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Full text of "Project Physics Unit Discoveries in Physics"



The Project Physics Course 



Supplemental Unit 



B 



Discoveries in Physics 




Supplemental Unit B 



Discoveries in Physics 



by 



David L. Anderson 

Oberlin College 



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, Chairman of the 

Department of Science Education, New 

York University, New York 
Fletcher G. Watson, Harvard Graduate 

School of Education 



This Supplemental Unit 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. 



Picture Credits 

Cover photographs: upper left, courtesy of 
Physics Today; upper right, Brown Brothers; 
center, courtesy of Professor M. S. Living- 
ston, Massachusetts Institute of Technology; 
lower left, Culver Pictures, Inc.; lower 
right, Cavendish Laboratory, University of 
Cambridge. 

Facing page 1, Haags Gemeentemuseum. 
Page 4, Yerkes Observatory and Lowell 

Observatory. 
Page 6, Fig. 1-2, New York PubUc Library; 

Fig. 1-3, Yerkes Observatory. 
Page 12, Fig. 1-7, The Bettmann Archives, 

Inc.; Fig. 1-8, Harvard Observatory. 
Page 13, Fig. 1-9, Yerkes Observatory. 
Page 17, Fig. 1-11, Lowell Observatory 

Photograph; Fig. 1-12, WIDE WORLD 

PHOTOS. 
Page 18, Lowell Observatory Photograph. 
Page 31, Deutsches Museum, Munich. 
Page 32, Cavendish Laboratory, University 

of Cambridge. 
Page 35, The Bettmann Archive, Inc. 
Page 39, Courtesy of Sir George Thomson. 
Page 46, Project Physics Fihn "The World of 

Enrico Fermi". 
Page 48, University of Chicago. 
Page 51, WIDE WORLD PHOTOS. 
Page 52, American Institute of Physics. 
Page 54, Segre Collection, Niels Bohr 

Library. 
Page 57, New York Pubhc Library. 
Page 59, Scientific American. 
Page 62, Los Alamos Scientific Laboratory. 
Page 76, National Accelerator Laboratory. 
Page 77, TASS from SOVFOTO. 
Page 79, Lawrence Radiation Laboratory. 
Page 83, Cavendish Laboratory, University 

of Cambridge. 
Page 84, Haags Gemeentemuseum. 
Page 85, Yerkes Observatory and Lowell 

Observatory; Cavendish Laboratory, 

University of Cambridge; Project 

Physics Film "The World of Enrico 

Fermi"; Los Alamos Scientific Laboratory. 



Copyright © 1973, Project Physics 

All Rights Reserved 

ISBN 0-03-086754-1 

34567 006 987654321 

Project Physics is a registered trademark 



Contents 



Prologue 1 

Chapter 1 New Findings in the Heavens — Uranus, Neptune, and Pluto 

Introduction 5 

The discovery of Uranus 6 

The stirange motion of Uranus 8 

Perturbations 10 

The discovery of Neptune 1 1 

The orbit of Neptune 14 

The discovery of Pluto 17 

Experiment 22 

Chapter 2 Cathode Rays and the Discovery of the Electron 

The discovery of cathode rays 33 

The wave theory of cathode rays 34 

A particle theory is proposed 35 

Properties of the particles: Schuster's calculations 36 

Hertz's experiments in support of the wave theory 39 

The wave theory collapses: the experiments of Thomson 40 

Enter the electron 42 

Chapter 3 Nuclear Fission 

Introduction 47 

Bombarding nuclei with neutrons 48 

The special problem of uranium 48 

The search for transuranic elements 49 

A discovery missed 50 

Alpha particles and another near-discovery 51 

The discovery is made 53 

The study of nuclear fission begins 55 

The chain reaction 56 

The war intervenes 57 

Some thoughts for our models of discovery 58 

Chapter 4 The Neutrino 

Introduction 63 

Products of radioactive decay 63 

Beta decay seems to violate conservation laws 65 

The neutrino is "invented" 67 

The problem of experimental detection 68 

The Reines-Cowan experiment 69 

Neutrinos conserve linear momentum 71 

The antineutrino 72 

The muon's neutrino and antineutrino 74 

Questions the neutrino may help to answer 78 

Some themes in scientific discovery 80 

Epilogue 84 
Index 92 



III 




Day and Night, by M. C. Escher. 



