearest 7 cm, the lengths 
of the tracks formed (Fig. 21-6). Insert a source 
of a radiation and a barrier (as in the preceding 
experiment on random events) with a small 
slot opening at such a height that the tracks 
form a fairly narrow beam moving parallel 
to the bottom of the chamber. Put the cloud 
chamber into operation according to the in- 
structions supplied with it. 

Practice watching the tracks until you can 
report the length of any of the tracks you see. 




Fig. 21-6 

When you are ready to take data, count 
and record the number of a's that come 
through the opening in the barrier in one 
minute. Measure the opening and calculate 
its area. Measure and record the distance from 
the source to the barrier. 

Actually you have probably not seen all the 
particles coming through the opening, since 
the sensitive region in which tracks are visible 
is rather shallow and close to the chamber 
floor. You will probably miss the a's above this 
layer. 

The range and energy of a particles 

The maximum range of radioactive particles 
as they travel through an absorbing material 
depends on several factors, including the den- 
sity and the atomic number of the absorber. 
The graph (Fig. 21-7) summarizes the results 




/.o 



3.0 3.0 -f.O so 6.0 



1.0 



8.0 



Fig. 21-7 Range of a-particles in air as a function of 
their energy. 



132 



Experiment 46 



of many measurements of the range of a 
particles traveling through air. The range- 
energy curve for particles in air saturated with 
alcohol vapor, as the air is in your chamber, 
does not differ significantly from the curve 
shown. You are therefore justified in using 
Fig. 21-7 to get a fair estimate of the kinetic 
energy of the oc particles you observed. 
Ql Was there a wide variation in a-particle 
energies, or did most of the particles appear to 
have about the same energy? What was the 
energy of the a particle that caused the longest 
track you observed? 

Now calculate the rate at which energy is 
being carried away from the radioactive 
source. Assume that the source is a point. 
From the number of a particles per minute 
passing through an opening of known area at a 
known distance from the source, estimate the 
number of a particles per minute leaving the 
source in all directions. 




Fig. 21-8 



For this estimate, imagine a sphere with 
the source at its center and a radius r equal 
to the distance from the source to the barrier. 
(Fig. 21-8.) From geometry, the surface area 
of the entire sphere is known to be 47rr^. You 
know the approximate rate c at which particles 
are emerging through the small opening, 
whose area a you have calculated. By propor- 
tion you can find the rate C at which the par- 
ticles must be penetrating the total area of the 
sphere: 

C_ 47rr' 
c a 



(The tt-particle source is not a point, but 
probably part of a cylinder. This discrepancy, 
combined with a failure to count those par- 
ticles that pass above the active layer, will in- 
troduce an error of as much as a factor of 10.) 

The total number of particles leaving the 
source per minute, multiplied by the average 
energy of the particles, is the total energy lost 
per minute. 

To answer the following questions, use the 
relationships 

1 MeV = 1.60 X lO-i^' joules 
1 calorie = 4.18 joules 

Q2 How many joules of energy are leaving 

the source per minute? 

Q3 How many calories per minute does this 

equal? 

Q4 If the source were placed in one gram of 

water in a perfectly insulated container, how 

long would it take to heat the water from 0° C 

to 100° C? 

Q5 How many joules per second are leaving 

the source? What is the power output in watts? 

Observing fi particles 

After removing all radioactive sources from 
near the Geiger tube, count the number of 
pulses caused by background radiation in 
several minutes. Calculate the average back- 
ground radiation in counts per minute. Then 
place a source of /3 radiation near the Geiger 
tube, and determine the new count rate. (Make 
sure that the source and Geiger tube are not 
moved during the rest of the experiment.) 
Since you are concerned only with the particles 
from the source, subtract the average back- 
ground count rate. 

Next, place a piece of absorbing material 
(such as a sheet of cardboard or thin sheet 
metal) between the source and the tube, and 
count again. Place a second, equally thick 
sheet of the same material in front of the first, 
and count. Keep adding absorbers and record- 
ing counts until the count rate has dropped 
nearly to the level of background radiation. 

Plot a graph on which the horizontal scale 
is the total thickness (number of) absorbers 



Experiment 46 



133 



and the vertical scale is the number of /3's 
getting through the absorber per minute. 

In addition to plotting single points, show 
the uncertainty in your estimate of the count 
rate for each point plotted. You know that be- 
cause of the random nature of radioactivity, 
the count rate actually fluctuates around some 
average value. You do not know what true 
average value is; it would ideally take an in- 
finite number of one-minute counts to deter- 
mine the "true" average. But you know that 
the distribution of a great number of one- 
minute counts will have the property that two- 
thirds of them will differ from the average by 
less than the square root of the average. (See 
Experiment 45.) 

For example, suppose you have observed 
100 counts in one given minute. The chances 
are two out of three that, if you counted for a 
very long time, the mean count rate would be 
between 90 and 110 counts (between 100 - 
VlOO and 100 + VlOO counts). For this reason 
you would mark a vertical line on your graph 
extending from 90 counts up to 110. In this 
way you avoid the pitfall of making a single 



measurement and assuming you know the 
"correct" value. (For an example of this kind 
of graph see notes for Film Loop 9 in Unit 1 
Handbook.) 

If other kinds of absorbing material are 
available, repeat the experiment with the same 
source and another set of absorbers. For 
sources that emit very low-energy /3 rays, it 
may be necessary to use very thin materials, 
such as paper or household aluminum foil. 

Range and absorption of fi particles 

Examine your graph of the absorption of par- 
ticles. 

Q6 Is it a straight line? 

Q7 What would the graph look like if (as is 
the case for a particles) all /3 particles from 
the source were able to penetrate the same 
thickness of a given absorber material before 
giving up all their energy? 
Q8 If you were able to use different absorb- 
ing materials, how did the absorption curves 
compare? 

Q9 What might you conclude about the ki- 
netic energies of /3 particles? 



134 



EXPERIMENT 47 HALF-LIFE— I 

The more people there are in the world, the 
more people die each day. The less water there 
is in a tank, the more slowly water leaks out 
of a hole in the bottom. 

In this experiment, you will observe three 
other examples of quantities that change at a 
rate that depends on the total amount of the 
quantity present. The objective is to find a 
common principle of change. Your conclusions 
will apply to many familiar growth and decay 
processes in nature. 

If you experimented earlier with rolling 
dice and with radioactive decay (Experiment 
45), you were studying random events you 
could observe one at a time. You found that the 
fluctuations in such small numbers of random 
events were relatively large. But this time you 
will deal with a large number of events, and 
you will find that the outcome of your experi- 
ments is therefore more precisely predictable. 

Part A. Twenty-sided Dice 

Mark any two sides of each 20-sided die with a 
(washable) marking pen. The chances wOl 
therefore be one in ten that a marked surface 
will be face up on any one die when you shake 
and roll the dice. When you have rolled the 
120 dice, remove all the dice that have a 
marked surface face up. Record the number 
of dice you removed (or line them up in a col- 
umn). With the remaining dice, continue this 
process of shaking, rolling, and removing the 
marked dice at least twenty times. Record the 
number you remove each time (or line them up 
in a series of columns). 

Plot a graph in which each roll is repre- 
sented by one unit on the horizontal axis, and 
the number of dice removed after each roll is 
plotted on the vertical axis. (If you have lined 
up columns of removed dice, you already have 
a graph.) 

Plot a second graph with the same hori- 
zontal scale, but with the vertical scale repre- 
senting the number of dice remaining in the 
tray after each roll. 

You may find that the numbers you have 
recorded are too erratic to produce smooth 
curves. Modify the procedure as follows: Roll 



the dice and count the dice with marked sur- 
faces face up. Record this number but do not 
remove the dice. Shake and count again. 
Do this five times. Now find the mean of the 
five numbers, and remove that number of dice. 
The eff'ect will be the same as if you had actu- 
ally started with 120 x 5 or 600 dice. Continue 
this procedure as before, and you will find that 
it is easier to draw smooth curves which pass 
very nearly through all the points on your two 
graphs. 

Ql How do the shapes of the two curves com- 
pare? 

Q2 What is the ratio of the number of dice 
removed after each shake to the number of 
dice shaken in the tray? 

Q3 How many shakes were required to re- 
duce the number of dice in the tray from 120 
to 60? from 60 to 30? from 100 to 50? 

Part B. Electric Circuit 

A capacitor is a device that stores electric 
charge. It consists of two conducting surfaces 
placed very close together, but separated by a 
thin sheet of insulating material. When the 
two surfaces are connected to a battery, nega- 
tive charge is removed from one plate and 
added to the other so that a potential diff"erence 
is established between the two surfaces. (See 
Sec. 14.6 of Unit 4 Text.) If the conductors are 
disconnected from the battery and connected 
together through a resistor, the charge will 
begin to flow back from one side to the other. 
The charge will continue to flow as long as 
there is a potential diff"erence between the 
sides of the capacitor. As you learned in Unit 4, 
the rate of flow of charge (the current) through 
a conducting path depends both on the resis- 
tance of the path and the potential difference 
across it. 



fCr:^ 




Fig. 21-9 An analogy: The rate of flow of water de- 
pends upon the difference in height of the water in the 
two tanks and upon the resistance the pipe offers to 
the flow of water. 



Experiment 47 



135 



To picture this situation, think of two 
partly filled tanks of water connected by a pipe 
running from the bottom of one tank to the 
bottom of the other (Fig. 21-9). When water is 
transferred from one tank to the other, the 
additional potential energy of the water is 
given by the difference in height, just as the 
potential difference between the sides of a 
charged capacitor is proportional to the poten- 
tial energy stored in the capacitor. Water flows 
through the pipe at the bottom until the water 
levels are the same in the two tanks. Similarly, 
charge flows through the conducting path con- 
necting the sides of the capacitor until there 
is no potential difference between the two 
plates. 

Connect the circuit as in Fig. 21-10, close 
the switch, and record the reading on the volt- 
meter. Now open the switch and take a series 
of voltmeter readings at regular intervals. Plot 
a graph, using time intervals for the horizon- 
tal axis and voltmeter readings for the vertical. 

■«4^t 





(j^) Chanel n^ the capacitor 




Cb) discharging through the reniton 

Fig. 21-10 

Q4 How long does it take for the voltage to 
drop to hall its initial value? from one-half to 
one-fourth? from one-third to one-sixth? 

Repeat the experiment with a different 
resistor in the circuit. Find the time required 
for the voltage to drop to half its initial value. 
Do this for several resistors. 
Q5 How does the time required for the volt- 



age to drop to half its initial value change as 
the resistance in the circuit is changed? 



Part C. Short-lived Radioisotope 

Whenever you measure the radioactivity of a 
sample with a Geiger counter, you must first 
determine the level of background radiation. 
With no radioactive material near the Geiger 
tube, take a count for several minutes and cal- 
culate the average number of counts per min- 
ute caused by background radiation. This 
number must be subtracted from any count 
rates you observe with a sample near the 
tube, to obtain what is called the net count 
rate of the sample. 

The measurement of background rate can 
be carried on by one member of your group 
while another prepares the sample according 
to the directions given below. Use this mea- 
surement of background rate to become fa- 
miliar with the operation of the counting 
equipment. You will have to work quite quickly 
when you begin counting radiation from the 
sample itself. 

First, a sample of a short-lived radioiso- 
tope must be isolated from its radioactive 
parent material and prepared for the measure- 
ment of its radioactivity. 

Although the amount of radioactive ma- 
terial in this experiment is too small to be 
considered at all dangerous (unless you drink 
large quantities of it), it is a very good idea to 
practice caution in dealing with the material. 
Respect for radioactivity is an important atti- 
tude in our increasingly complicated world. 

The basic plan is to (1) prepare a solution 
which contains several radioactive substances, 
(2) add a chemical that absorbs only one of the 
radioisotopes, (3) wash most of the solution 
away leaving the absorbing chemical on a 
piece of filter paper, (4) mount the filter paper 
close to the end of the Geiger counter. 

(1) Prepare a funnel-filter assembly by plac- 
ing a small filter paper in the funnel and 
wetting it with water. 

Pour 12 cc of thorium nitrate solution into 
one graduated cylinder, and 15 cc of dilute ni- 
tric acid into another cylinder. 

(2) Take these materials to the filter flask 



136 



Experiment 47 



which has been set up in your laboratory. Your 
teacher will connect your funnel to the filter 
flask and pour in a quantity of ammonium 
phosphomolybdate precipitate, (NH4)3PMo,2O40. 
The phosphomolybdate precipitate adsorbs the 
radioisotope radioactive elements present in 
the thorium nitrate solution. 

(3) Wash the precipitate by sprinkling sev- 
eral cc of distilled water over it, and then 
slowly pour the thorium nitrate solution onto 
the precipitate (Fig. 21-11). Distribute the solu- 
tion over the whole surface of the precipitate. 
Wash the precipitate again with 15 cc of dilute 
nitric acid and wait a few moments while the 
pump attached to the filter flask dries the 
sample. By the time the sample is dry, the ni- 
tric acid should have carried all the thorium 
nitrate solution through the filter. Left behind 
on the phosphomolybdate precipitate should be 
the short-lived daughter product whose radio- 
activity you wish to measure. 




Fig. 21-11 

(4) As soon as the sample is dry, remove the 
upper part of the funnel from the filter flask 
and take it to the Geiger counter. Make sure 
that the Geiger tube is protected with a layer 
of thin plastic food wrapping. Then lower it 
into the funnel carefully until the end of the 
tube almost touches the precipitate (Fig. 
21-12). 

You will probably find it convenient to 
count for one period of 30 seconds in each min- 
ute. This will give you 30 seconds to record the 
count, reset the counter, and so on, before be- 




Fig. 21-12 

background = 12 counts per minute, 
= 6 countb perJ^ ivinute. 





CO u n-t: 


net Co^n\. 


0- 'A 


d C3 


7^7 


l-l'/^ 


/^ 7 


^J/ 


2- ^'/^ 


/ 


' 


3 -3'/^ 




/ 


H - y^ 






Fig. 21-13 







ginning the next count. Record your results 
in a table like Fig. 21-13. Try to make about ten 
trials. 

Plot a graph of net count rate as a function 
of time. Draw the best curve you can through 
all the points. From the curve, find the time 
required for the net count rate to decrease to 
half its initial value. 

QQ How long does it take for the net count 
rate to decrease from one-half to one-fourth 
its initial value? one-third to one-sixth? one- 
fourth to one-eighth? 

Ql The half-life of a radioisotope is one of 
the important characteristics which helps to 
identify it. Using the Handbook of Chemistry 
and Physics, or another reference source, iden- 
tify which of the decay products of thorium 
is present in your sample. 



Experiment 47 



137 



Q8 Can you tell from the curve you drew 
whether your sample contains only one radio- 
isotope or a mixture of isotopes? 

Discussion 

It should be clear from your graphs and those 
of your classmates that the three kinds of 
quantities you observed all have a common 
property: It takes the same time (or number of 
rolls of the dice) to reduce the quantity to 
half its initial value as it does to reduce from 
a half to a fourth, from a third to a sixth, from 
a fourth to an eighth, etc. This quantity is the 
half -life. 

In the experiments on the "decay" of 
twenty-sided dice with two marked faces, you 
knew beforehand that the "decay rate" was 
one-tenth. That is, over a large number of 
throws an average of one-tenth of the dice 



would be removed for each shake of the tray. 
The relationship between the half-life of 
a process and the decay constant k is discussed 
on the gray page Mathematics of Decay in 
Chapter 21 of the Text. There you learned that 
for a large number of truly random events, the 
half life Tx is related to the decay constant X 
by the equation: 



T, = 



0.693 



Q9 From the known decay constant of the 
dice, calculate the half-life of the dice and 
compare it with the experimental value found 
by you or your classmates. 
QIO If you measured the half-life for capa- 
citor discharge or for radioactive decay, cal- 
culate the decay constant for that process. 



138 



EXPERIMENT 48 HALF LIFE— II 

Look at the thorium decay series in the table 
below. One of the members of the series, radon 
220, is a gas. In a sealed bottle containing thor- 
ium or one of its salts, some radon gas always 
gathers in the air space above the thorium. 
Radon 220 has a very short half-life (51.5 sec). 
The subsequent members of the series (polon- 
ium 214, lead 210, etc.) are solids. Therefore, 
as the radon 220 decays, it forms a solid deposit 
of radioactive material in the bottle. In this 
experiment you will measure the half-life of 
this radioactive deposit. 

Although the amount of radioactive ma- 
terial in this experiment is too small to be con- 
sidered at all dangerous (unless you drank 
large quantities of it), it is a very good idea to 
practice caution in dealing with the material. 



THE THORIUM DECAY SERIES 

MODE 

NAME SYMBOL OF DECAY HALF-LIFE 

Thorium 232 soTh"^ a 1.39 x 10'" yrs. 

Radium 228 ssf^a^^ P 6.7 years 

Actinium 228 ggAc"* /3 6.13 hours 

Thorium 228 9oTh"8 « 1.91 years 

Radium 224 ssRa"" « 3.64 days 

Radon 220 gsR""" " 51.5 sec 

Polonium 216 84Po2'« a 0.16 sec 

Lead 212 szPb^" )8 10.6 hours 

Bismuth 212 gsBi^'^ a or )8* 60.5 min 

Polonium 212 84Po^'^ " 3.0 x 10"' sec 

Thallium 208 g.TI^"* /3 3.10 min 

Lead 208 «,Pb="'« Stable 3.10 min 



*Bismuth 21 2 can decay in two ways: 34 per cent decays 
by a emission to thallium 208; 66 per cent decays by 
/3 emission to polonium 212. Both thallium 208 and 
polonium 212 decay to lead 208. 



thorium 
nitrat& 




to i-HSO'i. 



Fig. 21-14 






Respect for radioactivity is an important atti- 
tude in our increasingly complicated world. 

The setup is illustrated in Fig. 21-14. The 
thorium nitrate is spread on the bottom of a 
sealed container. (The air inside should be 
kept damp by moistening the sponge with 
water.) Radon gas escapes into the air of the 
container, and some of its decay products are 
deposited on the upper foil. 

When radon disintegrates in the nuclear 
reaction 



«Rn=^ 



,Po2>« + ,He^ 



the polonium atoms formed are ionized, ap- 
parently because they recoil fast enough to lose 
an electron by inelastic collision with air mole- 
cules. 

Because the atoms of the first daughter 
element of radon are ionized (positively 
charged), you can increase the amount of de- 
posit collected on the upper foil by charging it 
negatively to several hundred volts. Although 
the electric field helps, it is not essential; you 
will get some deposit on the upper foil even if 
you don't set up an electric field in the con- 
tainer. 

After two days, so much deposit has accu- 
mulated that it is decaying nearly as rapidly 
as the constant rate at which it is being formed. 



Experiment 48 



139 



Therefore, to collect a sample of maximum 
activity, your apparatus should stand for about 
two days. 

Before beginning to count the activity of 
the sample, you should take a count of the 
background rate. Do this far away from the 
vessel containing the thorium. Remove the 
cover, place your Geiger counter about one mm 
above the foil, and begin to count. Make sure, 
by adjusting the distance between the sample 
and the window of the Geiger tube, that the 
initial count rate is high— several hundred per 
minute. Fix both the counter and the foil in 
position so that the distance will not change. 
To get fairly high precision, take a count over 
a period of at least ten minutes (see Experi- 
ment 45). Because the deposit decays rather 
slowly, you can afford to wait several hours be- 
tween counts, but you will need to continue 
taking counts for several days. Make sure that 
the distance between the sample and the 
Geiger tube stays constant. 

Record the net count rate and its uncer- 
tainty (the "two-thirds" range discussed in 
Experiment 45). Plot the net count rate against 
time. 

Remember that the deposit contains sev- 
eral radioactive isotopes and each is decaying. 
The net count rate that you measure is the sum 
of the contributions of all the active isotopes. 
The situation is not as simple as it was in Ex- 
periment 46, in which the single radioactive 
isotope decayed into a stable isotope. 
Ql Does your graph show a constant half- 
life or a changing half-life? 