Discoveries in Physics 



Prologue Some Models for Scientific Discovery 

In this unit we shall examine in some detail four scientific discoveries: the 
finding of the planets Uranus, Neptune, and Pluto, the discovery and iden- 
tification of cathode rays, the discovery and understanding of nuclear fis- 
sion, and the experimental verification of the existence and the properties 
of the neutrino. Each of these discoveries is interesting in itself and is 
worth studying for that reason. But the four of them, taken together, can 
also provide us with good examples for thinking about the processes of 
scientific discovery. How do scientific discoveries happen? How do scien- 
tists go about solving problems? 

Of course, one question we should raise at the outset is whether it is 
possible to make any useful generalizations about the processes of scien- 
tific discovery. Do the histories of individual discoveries fit into some sort 
of general pattern? This is the sort of basic question scientists themselves 
ask about phenomena they study; they look at some group of objects— the 
stars, forexample — and try tofitthem into categories according to their 
various characteristics. They ask how stars differ from each other and how 
they resemble each other. They make models of stars — not in the model 
railroad sense, but in terms of diagrams, equations, and graphs. They try 
to see whether their models of stars exhibit the properties real stars are 
observed to have. The better a model accounts for observable properties 
in terms of known physical principles, the more reliable and useful the 
model is. 

In an analogous way, then, we ask whether there is any model that 
would describe what goes on in actual scientific discoveries — a model 
using concepts or pictures from real life. Several such models of the sci- 
entific process have been suggested. Some scientific discoveries are, for 
example, very much like voyages of discovery. The explorer sets out on an 
uncharted sea, and if he is lucky he finds new lands and perhaps civiliza- 
tions. But the work of the scientist has also been compared to an army 
campaign, with interesting problems of strategy and tactics, with hard- 
won victories and occasional setbacks. Another way to look at great scien- 
tific discoveries is to compare them to the completion of a jigsaw puzzle, 
in which pieces have been slowly fitted together to reveal a previously 
hidden picture. But scientific work has also been described as being like 
the work of a detective in a "whodunit," in which all sorts of clues are 
sought, and in which much ingenuity is needed both to find the clues and 
to fit them together. 



2 Discoveries in Physics 

So at least four models for the processes of science have been 
suggested, and there could undoubtedly be others. In scientific work it- 
self, when we find that nnany models present themselves, we can be fairly 
sure that either (a) one of the models, or a modification of it, will turn out 
to be by far the best, after more data are found, or (b) the phenomena are 
too complex to be explained adequately by any single model. In the sec- 
ond situation, each of several models says something true about the phe- 
nomena, but no one of them is adequate to give a complete picture. (In 
physics, for example, neither the simple particle model nor the simple 
wave model is adequate to describe the observable behavior of beams of 
light, but both models provide us with useful insights when we are experi- 
menting with or thinking about light.) As you read about the four discover- 
ies described in this unit, think about the models of discovery suggested 
above-and other models you may think up. Ask yourself which of them 
are adequate to describe the events of the particular discoveries and to 
help us think about scientific discovery in general. 

In addition to thinking about models to describe the nature of scien- 
tific discoveries, we can also look at particular discoveries in a variety of 
other ways. We can ask some rather specific questions. Why, for instance, 
are some new ideas accepted quickly and eagerly, while others are 
rejected? And why are some discoveries made in duplicate-that is, by dif- 
ferent men in different places, but at almost the same time? Consider also 
the importance of engineering and technological developments which 
often spring from some new scientific discovery. But sometimes an impor- 
tant scientific discovery can be made only after an engineering develop- 
ment. 