Look again at the thorium series and in 
particular at the half-lives of the decay pro- 
ducts of radon. Try to interpret your observa- 
tions of the variation of count rate with time. 
Q2 Which isotope is present in the greatest 
amount in your sample? Can you explain 
why this is so? Make a sketch (like the one 
on page 22 of Unit 6 Text) to show approxi- 
mately how the relative amounts of the differ- 
ent isotopes in your sample vary with time. 



Ignore the isotopes with half-lives of less than 

one minute. 

You can use your measurement of count 

rate and half-life to get an estimate of the 

amount of deposit on the foil. The activity, 

AN 

-rr, depends on the number of atoms present, 

N: 



AN 
At 



XN. 



The decay constant X is related to the half-life 

Ti by 

. 0.693 



Use your values of counting rate and half- 
life to estimate N, the number of atoms pres- 
ent in the deposit. What mass does this repre- 
sent? (1 amu = 1.7 X IQ-^^ kg.) The smallest 
amount of material that can be detected with a 
chemical balance is of the order of 10~^ gram. 

Discussion 

It is not too difficult to calculate the speed and 
hence the kinetic energy of the polonium atom 
In the disintegration 



sRn^ 



4Po2»« + oHe" 



the oc particle is emitted with kinetic energy 
6.8 MeV. Combining this with the value of its 
mass, you can calculate v^ and, therefore, v. 
What is the momentum of the a particle? Mo- 
mentum is of course conserved in the disin- 
tegration. So what is the momentum of the 
polonium atom? What is its speed? What is its 
kinetic energy? 

The ionization energy— -the energy required 
to remove an outer electron from the atom — 
is typically a few electron volts. How does 
your value for the polonium atom's kinetic 
energy compare with the ionization energy? 
Does it seem likely that most of the recoiling 
polonium atoms would ionize? 



140 



EXPERIMENT 49 
RADIOACTIVE TRACERS 

In this group of experiments, you have the op- 
portunity to invent your procedures yourself 
and to draw your own conclusions. Most of the 
experiments will take more than one class 
period and will require careful planning in 
advance. You will find below a list of books 
and magazine articles that can help you. 



A Caution 

All these experiments take cooperation from 
the biology or the chemistry department, and 
require that safety precautions be observed 
very carefully so that neither you nor other 
students will be exposed to radiation. 

For example, handle radioisotopes as you 
would a strong acid; if possible, wear dispos- 
able plastic gloves, and work with all con- 
tainers in a tray lined with paper to soak up 
any spills. Never draw radioactive liquids 
into a pipette by mouth as you might do with 
other chemical solutions; use a mechanical 
pipette or a rubber bulb. Your teacher will 
discuss other safety precautions with you be- 
fore you begin. 

None of these activities is suggested just 
for the sake of doing tricks with isotopes. 
You should have a question clearly in mind 
before you start, and should plan carefully 
so that you can complete your experiment in 
the time you have available. 



Tagged Atoms 

Radioactive isotopes have been called tagged 
atoms because even when they are mixed with 
stable atoms of the same element, they can 
still be detected. To see how tagged atoms are 
used, consider the following example. 

A green plant absorbs carbon dioxide (CO2) 
from the air and by a series of complex chem- 
ical reactions builds the carbon dioxide (and 
water) into the material of which the plant is 
made. Suppose you tried to follow the steps 
in the series of reactions. You can separate 
each compound from the mixture by using 
ordinary chemical methods. But how can you 



trace out the chemical steps by which each 
compound is transformed into the next when 
they are all jumbled together in the same 
place? Tagged atoms can help you. 

Put the growing green plant in an atmos- 
phere containing normal carbon dioxide, to 
which has been added a tiny quantity of CO2 
molecules which contain the radioactive iso- 
top carbon 14 in place of normal carbon 12. 
Less than a minute later the radioactivity can 
be detected within some, but not all, of the 
molecules of complex sugars and amino acids 
being synthesized in the leaves. As time goes 
on, the radioactive carbon enters step by step 
into each of the carbon compounds in the 
leaves. 

With a Geiger counter, in effect, one can 
watch each compound in turn to detect the 
moment when radioactive molecules begin to 
be added to it. In this way, the mixture of 
compounds in a plant can be arranged in their 
order of formation, which is obviously a useful 
clue to chemists studying the reactions. Photo- 
synthesis, long a mystery, has been studied in 
detail in this way. 

Radioactive isotopes used in this manner 
are called tracers. The quantity of tracer ma- 
terial needed to do an experiment is aston- 
ishingly small. For example, compare the 
amount of carbon that can be detected by an 
analytical balance with the amount needed to 
do a tracer experiment. Your Geiger counter 
may, typically, need 100 net counts per minute 
to distinguish the signal from background 
radiation. If only 1% of the particles emitted 
by the sample are detected, then in the small- 
est detectable sample, 10,000 or 10^ atoms 
are decaying each minute. This is the number 
of atoms that decay each minute in a sample of 
only 4 X 10~^ micrograms of carbon 14. Under 
ideal conditions, a chemical balance might 
detect one microgram. 

Thus, in this particular case, measurement 
by radioactivity is over ten thousand times 
more sensitive than the balance. 

In addition, tracers give you the ability 
to find the precise location of a tagged sub- 
stance inside an undisturbed plant or animal. 
Radiation from thin sections of a sample 



Experiment 49 



141 



placed on photographic film produces a visible 
spot. (Fig. 21-14.) This method can be made so 
precise that scientists can tell not only which 
cells of an organism have taken in the tracer, 
but also which parts of the cell (nucleus, mito- 
chondria, etc.). 



Choice of Isotope 

The choice of which radioactive isotope to 
use in an experiment depends on many factors, 
only a few of which are suggested here. 

Carbon 14, for example, has several prop- 
erties that make it a useful tracer. Carbon 
compounds are a major constituent of all liv- 
ing organisms. It is usually impossible to fol- 
low the fate of any one carbon compound that 
you inject into an organism, since the added 
molecules and their products are immediately 
lost in the sea of identical molecules of which 
the organism is made. Carbon 14 atoms, how- 
ever, can be used to tag the carbon compounds, 
which can then be followed step by step 
through complex chains of chemical processes 
in plants and animals. On the other hand, the 
carbon 14 atom emits only /3 particles of rather 
low energy. This low energy makes it imprac- 
tical to use carbon 14 inside a large liquid or 
solid sample since all the emitted particles 
would be stopped inside the sample. 

The half-life of carbon 14 is about 6000 
years, which means that the activity of a 
sample will remain practically constant for the 
duration of an experiment. But sometimes the 
experimenter prefers to use a short-lived iso- 
top so that it will rapidly drop to negligibly 
low activity in the sample— or on the laboratory 
table if it gets spilled. 

Some isotopes have chemical properties 
that make them especially useful for a specific 
kind of experiment. Phosphorus 32 (half-life 
14.3 days) is especially good for studying the 
growth of plants, because phosphorous is used 
by the plant in many steps of the growth pro- 
cess. Practically all the iodine in the human 
body is used for just one specific process — 
the manufacture of a hormone in the thyroid 
gland which regulates metabolic rate. Radio- 
active iodine 131 (half-life 8.1 days) has been 



immensely useful as a tracer in unravelling 
the steps in that complex process. 

The amount of tracer to be used is deter- 
mined by its activity, by how much it will be 
diluted during the experiment, and by how 
much radiation can be safely allowed in the 
laboratory. Since even very small amounts of 
radiation are potentially harmful to people, 
safety precautions and regulations must be 
carefully followed. The Atomic Energy Com- 
mission has established licensing procedures 
and regulations governing the use of radio- 
isotopes. As a student you are permitted to use 
only limited quantities of certain isotopes 
under carefully controlled conditions. How- 
ever, the variety of experiments you can do is 
still so great that these regulations need not 
discourage you from using radioactive isotopes 
as tracers. 

One unit used to measure radioactivity of 
a source is called the curie. When 3.7 x 10'" 
atoms within a source disintegrate or decay in 
one second, its activity is said to be one curie 
(c). (This number was chosen because it was 
the approximate average activity of 1 gram of 
pure radium 226.) A more practical unit for 
tracer experiments is the microcurie (fjuc) 
which is 3.7 x 10^ disintegrations per second 
or 2.2 X 10" per minute. The quantity of radio- 
isotope that students may safely use in experi- 
ments, without special license, varies from 0.1 
/Ltc to 50 /xc depending on the type and energy 
of radiation. 

Notice that even when you are restricted 
to 0.1 fJuc for your experiments, you may still 
expect 3700 disintegrations per second, which 
would cause 37 counts a second in a Geiger 
counter that recorded only 1% of them. 
Ql What would be the "f range" in the activ- 
ity (disintegrations per minute) of a 1 ^tc 
source? 

Q2 What would be the "-j range" in counts per 
minute for such a source measured with a Gei- 
ger counter that detects only 1% of the dis- 
integrations? 

Q3 Why does a Geiger tube detect such a 
small percentage of the fi particles that leave 
the sample? (Review that part of Experiment 
46 on the range of fS particles.) 



142 



Experiment 49 



Part A. Autoradiography 

One rather simple experiment you can almost 
certainly do is to re-enact Becquerel's original 
discovery of radioactivity. Place a radioactive 
object — lump of uranium ore, luminous watch 
dial with the glass removed, etc.— on a Pola- 
roid film packet or on a sheet of x-ray film in 
a light-tight envelope. A strong source of ra- 
diation will produce a visible image on the film 
within an hour, even through the paper wrap- 
ping. If the source is not so strong, leave it in 
place overnight. To get a very sharp picture, 
you must use unwrapped film in a completely 
dark room and expose it with the radioactive 
source pressed firmly against the film. 

(Most Polaroid film can be developed by 
placing the packet on a flat surface and pass- 
ing a metal or hard-rubber roller firmly over 
the pod of chemicals and across the film. Other 
kinds of film are processed in a darkroom ac- 
cording to the directions on the developer 
package.) 

This photographic process has grown into 
an important experimental technique called 
autoradiography. The materials needed are 
relatively inexpensive and easy to use, and 
there are many interesting applications of the 
method. For example, you can grow plants in 
soil treated with phosphorus 32, or in water to 
which some phosphorus 32 has been added, 
and make an autoradiograph of the roots, stem, 
and leaves (Fig. 21-15). Or each day take a 
leaf from a fast-growing young plant and show 




Fig. 21-15 Autoradiograph made by a high school stu- 
dent to show uptake of phosphorus-32 in coleus leaves. 



how the phosphorous moves from the roots to 
the growing tips of the leaves. Many other 
simple autoradiograph experiments are de- 
scribed in the source material listed at the end 
of this experiment. 

Part B. Chemical Reactions and 
Separations 

Tracers are used as sensitive indicators in 
chemical reactions. You may want to try a 
tracer experiment using iodine 131 to study 
the reaction between lead acetate and potas- 
sium iodide solutions. Does the radioactivity 
remain in the solute or is it carried down with 
the precipitate? How complete is the reaction? 

When you do experiments like this one 
with liquids containing /3 sources, transfer 
them carefully (with a special mechanical 
pipette or a disposable plastic syringe) to a 
small, disposable container called a planchet, 
and evaporate them so that you count the dry 
sample. This is important when you are using 
/3 sources since otherwise much of the radia- 
tion would be absorbed in the liquid before it 
reached the Geiger tube. 

You may want to try more elaborate ex- 
periments involving the movement of tracers 
through chemical or biological systems. Stu- 
dents have grown plants under bell-jars in an 
atmosphere containing radioactive carbon di- 
oxide, fed radioactive phosphorus to earth- 
worms and goldfish, and studied the metab- 
olism of rats with iodine 131. 

Some Useful Articles 

"Laboratory Experiments with Radioisotopes 
for High School Demonstrations," edited by 
S. Schenberg; U.S. Atomic Energy Commis- 
sion, 1958. Order from Superintendent of 
Documents, Government Printing Office, 
Washington, D.C. 20402 for thirty-five cents. 

"Radioactive Isotopes: A Science As- 
sembly Lecture." Illustrated. Reprints of this 
article available from School Science and 
Mathematics, P.O. Box 246, Bloomington, In- 
diana 47401 for twenty-five cents. 

"Radioisotope Experiments for the Chem- 
istry Curriculum" (student manual 17311) 
prepared by U.S. Atomic Energy Commission. 



Experiment 49 



143 



Order from Office of Technical Services, Wash- 
ington, D.C. 20545, for two dollars. (A com- 
panion teacher's guide is also available at one 
dollar from the same source.) 

American Biology Teacher, August 1965, 
Volume 27, No. 6. This special issue of the 
magazine is devoted to the use of radio- 
isotopes and contains several articles of use 
in the present exercise on tracers. Order single 
copies from Mr. Jerry Lightner, P.O. Box 2113, 
Great Falls, Montana 59401 for seventy-five 
cents. 

Scientific American, May 1960. The Ama- 
teur Scientist section (by C. L. Stong), page 
189, is devoted to a discussion of "how the 
amateur scientist can perform experiments 



that call for the use of radioactive isotopes." 
Copies of the magazine are available in many 
libraries or can be obtained from Scientific 
American, 415 Madison Ave., New York, New 
York 10017. (Reprints of this article are not 
available). 

Scientific American, March 1953. The 
Amateur Scientist section is on "scintillation 
counters and a home-made spinthariscope for 
viewing scintillations." 

"Low Level Radioisotope Techniques," 
John H. Woodburn, The Science Teacher 
magazine, November 1960. Order from The 
Science Teacher, 1201 16th Street, N.W., 
Washington, D.C. 20036. Single copies are one 
dollar. 




Safe disposal of radioactive wastes with long half-lives is becoming a significant 
problem. Here steel cases containing dangerously large amounts of radioactive wastes 
from nuclear reactors are being buried. 







ACTIVITIES 



lAGNETIC DEFLECTION OF (B FUYS 

''Clamp a radioactive (3 source securely a dis- 
tance of about a foot from a Geiger tube. 
Place a sheet of lead at least 1 mm thick be- 
tween source and counter to reduce the count 
to background level. Hold one end (pole)\pf a 
strong magnet above or to the side of the sh^et, 
and change its position until the count rate 
creases appreciably. By what path do the 
rays reach the counter? Try keeping the mag\ 
net in the same position but reversing the twc 
poles ; does the radiation still reach the counter^ 
Determine the polarity of the magnet by usinj 
a compass needle. If /3rays are particles, wha^ 
is the sign of their charge? (See Experiment 
for hints.) 





MEASURING THE ENERGY OF 
fi RADIATION 
With a device called a )8-ray spectronj^ter, you 
can sort out the (B particles emitteciby a radio- 
active source according to their energy just as 
a grating or prism spectroscop^preads out the 
colors of the visible spectrum. You can make a 
simple /3-ray spectrometer/with two disk mag- 
nets and a packet of 4"^<<^" Polaroid film. With 
it you can make a fairly good estimate of the 
average energy oijme /3 particles emitted from 
various sources^y observing how much they 
are deflectedoy a magnetic field of known in- 
tensity. 

Mount two disk magnets as shown in the 



Activity, "Measuring Magnetic Field Inten- 
sity," in the Unit 4 Handbook, Chapter 14. Be 
sure the faces of the magnets are parallel and 
opposite poles are facing each other. 




Bend a piece of sheet metal into a curve so 
that it will hold a Polaroid film packet snugly 
around the magnets. Place a (i source behind a 
barrier made of thin sheet lead with two nar- 
row slits that will allow a beam of /3 particles 
to enter the magnetic field as shown in Fig. 
21-16. Expose the film to the ^3 radiation for 



Pod jf cle.ve.1 ofit-r 
chain CO.,' i 




hooo 4J sa 

hlirx packt.'t 



isc rna.<fne.t 



She-ert me.ta.1 b^ckini 



Fig. 21-16 



two days. Then carefully remove the magnets 
without changing the relative positions of the 
film and /3 source. Expose the film for two more 
days. The long exposure is necessary because 
the collimated beam contains only a small 
fraction of the /3 given off by the source, and 
because Polaroid film is not very sensitive to 
/3 radiation. (You can shorten the exposure 
time to a few hours if you use x-ray film.) 

When developed, your film will have two 
blurred spots on it; the distance between 
their centers wUl be the arc length a in Fig. 
21-17. 



Activities 



145 



T 



■D 



■-y 



(measured with the current balance as de- 
scribed in the Unit 4 Handbook), and the 
charge on the electron, and can find R, you can 
compute the momentum. A little geometry will 
enable you-'tD calculate R from a, the arc 
lengthyand r, the radius of the magnets. A 
detailea^-sokrtion will not be given here, but a 
hint is shown in Fig. 21-18. 



Fig. 21-17 



An interesting mathematical problem is to 
find a relationship between the angle of de- 
flection, as indicated by a, and the average^ 
energy of the particles. It turns out that yoi 
can calculate the momentum of the particle 
fairly easily. Unfortunately, since the /3 par- 
ticles from radioactive sources are trav^ing 
at nearly the speed of light, the simple rela- 
tionships between momentum, velocity, and 
kinetic energy (which you learned ^bout in 
Unit 3) cannot be used. Instead, you would 
need to use equations derived frorn the special 
theory of relativity which, although not at all 
mysterious, are a little beyonci the scope of 
this course. (The necessary relations are devel- 
oped in the supplemental i/nit, "Elementary 
Particles.") A graph (Fig. 21-19) that gives the 
values of kinetic energy /or various values of 
momentum is provided/ 

First, you need an expression which will 
relate the deflectiori to the momentum of the 
particle. The relationship between the force 
on a charged particle in a magnetic field and 
the radius of idie circular path is derived in 
Sec. 18.2 of Unit 5 Text. Setting the magnetic 
force equal /o the centripetal force gives 



Bqv = 



mv" 



which simplifies to 

mv = BqR 
If you know the magnetic field intensity B 



^Z 




/? 



Fig. 21-18 



The angle 6 is equal to - — x 360°, and you 

should be able to prove that if tangents are 
drawn from the center of curvature to the 
points where the particles enter and leave the 
field, the angle between the tangents at is 
also 6. With this as a start, see if you can cal- 
culate R. 

The relationship between momentum and 
kinetic energy for objects traveling at nearly 
the speed of light 



\'p'c' + m,;'c' 



is discussed in most college physics texts. 
The graph in Fig. 21-19 was plotted using data 
calculated from this relationship. 

From the graph, find the average kinetic 
energy of the (3 particles whose momentum 
you have measured. Compare this with values 
given in the Handbook of Chemistry and 
Physics, or another reference book, for the 
particles emitted by the source you used. 

You will probably find a value listed which 
is two to three times higher than the value 
you found. The value in the reference book is 



146 



Activities 



i^ 




0.5 ■ 



0.0 

2 4 Gj e /o /Z If- 

mv=F qBR 
{y.loj"'kj-tr^/se.<.J 

Fig. 21-19 Kinetic energy versus momentum for elec- 
trons (m^c^ = 0.51 1 meV) 

the maximum energy that any one /3 particle 
from the source/can have, whereas the value 
you found was/the average of all the ^S's reach- 
ing the film/ This discrepancy between the 
maximum «iergy (which all the /3's should 
theoretically have) and the average energy 
puzzled pnysicists for a long time. The ex- 
planation, suggested by Enrico Fermi in the 
mid-1930's, l^d-ta~the~TiiscQvery of a stranj 
new..paTticle called the neutrino^ 
^ant to find out about. 



jvery of a strange 
rino^W^iieh^yOuwill 



A SWEET DEMONSTRATION 

In Experiment 46, "Half-Life I," it is difficult 
to show that the number of dice "decaying" is 
directly proportional to the initial number of 
dice, because statistical fluctuations are fairly 
large with only 120 dice. An inexpensive way 
to show that AN is directly proportional to N is 
to use at least 400 sugar cubes (there are 198 
in the commonly available 1 pound packages). 
Mark one face with edible food coloring. Then 



shake them and record how many decayed as 
described in Experiment 46. 