More generally, we might ask whether there are any particular circum- 
stances in which discoveries are especially likely to be made. In what polit- 
ical, economic, philosophical, and theological systems or climates have 
great discoveries been made? What are the roles of industrial or academic 
or governmental laboratories? The chapters which follow will not answer 
all the questions raised here, but they will provide you with some case his- 
tories which may be helpful in thinking about the conditions surrounding 
scientific discoveries. 

We hope particularly that you will see that the word "science" has 
two meanings, and that both are necessary. On the one hand there is the 
scientist as a seeker of harmonies and constancies in the jungle of expe- 
rience. He aims at knowledge and prediction, particularly through dis- 
covery of laws. This aspect of science is the speculative, creative, even 
subjective contribution of an individual, working on his own task by his 
own usually unexamined methods, motivated in his own way, and not 
always attending to the long-range philosophical problems of science. 
The other aspect of science comes to the fore when an individual's work 
is written up, published, and assimilated into the whole stream of such 
individual contributions. This is science as a public, shared activity, sci- 
ence as a growing network synthesized from these individual contribu- 
tions. Here, science has become "objective" by the acceptance of those 



Prologue 

ideas-or even those parts of ideas- which do indeed prove meaningful 
and useful to generation after generation of scientists. The cold tables of 
physical and chemical constants, the bare equations in textbooks, are 
only the hard core, the residue distilled from individual triumphs of in- 
sight, checked and cross-checked by the multiple testimony of general 
experience. 



1.1 Introduction 5 

1.2 The discovery of Uranus 6 

1.3 The strange motion of Uranus 8 

1.4 Perturbations 10 

1.5 The discovery of Neptune 11 

1.6 The orbit of Neptune 14 

1.7 The discovery of Pluto 17 




Recent discoveries: upper left, the second satellite of Neptune; lower left, Pluto; right, satellites of Uranus — the faint fifth 
satellite is overwhelmed by the over-exposed image of the planet. 



CHAPTER ONE 



New Findings in the Heavens 
Uranus, Neptune, and Pluto 



1.1 Introduction 

Great scientific theories are comprehensive. They explain a large For a review, see Chapter 8 of the 

number of phenomena that previously had seemed to be unrelated. Project Physics Text. 

Newton's theory of universal gravitation is such a theory. Although 
the theory was originally developed to account for the major motions 
of the moon and of the planets, Newton showed in the Principia that 
he could go on to use it to explain the variation in g (the accelera- 
tion of a freely falling object) from place to place, the behavior of 
the tides, the slow wobble of the earth's axis, and a variety of small 
peculiarities in the motion of the moon. 

A great theory may also suggest to us where or how to look for 
new, previously unsuspected phenomena. If later observation shows 
the prediction to be correct, it is strong evidence that the theory is 
sound; it fits with observed phenomena. Here again the theory of uni- 
versal gravitation provides a good example. Newton predicted from 
the theory that the rotating earth should bulge sUghtly at the equator, 
and indeed the earth was found to be oblate rather than perfectly 
spherical. He also predicted that projectiles shot horizontally at high 
speed could travel around the earth in circular or elliptical orbits or, if 
their speed were high enough, could escape from the earth along para- 
bohc or hyperboHc paths. Today, almost 300 years later, many ar- 
tificial earth sateUites move as Newton's theory said they would. 

When Newton formulated his theory of universal gravitation, he 
was unaware of the existence of any planets other than those known 
since ancient times: Mercury, Venus, Earth, Mars, Jupiter, and Sa- 
turn. We shall see, however, that his theory was instrumental in the 
discovery, about 120 years after his death, of another planet, Neptune. 
The story of the discovery of Neptune will involve us in the related dis- 
coveries of Uranus and Pluto. All three of these planets are too dim to 
be seen without a telescope. The existence and position of Neptune 
were predicted by means of the theory of gravitation. The subsequent 
observation of Neptune in the predicted position was one of the 
crowning triumphs of Newton's theory. 



New Findings in the Heavens — Uranus, Neptune, and Pluto 




Fig. 1-2 William Herschel 
(1738-1822) with diagram showing 
Uranus and its two brightest 
satellites, Oberon and Titania, 
discovered by him on January 1 1 , 
1787. 