IONIZATION BY RADIOACTIVITY 

Place a different radioactive sample inside 
each of several identical electroscopes. Charge 
the electroscopes negatively (as by rubbing a 
hard, rubber comb on wool and touching the 
comb to the electroscope knob). Compare the 
times taken for the electroscopes to com- 
pletely lose their charges, and interpret your 
observations. \ 

Place no sample in one electroscope so 
that you can check how fast it discharges with- 
out a sample present. What causes this type of 
discharge? 

EXPONENTIAL DECAY IN 
CONCENTRATION 

Stir 10 drops of food coloring into 1000 cc of 
water. Pour off' 100 cc into a beaker. Add 100 cc 
of water, stir up the mixture, and pour off 
second 100-cc sample. Keep repeating until 
you have collected 10 to 15 samples. 

Questions: 

The original concentration was 10 drops/1000 
cc or 1 drop/ 100 cc. What is the concentration 
after one removal and the addition of pure 
water (one dilution cycle)? What is the con- 
centration after two cycles? after three cycles? 
and after n cycles? [Answer: (0.9)" drops/ 100/ 
cc] 

What is the number of cycles required/to 
reduce the concentration to approximat^y 2 
of its original concentration? 

How many times would you have td repeat 
the process to get rid of the dye cefmpletely? 



/\ 




Chapter 



23 



The Nucleus 



ACTIVITY 



NEUTRON DETECTION PROBLEM 
ANALOGUE (CHADWICK'S PROBLEM) 

It is impossible to determine both the mass and 
the velocity of a neutron from measurements 
of the mass and the final velocity of a target 
particle which the neutron has hit. To help 
you understand this, try the following: 




Fig. 23-1 



i' 



Set up an inclined groove on a table as 
shown in Fig. 23-1. Let a small ball bearing 
roll part way down the groove, hitting the 
larger target ball and knocking it off the table. 
Note the point where the target ball strikes 
the floor. Now use another smaller ball as the 
projectile. Can you adjust the point of release 
until the target ball strikes the savn.e spot 
on the floor as it did when you used the large 
projectile? If so, then two diff"erent combina- 
tions of mass and velocity for the projectile 
cause the same velocity of the target ball. 
Are there more combinations of mass and ve- 
locity of the target ball. Are there more com- 
binations of mass and velocity of the "neutron" 
that will give the same result? 





Now repeat the experiment, but this time 
iave the same projectile collide in turn with 
two different target balls of different masses, 
and measure the velocities of the targets. 

Use these velocity values to calculate the 
mass of the incoming neutron. (Hint: Refer to 
Sec. 23.4, Text. You need only the ratio of the 
final velocities achieved by the different tar- 
gets; therefore, you can use the ratio of the two 
distances measured along the floor from di- 
rectly below the edge of the table, since they 
are directly proportional to the velocities.) 
See also Film Loop 49. 




"Incredible as it may seem to those of us who lite in the world 
of anti-matter, a mirror image exists — the reterse of ourselves — 
which we can only call the world of matter." 

Drawing by Alan Dunn, S 1965 The New Yorker Magazine, Inc. 



FILM LOOP 



FILM LOOP 49: COLLISIONS WITH AN 
OBJECT OF UNKNOWN MASS 

In 1932, Chadwick discovered the neutron by 
analyzing collision experiments. This film 
allows a measurement similar to Chadwick's, 
using the laws of motion to deduce the mass of 
an unknown object. The film uses balls rather 
than elementary particles and nuclei, but the 
analysis, based on conservation laws, is re- 
markably similar. 




The first scene shows collisions of a small 
ball with stationary target balls, one of similar 
mass and one a larger ball. The incoming ball 
always has the same velocity, as you can see. 

The slow-motion scenes allow you to mea- 
sure the velocity acquired by the targets. The 
problem is to find the mass and velocity of 
the incoming ball without measuring it di- 
rectly. The masses of the targets are M, = 352 
grams, M2 = 4260 grams. 




Chadwick used hydrogen and nitrogen nu- 
clei as targets and measured their recoil 
velocities. The target balls in the film do not 
have the same mass ratio, but the idea is the 
same. 

The analysis is shown in detail on a grey 
page in Chapter 23 of the Text. For each of 
the two collisions, equations can be written 
expressing conservation of energy and conser- 
vation of momentum. These four equations 
contain three quantities which Chadwick 
could not measure, the initial neutron velocity 
and the two final neutron velocities. Some al- 
gebraic manipulation allows us to eliminate 
these quantities, obtaining a single equation 
which can be solved for the neutron mass. If 
Vj' and V2' are the speeds of targets 1 and 2 
after collision, and M, and M.^ the masses, the 
neutron mass m can be found from 

TnCi;,' - V2') ^ M2V2' - MiVi' 



or 



_ M2V2' - MiVi' 

m ; ; 

V, - V2 

Make measurements only on the targets, 
as the incoming ball (representing the neu- 
tron) is supposed to be unobservable both be- 
fore and after the collisions. Measure v, ' and 
V2' in any convenient unit, such as divisions 
per second. (Why is the choice of units not im- 
portant here?) Calculate the mass m of the in- 
visible, unknown particle. In what ways might 
your result differ from Chadwick's? 



Chapter 



24 



Nuclear Energy; Nuclear Forces 



ACTIVITIES 




d 



TWO MODELS OF A CHAIN REACTION 
Mousetraps 

Carefully put six or more set mousetraps 
in a large cardboard box. Place two small corks 
on each trap in such a position that they will 
be thrown about vidTeritly when the trap is 
sprung. Place af sheet ai clear plastic over 
the top. Then drop one ( ork in through the 
comer before you slide the cover completely 
on. Can you imagine the situation with tril- 
hons of tiny mousetraps and corks in a much 
smaller space? 

Questions: What in the nucleu^s is represented 
by the potential energy of the mousetrap 
spring? What do the corks represent? Does 
the model have a critical size? How might 
you control the reaction? Describe the effect 
of the box cover. 

Match Heads 

Break off the heads of a dozen wooden 
matches about g" inch below the match head. 
Arrange the match heads as shown in the 
drawing. Place wads of wet paper at certain 
points. Light a mar£cE~"^d place it at point A. 




WADS OF 
PAPER 



*<^e^a^ 



Observe what happens to theV right and left 
sides of the arrangement. What component of 
a nuclear reactor is represented by the wet 
paper? How could you modify this model to 
demonstrate the function of a moderator? 

Comment on how good an analogue this is 
of a nuclear chain reaction. (Adapted from A 
Physics Lab of Your Own, Steven L. Mark, 
Houghton Mifflin Co., Boston, 1964.) 



MORE INFORMATION ON NUCLEAR 
FISSION AND FUSION 

The U.S. Atomic Energy Commission has is- 
sued the following booklets on the practical 
applications of nuclear fission and fusion: 

"Nuclear Reactors" 

"Power Reactors in Small Packages" 

"Nuclear Power and Merchant Shipping" 

"Atomic Fuel" 

"Direct Conversion of Energy" 

"Power from Radioisotopes" 

"Atomic Power Safety" 

"Controlled Nuclear Fusion" 
All are available free by writing USAEC, 
P.O. Box 62, Oak Ridge, Tenn. 37831. 

PEACEFUL USES OF RADIOACTIVITY 

Some of the uses of radioactive isotopes in 
medicine or in biology can be studied with 
the help of simple available equipment. See 
Experiment 48, "Radioactive Tracers," in 
Chapter 21 of this Handbook. 

A few USAEC booklets that may provide 
useful information are: 

"Food Preservation by Irradiation" 
"Whole Body Counters" 
"Fallout from Nuclear Tests" 
"Neutron Activation Analysis" 
"Plowshare" 

"Atoms, Nature and Man" 
"Radioisotopes in Industry" 
"Nuclear Energy for Desalting" 
"Nondestructive Testing" 
For experiments see: "Laboratory Experi- 
ments with Radioisotopes," U.S. Government 
Printing Office, Washington. D.C. twenty-five 
cents. 

For necessary safety precautions to be 
taken in working with radioactive materials, 
see "Radiation Protection in Educational 
Institutions," NCRP Publication, P.O. Box 
4867, Washington, D.C. 20008. Seventy-five 
cents. 



150 



Activities 



Additional Books and Articles 



On the following pages are three separate 

bibliographies : 

1/ 
Science and Literature '^ i 

Collateral Reading for Physics Courses ^ 

Technology, Literature and Art since .^ '^ 

World War II 




Skim through them to see the variety of kinds of books and articles 
that have been written on these topics. If you find an item that 
looks particularly interesting, see if you can find it in the library— 
or if you can get the library to order it. 



Table of Some "Elementary" Particles 



Family 










Electric 




Average lifetime 


name 


Particle name 


Symbol 


Rest mass* 


charge 


Antiparticle 


(seconds) 


Photon 


photon 




y (gamma ray) 





neutral 


same particle 


infinite 


Leptons 


neutrino 




"■"^ 





neutral 


". V 


infinite 




electron 




e- 


1 


negative 


e+ (positron) 


infinite 




yu-meson 


(muon) 


(W" 


207 


negative 


M^ 


10-6 


Mesons 


TT-mesons (pions) 


7r+ 


273 


positive 


TT- same as 


10-8 








7r~ 


273 


negative 


tt" the 


10-8 








it" 


264 


neutral 


ir° particles 


10-16 




K-mesons (Kaons) 


K+ 


966 


positive 


K- (negative) 










K" 


974 


neutral 


K' 


10-10 and 10-7 




7;-meson 


(eta) 


v° 


1073 


neutral 


v" 


10-18 


Baryons 


proton 




P 


1836 


positive 


p (antiproton) 


infinite 




neutron 




n 


1839 


neutral 


n (antineutron) 


103 




lambda 




A" 


2182 


neutral 


A" 


10-10 




Sigma 




2+ 


2328 


positive 


2- (negative) 


10-10 








2- 


2341 


negative 


2+ (positive) 


10-10 








2° 


2332 


neutral 


2° 


10-20 




xi 




s- 


2580 


negative 


i+ (positive) 


10-10 








s+ 


2570 


neutral 


i" 


10-10 




omega 




n- 


3290 


negative 


n+ 


10-10 



Mass of electron is 1 unit on this scale 



175 



INDEX/TEXT SECTION 



Accelerator, electron, 14 

linear, 63 

particle, 14, 60-65 
Activation energy, 101 
Activity, 21,23 
Alchemy, 68 
Alpha rays, 13-16 

alpha decay, 18-19 

charge, 15-16 

mass, 15-16 

particles, 17, 18, 19,80 
Antineutrino, 41, 60 
Arms race, 115 

Artificial transmutation, 51-53 
Artificially induced radioactivity, 

70-71 
Aston, Francis William, 38, 39, 76 

whole number rule, 45, 50 
Atom, 1,8, 17, 18,21,32,35 

neutral, 39 
Atomic bomb, 88 

Energy Commission (AEC), 39, 
40, 65, 92, 93 

mass, 8, 9, 12, 19, 34, 35, 36, 47, 
76 

mass unit (amu), 45, 76 

nucleus, 58 

number, 44, 69 
Autoradiograph, 103 

Bacon, Sir Francis, 113 
Bainbridge, K. T., 30 
Becker, H., 54 
Becquerel, Henri, 5, 6, 7, 15 

rays, 7, 8, 13 
Beryllium, 54 
Beta rays, 13-16 

charge, 15-16 

mass, 15-16 

particles, 15, 18,41,83 
Binding energy, 77-79, 83, 99 

average, 78 
Blackett,P. M. S.,52 
Bohr, Aage, 103 
Bomb 

atomic, 88 

hydrogen, 98 
Bothe, W. G., 54 
British Association for the Ad- 
vancement of Science, 50 
Brookhaven Cosmotron, 63 
Bubble chamber, 66-67, 69 

Cambridge Electron Accelerator, 14 
Carbon, 86 

standard for atomic mass, 47 
Casimir, H. D. G., 114 



Cathode rays, 5, 15 

particles, 35, 36 

tube, 7, 35 
Chadwick, James, 51, 54, 55 

neutron-hypothesis, 56 
Chain reaction, 84-87 
Chemical properties, 31 
Chemical reaction, 75 
Cloud chamber, 52 
Cobalt, 18, 60 
Cold war, 92 

Collective model of nucleus, 103 
Collision, 86, 95-96 

elastic, 52 
Compton, Arthur H., 52 
Cosmic rays, 70 
Cowan, Clyde, 60 
Curie, Irene, 54, 70, 71, 81 
Curie, Marie, 6, 8, 9, 10-11, 12, 19, 

21 
Curie, Pierre, 6, 8, 9, 10-11, 17, 18, 

19, 21 
Curium, 82 
Cyclotron, 48 

Debierne, Andre, 17 
Decay constant, 23 

fraction, 23 

mathematics of, 23 

radioactive, 19, 53 

rate of, 21-24 
Dempster, A. J., 36 
Desalting plant, 92, 93 
Deuterium, 44, 76, 79, 95 

oxide, 44 
Deuteron, 77 
Discharge tube, 35, 38 

Einstein, Albert, 80, 112 
Eisenhower, Dwight David, 92 
Electric field, 35 
Electric force, 77 
Electromagnetic method of isotope 

separation, 39 
Electrometer, 8, 65 
Electron (see also Beta rays and 
Cathode rays), 15, 35, 41 

accelerator, 14 
Electron-volt (ev), 55 
Electroscope, 7, 15, 65 
Element, definition of, 32 

list of, 28-29 

periodic properties, 22, 24 

periodic table, 27 

radioactive, 82 

transuranium, 82 
Energy, activation, 101 



excitation, 101 

kinetic, 77, 80, 95 

of nuclear binding, 76-77 
Equation 

of radioactive transformation, 
18,41, 53 
Excitation energy, 101 
Excited state, 69 

Fajans, A., 33 
Fallout, radioactive, 88-89 
Fermi, Enrico, 60, 81, 82, 87, 98 
Fields, magnetic, 15, 35, 96 

electric, 35 
Fission, 75, 81, 88-93 
Fluorescence, 5 
Fraction, of decay, 23 
Franck, James, 88 
French Academy of Sciences, 9 
Frisch, Otto R., 83 
Fusion, 75, 81, 95-96 

controlled, 96 

proton-proton, 98 

in stars, 97-98 

Galileo, 117 

Gamma rays, 13-16, 17, 67, 77, 81 

charge (O), 15-16 

mass (O), 15-16 

particles (photon), 16-17, 18, 
33,50,51,52 
Gas diffusion method, 39 

plant, 40 
Genetic effects of radiation, 

defined, 89 
Germanium, 39, 41 
Glaser, D. A., 66 
Gold, transmutation of, 68 
Goldstein, 35 
Graphite, 86 

-moderated reactor, 91 

Hahn, Otto, 82, 83 
Half-life, 21-24, 81, 82 
"Heavy water," 44 
Helium, 16, 97 
Hiroshima, Japan, 88 
Hydrogen bomb, 98 
"heavy," 44 

Industrial Revolution, 116 
Infrared light, 7 
Iodine, radioactive, 105 
Ionization, rate of, 7 
Ionizing power, 14 
Isotopes, 35, 37, 38, 40, 41, 58, 68 
applications of, 105 



177 



Index/Text Section 



concept of, 31-32 
derivation of, 32 
of gold, 68 
of lead, 34 
separation of, 38-39 
tracers, 103 

Jeans, Sir James, 17 

Joliot, Frederic, 54, 70, 71, 88 

Joule (unit), 76 

Kepler, Johannes, 113 
Kinetic energy, 77, 80, 95 
theory, 24 

Laborde, A., 18 
Lawrence, Ernest O., 48 
Lawrence Radiation Laboratory, 

University of California, 67 
Lead, 32 

isotopes of, 34 
Linear accelerator, 63 
Liquid-drop model of nucleus, 

100-102 
Lithium-7 nucleus, 80 
Livingston, S. M., 48 

Magnetic fields, 15, 16, 35, 96 
Manhattan Project, 92 
Mass, atomic, 19 

energy balance, 79-81 

number, 39 

spectrogram, 39 

spectrograph, 30, 37, 38, 76 

spectrometer, 36, 45 
Meitner, Lise, 83 
Model of nucleus 

collective, 103 

liquid drop, 100-102 

shell, 102-103 
Moderators, 85 
Mousetrap (Rutherford's), 16-17 

Nagasaki, Japan, 88 
Neptunium, 83 
Neutral atoms, 35, 39, 76 
Neutrino, 41, 59-60, 71 
Neutron, 53, 68-69, 76, 82, 85 

capture, 100 

discovery, 53-55, 57-58 

fast, 85 

fission, 86 

induced reaction, 69 

mass, 57 

physics, 58 

slow, 85 

transformation, 59 



Newton, Isaac 

Principia, 118 
Nobel Prize, 6, 10, 19, 33, 52, 54, 

71, 74, 76-79 
Nuclear 

bomb, 88 

chain reactions, 88 

energy, 92 

fission, 75, 81-93 

forces, 99-100 

fusion, 75, 81,95-96 

models, 100-103 

physics, 1,2,49, 106 

power plant, 75 

power station, 2, 3 

reaction, 41, 60, 68-69, 75-76, 
79-81 

reactor, 85, 86, 88, 91 

rocket, 93 

science, 94 

species (see Nuclide) 

stability, 77-79 

weapons, 88-89, 98 
Nucleon, 78 
Nucleus, 1,49,58 

structure of, 45-51 
Nuclide, 32, 39, 40, 42, 43, 44, 71, 
79, 81, 82, 84 

Oppenheimer, Robert, 98 
Oscilloscope, 45 

Paraffin, 54-55 

Paris Institute of Radium, 10 

Particle, charged, 15 

Particle accelerator, 14, 60-65 

types of, 64 
Pauh, Wolfgang, 60 
PauUng, Linus, 10 
Penetrating power, 12-14 
Periodic properties of elements, 

22-24 
Periodic Table of Elements, 27 
Phosphorescence, 5, 6 
Phosphorus, 71 
Photographic plate, 6, 7, 38 
Pitchblende, 8, 9, 12, 34 
Plasma, 96 
Plutonium, 83, 84 
Pollution, radioactive, 89-90 

thermal, 89 
Polonium, 6, 9, 19, 20, 21, 32, 70 
Population explosion, 115 
Positive electron (see Positron) 
Positive rays, 35-36 
Positron, 70 
Proton, 50, 58, 76 

178 



-electron hypothesis, 49, 50 
-neutron theory, 58-59 
synchrotron, 63 
Prout, WilUam, 50 

Rabi, I.I.,98, 116 
Radiation biology, 103 

medicine, 103 

penetrating power, 12-16 

shields, 14 
Radioactive atoms, 32 

decay, 21-24, 53 

decay series, 19-21 

elements, 6, 8-9, 12, 82 

fall out, 88-89 

half-hfe, 21-24 

isotopes, 103 

pollution, 89-90 

rock, 4 

transformations, 17-19 
Radioactivity, 1-2 

artificially induced, 70-71 

discovery of, 5-7 
Radiochemistry, 71 
Radioisotopes, 105 
Radionuclide, 40 
Radium, 6, 9, 12 

"Radium A," 19 

Radium 226, 20, 21 

atomic mass of, 12 

chloride, 9, 12 
Radon, 17, 19,21 

gas, 20 
Ramsey, Sir WiUiam, 16, 33 
Rare gases, 33 
Reaction 

controlled, 96 

nuclear, 41, 60, 68-69, 75-76, 
79-81 

in stars, 97-98 
Reines, Frederick, 60 
Relative abundances of isotopes, 
41, 44-45 

table of, 42 
Richards,!. W., 34 
Rontgen, 5, 6 
Royds.T. D., 17 

Rutherford, Ernest, 12, 13, 16, 18, 
19,33,38,50,51,53,99 

Rutherford-Bohr model, 49 

"mousetrap," 16—17 

Schmidt, Gerhardt, 8 
Separation, of isotopes, 36, 38-39 
Shell model of nucleus, 102-103 
Shower, of electrons and positrons, 
70 



I 



Soddy, Frederick, 16, 17, 18, 19, 32, 

33 
Somatic effects of radiation, 89 
Sorbonne, Paris, 10 
Spectroscope, 17 
Stable isotopes, 41, 44-45 
Stars, fusion reaction in, 97-98 
Statistical law, 24 
Steam turbine, 89-90 
Strassmann, Fritz, 82, 83 
Strontium, 82 
Sulfur, radioactive, 103 
Sun, mass of, 97 

Thermal pollution, 89 
Thermonuclear explosions, 98 



Thomson, J. J., 15, 35, 36, 38 
Thorium, 8, 19, 32, 34 
Transformation, radioactive, 17-19 

rules of, 32-33 
Transmutation, 53 

artificial, 51-53 
Transuranium elements, 82 
Tritium, 95 
Turbine, steam, 89-90 

Ultraviolet light, 7 
Uranium, 6, 7, 12, 20, 24, 32, 79, 
84, 85, 86, 92, 100 

compounds of, 7 

fission, 83 

isotope, 81 



Index/Text Section 

oxide, 8, 9 

-radium series, 19, 41 

series, 34 

Uranium 235, 19 
Urey, H. C, 44 

U.S. Atomic Energy Commission 
(AEC),39,40, 65, 92,93 

Van de Graaf generator, 61 
Velocity selector, 37 
Villard, P., 13 

Wheeler, 101 

Wilson, C. T. R., 52 

Wilson cloud chamber, 52, 65, 70 

X rays, 5, 6, 7 



179 



INDEX/HANDBOOK SECTION 



Activities 

additional books and articles, 150-174 
exponential decay in concentration, 146 
ionization by radioactivity, 146 
magnetic deflection of beta rays, 144 
measuring the energy of beta radiation, 144-146 
more information on nuclear fission and fusion, 

149 
neutron detection problem analogue 

(Chadwick's problem), 147 
peaceful uses of radioactivity, 149 
a sweet demonstration, 146 
two models of a chain reaction, 149 
Additional books and articles (activity), 150-174 
Alpha particle(s), observation of (experiment), 131 

range and energy of (experiment), 131-132 
Amateur Scientist Section, Scientific American 

(May 1960, March 1953), radioactive isotope 
experiments, 143 
American Biology Teacher (August 1965), use of 

radioisotopes, 143 
Autoradiography (experiment), 142 

Background radiation, measurement of, 135 
Becquerel, discovery of radioactivity, 142 
Beta particle(s), momentum of, 145 

observation of (experiment), 132-133 

range and absorption of, 133 
Beta radiation, measuring energy of (activity), 

144-146 
Beta ray(s), magnetic deflection of (activity), 144 
Beta ray spectrometer, 144 

Capacitor, described, 134 
Carbon 14, half-life of, 141 

as tracer, 141 
Chadwick, and collision experiments, 148 
Chain reaction models (activity), 149 
Change, common principle of, 134 
Chemical reactions and separations, 142 
Cloud chamber, and random event experiment, 
126-127 

and study of alpha and beta particles, 131 
Collision experiments, Chadwick's, 148 
Collisions with an object of unknown mass 

(film loop), 148 
Curie, 141 

Data, recording of, 127-128 
Data page, 127 

Decay constant, and half-life, 137 
Dice, twenty-sided, and common principle of 
change, 134 
and random behavior, 126 
Distribution table, 128 

Electric circuit, and common principle of change 
(experiment), 134-135 



Experiments 

half-Ufe I, 134-137 

half-life 11, 138-139 

random events, 126-130 

range of alpha and beta particles, 131-133 
Exponential decay, in concentration (activity), 146 

Fermi, Enrico, and beta particle energy, 146 
Film loop 

colUsions with an object of unknown mass, 148 

Gamow, George, "The Law of Disorder," 126 
Geiger counter, and random event experiment, 127 
and short-lived radioisotope experiment, 135-137 
and study of alpha and beta particles, 131, 
132-133 
Graph, bar, 128 

of random data, 128 

Half-life I (experiment), 134-137 

II (experiment), 138-139 

of carbon 14, 141 

and decay constant, 137 

described. 137 

of radon 220, 138-139 
Handbook of Chemistry and Physics, 136 
Histogram, 128 

Icosahedral dice, see twelve-sided dice 
Iodine 131, as tracer, 141, 142 
Ionization energy, defined, 139 
Ionization by radioactivity (activity), 146 
Isotope, choice of for experiment, 141 

"Laboratory Experiments with Radioisotopes for 
High School Demonstrations" (S. Schenberg, 
ed.), 142 
"Law of disorder, The" (George Gamow)V^^ 
"Low Level Radioisotope Techniques" (John '. 
Woodburn), 143 

Mark, Steven L., A Physics Lab of Your Own, 149 

Mass, of neutron, 147 

Matchheads, in chain reaction model, 149 

Microcurie, 141 

Momentum, of beta particle, 145 

Mousetraps, in chain reaction model, 149 

Net count rate, of radioactive sample, 135 

Neutrino, 146 

Neutron, determining mass and velocity of 

(activity), 147 
Nuclear fission and fusion, information on 

(activity), 149 

Phosphorus 32. as tracer, 141 

Photosynthesis, radioisotopes in study of, 140-141 




180 



Index/Handbook Section 



Physics Lab of Your Own, A (Steven L. Mark), 149 
Polonium atom, ionization energy of, 139 

kinetic energy of, 139 
Prediction, of random events, 126, 128-130 
Probability theory, 126 

see also random event 

Radioactive decay, see half-life 
"Radioactive Isotopes: A Science Assembly 

Lecture," 142 
Radioactive materials, see alpha ray, beta ray, 

radioisotope(s) 
Radioactive samples, measuring activity of, 

126-127, 130 
Radioactive wastes, safe disposal of, 143 
Radioactivity, and ionization (activity), 146 

peaceful uses of, information on (activity), 149 
"Radioisotope Experiments for the Chemistry 

Curriculum," 142 
Radioisotopes, handling of, 140 

short-lived, 135-137 

as tracers, 140-141 
Radon 22, half -life of, 138-139 
Random data, graph of, 128 
Random events (experiment), 126-130 

described, 126 

prediction of, 1^8-130 



Range of alpha and beta particles (experiment), 
131-133 



Schenberg, S. (ed.), "Laboratory Experiments with 
Radioisotopes for High School Demonstra- 
tions," 142 

Scientific American, Amateur Scientist Section 

(May 1960, March 1953), radioactive isotope 
experiments, 143 

Short-lived radioisotope (experiment), 135-137 

Sugar cubes, in radioactive decay activity, 146 



Tagged atoms, use of (experiment), 140-141 
Theory of probability, 126 
Thorium decay series, 138-139 
Tracers, 140-143 

Twenty-sided dice, and common principle of 
change (experiment), 134 
and random behavior, 126 



Velocity, of neutron, 147 



Woodburn, John H., "Low Level Radioisotope 
Techniques," 143 




181 



staff and Consultants 



Nickerson Rogers, The Loomis School, Windsor, 

Conn. 
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. 
Bemhard 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 Sch9€ 

Baltimore, Md. 
Devon Showley, Cypress Junior CoUeg^, 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 Catholie 

High School of Baltimore, Md. 
M. Daniel Smith, Earlham College, Rjj?j^ond, 

Ind. 
Sam Standring, Santa Fe High S€h6ol, Santa Fe 

Springs, Calif. X ^ 

Albert B. Stewart, AntiochX5ollege, Yellow 

Springs, Ohio 
Robert T. Sullivan, BiJrnt Hills-Ballston Lake 

Central School, N.Y. 
Loyd S. Swensdn, University of Houston, Texas 
Thomas E, Thorpe, West High School, Phoenix, 

Ariz., 
June Goodfield Toulmin, Nuffield Foundation, 

^ondon, 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 



-^ 



182 



I 



Answers to End-of-Section Questions 



Chapter 21 

Q1 It was phosphorescent. Becquerel wrapped a 
photographic plate in thick black paper to keep light 
out. Then he placed a small piece of the uranium 
compound on top of the black paper and allowed 
sunlight to fall on it. Upon developing the plate he 
found the silhouette of the mineral sample recorded 
on the plate. When he tried putting metallic objects 
between the sample and the plate he found their 
outlines recorded even when a layer of glass was 
also introduced to eliminate possible chemical action. 
Q2 No treatment was needed — the emission was 
spontaneous. 

Q3 They were puzzling because they needed nothing 
to start them, and there was nothing that could stop 
them. They were similar to X rays in that both were 
very penetrating radiations, and both could ionize. 
Q4 It isn't — although slight differences might be 
observed because of the other element absorbing 
some of the radiation. 

Q5 The radioactivity was much greater than ex- 
pected for the amount of uranium in the ore. 
Q6 Separating it from barium, which is almost 
identical chemically. 

Q7 From most to least penetrating: 7, jS, a. Pene- 
trating power is inversely related to ionizing power 
because rays which are easily stopped (have low 
penetrating power) do so because they are expending 
their energy ionizing many atoms of the stopping 
material (high ionizing power), and vice-versa. 
Q8 y3 particles were found to have the same q/m 
ratio as electrons. 

Q9 a rays were deflected much less than p rays by 
a magnetic field. 

Q10 Its emission spectrum, when caused to glow 
by an electric discharge, was the same as helium's. 
Q11 It occurs when only a single pure element is 
present, and isn't affected by chemical combinations 
of that element. 

Q12 An example would be the decay of radon into 
polonium with the emission of an alpha particle 
(Rn-» Po + He). It was contrary to the ideas of 
indivisibility of atoms held by 19th century chemists. 
Q13 (1) Many of the substances in a series have 
similar chemical properties. 

(2) There are only small percentage differences 
in atomic mass. 

(3) Many of the substances decayed very 
rapidly into something else; all three kinds 
of rays are given off by the mixture. 

Q14 At the start, the emission will be relatively 
slow and will consist entirely of alpha particles. 
Later, the emission will be greater and will contain, 
besides alpha particles, beta and gamma rays. 
Q15 The law of radioactive decay is a statistical 
law; it says nothing about how long it will take any 
given atom to decay. To specify a "life time" would 
be to predict when the last atom would decay. We 
do not know any way of doing that. 



Q16 1/16 of it. 

Q17 We do not know. The statistical half-life laws 
do not apply to small numbers of atoms, and we do 
not have any other laws which make predictions 
about individual atoms, or even about small numbers 
of atoms. 

Chapter 22 

Q1 They were chemically the same as previously 

known elements. 

Q2 The atomic mass equals 12 amu. It occupies 

position 6 in the list of elements. 

Q3 Decreases 4 units; stays essentially the same. 

Q4 Decreases by 2 + charges; increases by 1 + 

charge. 

Q5 The rules are: 

(1) In alpha decay, the mass number decreases 
by 4, and the atomic number decreases by 2. 

(2) In beta decay, the mass number remains the 
same, and the atomic number increases by 1. 

(3) In gamma decay, both the mass number and 
the atomic number remain the same. 

Example: g.U-^^-^ 90^-^*+ « 

In the Rutherford-Bohr model of the atom, the entire 
positive charge and almost the entire mass are con- 
tained in the nucleus. Since alpha, beta, and gamma 
rays are ejected from the nucleus they will carry 
away from it both mass and charge. The alpha par- 
ticle carries 2 positive charges and 4 amu; hence 
rule (1). The beta particle carries 1 negative charge 
and negligible mass; hence rule (2). The gamma ray 
has no mass and is uncharged; hence rule (3). 
Q6 By subtracting a particle masses from the mass 
of the parent of the decay series. 
Q7 It must have a "velocity selector" which will 
allow only ions of a single speed to enter the mag- 
netic field. This can be done with crossed electric 
and magnetic fields. 

Q8 (1) Faint second line in mass spectrum of pure 
neon. 

(2) Different atomic masses of samples of neon 
separated by diffusion. 

(3) More intense second line in mass spectrum 
of one of the samples separated by diffusion. 

Q9 More massive atoms have a lower average 

speed and so diffuse more slowly than the less 

massive ones. 

Q10 .^Pt'"^; platinum. 

Q11 (A — 4). The rule is: emission of an alpha 

particle results in a decrease in A of 4 units. 

Q12 (Z + 1). The rule is: emission of a negative /3 

particle results in an increase in Z of 1 unit. 

Q13 An isotope of hydrogen with twice the atomic 

mass of ordinary hydrogen. 

Q14 Heavy water is the compound D2O. In other 

words, it is made with heavy hydrogen (= deuterium) 

rather than ordinary hydrogen. 

Q15 The third isotope has a very low abundance. 



183 



Q16 (.C12 is the current standard. It was chosen 
mainly because it readily fornns many compounds 
and so is available for measuring other masses by 
mass spectrograph techniques which are much more 
accurate than chemical methods. 



Chapter 23 

Q1 Several atomic masses (which were not recog- 
nized as the average of several isotopes) were not 
close to whole multiples of the atomic mass of 
hydrogen. 

Q2 12 protons and 6 electrons. 
Q3 Yes, roughly. .,He^ would contain 4 protons and 
2 electrons inside the nucleus. (It does not work out, 
however, when very careful mass measurements 
are made.) 

Q4 The number of tracks observed in a cloud 
chamber did not include any that would correspond 
to the original a particle breaking up into fragments. 
Q5 The way it knocked protons out of paraffin 
would be for 7 rays a violation of the principles of 
energy and momentum conservation. 
Q6 A neutron has no charge, and so isn't deflected 
by magnetic or electric fields, nor does it leave a 
track in a cloud chamber. 

Q7 The laws of conservation of momentum and 
kinetic energy were applied to neutron-proton and 
neutron-nitrogen head-on collisions. This yielded four 
equations in the four variables: m,,, v^^, v,^' (proton 
collision), and v,/ (nitrogen collision). The latter 
three were eliminated, and m^^ found. 
Q8 7 protons and 7 neutrons. 
Q9 A nucleus of 2 protons and 2 neutrons, sur- 
rounded by 2 electrons. 

Q10 A neutron in the nucleus changes into a proton 
and a li particle, which immediately escapes. 
Qtl Without the extra particle, there was no way 
to explain the disappearance of energy in /i-decay. 
Q12 The repulsive electric force exerted by the 
large charge of the heavy nucleus on an a particle 
prevents it from reaching the nucleus. 
Q13 Protons have only a single charge. 
Q14 Some devices for producing projectiles are: 
Van deGraaff generators, linear accelerators, cyclo- 
trons, synchrotrons, etc. Devices which detect nuclear 
reactions are: cloud chambers, spark chambers, 
photographic emulsions, and bubble chambers. 
Q15 They have no electric charge and so are not 
repelled by nuclei. 



Q16 ,,Si28 

Q17 gCi '. 7 protons, 6 neutrons before; 6 protons, 

7 neutrons after. 

Chapter 24 

Q1 No, in some nuclear reactions energy is 

absorbed. 

Q2 It can go off as 7 rays or as the KE of the 

product particles. 

Q3 The binding energy of the deuteron nucleus is 

the energy that would be required to break up the 

nucleus into its constituent particles: a proton and 

a neutron. 

Q4 A nuclide with a high average binding energy 

is more stable. 

Q5 No. Light nuclei are lower on the curve than 

heavy nuclei. 

Q6 Capture of a neutron by a uranium nucleus, then 

the /3 decay of the new nucleus. 

Q7 Neutrons. 

Q8 A substance which slows down neutrons. 

Q9 It slows down neutrons well (because of the 

abundance of H atoms), but it also absorbs many 

(to form "heavy" water). 

Q10 By "control rods," made of a material which 

absorbs neutrons. The farther in the rods, the slower 

the reaction. 

Q11 The positively charged nuclei repel each other 

and high speeds are necessary for the nuclei to come 

near enough in collisions to fuse. 

Q12 Since at very high temperatures the gas is 

ionized, a properly shaped magnetic field could 

deflect the charged particles away from the walls. 

Q13 Decreasing. 

Q14 The protons in a nucleus repel each other with 

intense electric forces. 

015 The average binding energy curve suggests 

that each particle in the nucleus is bound only by its 

immediate neighbors. 

Q16 An excited nucleus becomes distorted in 

shape; electric repulsion between bulges then forces 

them apart. 

Q17 In the case of U-^^, the excitation energy due 

to neutron capture alone is less than the activation 

energy required for fission. For U-^\ the excitation 

energy is greater than the activation energy. 

Q18 They correspond to completed shells (or sets 

of energy states) of protons and neutrons in the 

nucleus. 

Q19 Neither; they each have different strengths 

and weaknesses. 




184 




Brief Answers to Study Guide Questions 



Chapter 21 




Chapter 23 


21.1 


Information 




23.1 


Information 


21.2 


Discussion 




23.2 


Discussion 


21.3 


(a) 1.2 X 10-13 joule 




23.3 


235 protons; 143 electrons 




(b) 0.75 MeV 




23.4 


Equations 


21.4 


(a) 5.7 X 10-2 m 




23.5 


Equations 




(b)210m 




23.6 


(a) y (b) A|28 (c) Mgz* (d) Mg25 




(c) R„ = 3700R, 




23.7 


(a) Discussion 


21.5 


Charges are positive; 


field is into the page. 




(b) in Unit 3 under conservation laws. 


21.6 


(a) 1.8 X 10+ newtons/coul 


23.8 


1.10 amu, 5.2% 




(b) 1.8 X 103 volts 




23.9 


Table 




(c) undeflected 




23.10 


(a) 78 


21.7 


(a) 7 (b) a (C) a (d) y (e) y 




(b)79 




(f)aOr7(g)i3(h)a(i) 


a(j)|3 




(c) 80 


21.8 


Discussion 






{d)80 


21.9 


(a) one-half 

(b) three-quarters 

(c) discussion 




23.11 


(a) „Na2* 

(b) „Na24 

(c) „Na24 


21.10 


10% 






(d) iiNa24 


21.11 


(a) graph 




23.12 


Discussion 




(b) proof 




23.13 


Discussion 




(c) 5.0 X 1020 atoms 




23.14 


Discussion 


21.12 


(a) 5.7 X 10-13 joules/disintegration 


23.15 


Discussion 




(b) 45 watts 




23.16 


Less by 0.02758 amu 


21.13 


3.70 X 105 disintegration/sec 






21.14 


The number remains constant. 


Chapter 24 


21.15 


(a) about 4 days 




24.1 


Information 




(b) discussion 




24.2 


4.95 MeV 



Chapter 22 

22.1 Information 

Discussion 

Discussion 

(a) Discussion 

(b) Discussion 

(a) 5.4 cm 

(b) 5.640 m 

(c) 0.0048 m 
Equations 
Chart 
Diagram 
Diagram 

4,000 years; 23,000 years 

(a) 12.011 amu 

(b) 6.941 amu 

(c) 207.2 amu 
4.0015 amu 

(a) Va 

(b) about 1/2 

(c) about 2.25 X lO" years 

(d) yes 



22.2 
22.3 
22.4 

22.5 



22.6 

22.7 

22.8 

22.9 

22.10 

22.11 



22.12 
22.13 



24.3 7.07 MeV/nucleon 

24.4 Opposite directions, each 8.65 MeV 

24.5 Absorbed, 1.19 MeV 

24.6 0.56 MeV 

24.7 8.61 MeV 

24.8 Neutron capture, /3-decay, ^-decay 

24.9 Bai+i is 1180 MeV; Kr'^^ js 800 MeV; 
U-3-i is 1790 MeV. Discussion 

24.10 208 MeV 

24.11 Diagram 

24.12 Discussion 

24.13 Discussion 

24.14 Discussion 

24.15 26.7 MeV 

24.16 (a) 4.33 X 1 on kg/sec 

(b) 5.23 X 10-3 horsepower 

24.17 Equations 

24.18 1.59 MeV released 

24.19 U-33 is fissionable 

24.20 Pu-'i is fissionable 

24.21 Discussion 



HOLT, RINEHART AND WINSTON, INC.