1.2 The discovery of Uranus 

Before we can discuss the discovery of Neptune, we must first con- 
sider the discovery of Uranus, an event which owed much to chance. 
Uranus was found in 1781 by WiUiam Herschel (1738-1822), who was 
not looking for any new planet at all. 

Herschel, who was originally a musician, immigrated to England 
from Germany when he was nineteen years old. In his spare time he 
took up the study of languages, then mathematics, and then as- 
tronomy. He began building his own telescopes and within a few years 
was making better telescopes than were then available to professional 
astronomers. 

When he was in his early forties Herschel embarked on the 
tremendous task of counting the number of stars visible in various 
parts of the sky through his best telescope. His primary object was to de- 
termine how the stars are distributed in the three-dimensional space 
around us. In other words, he was trying to find the size and shape of 
what we now call our galaxy. 

As he was carrying out his observations, he happened to notice, on 
the night of March 13, 1781, an unusual object among the stars of the 
constellation Gemini. The object, just a bit too faint to be seen without 
a telescope, appeared as a disc rather than as a point of hght. Herschel 
knew that stars are too far away to show up in telescopes as anything 
but points of Ught, whereas planets and comets, being much closer, 
can be seen as discs. The observation that in the course of several days 
the object moved relative to the stars confirmed his suspicion that it 
was not a star. 

In spite of the fact that the object lacked any hint of a tail or of any 
fuzziness, Herschel assumed that the newly discovered object was a 
comet, not a planet. This was not surprising; most of the astronomers 
to whom Herschel communicated the news of his discovery agreed 
with him. New comets were being discovered fairly frequently, 
whereas no one since the dawn of recorded history had ever found a 
new planet. 



Fig. 1-3 Uranus (overexposed) and 
its five satellites. 




Section 1.2 



The only problem, then, was to determine the shape, size, and ori- 
entation of the orbit of the "comet," the so-called elements of the 
orbit, from its observed positions at various times. The process of de- 
termining elements from observational data is tedious, particularly 
if one does not have data from observations over a long period of 
time. (A "long period of time" here means about the length of time it 
takes for the object to make a circuit around the sun.) In addition, 
there was in Herschel's time no way to calculate elements from 
observational data without depending on unreUable guesses as 
to the shape of the orbit. Not until 1809 was a method developed for 
calculating elements without having to guess at the shape of the 
orbit; the inventor of this method was the brilliant mathematician 
Karl Friedrich Gauss (1777-1835). Gauss' method did assume that 
the orbit was a conic section (that is, an ellipse, a parabola, or a hyper- 
bola), an assumption that was justified by Newtonian physics. Unfor- 
tunately, Herschel, working in 1781, was obhged to base his calcula- 
tions on uncertain hypotheses about the type of orbit he was studying. 
His attempts to find the elements of the orbit of his supposed comet 
were unsuccessful. Some comets have parabolic or very eccentric 
elliptical orbits which bring them quite close to the sun at periheUon. 
The data for Herschel's object did not fit into any such orbit. 

In May of 1781 a French astronomer calculated an orbit in which 
the perihelion distance would be more than twelve times the distance 
from the earth to the sun. This is an astonishingly large perihelion dis- 
tance for a comet. Perhaps the object was not a comet after all; 
perhaps it was a distant planet. Shortly thereafter, Lexell, a Russian 
astronomer visiting in London, computed the elements on the as- 
sumption that the orbit was circular. This orbit had a radius nineteen 
times that of the earth's orbit, and was more than twice the radius of 
the orbit of Saturn. LexeU's results made generally acceptable the 
idea that the new object was a planet far beyond the orbit of Saturn. 
Within two years of Herschel's original observation, the French math- 
ematician Laplace and others used the accumulated data to compute 
the elements of an elliptical orbit. Since Uranus (as the new planet 
eventually came to be called) takes 84 years to make one revolution 
around the sun, it is obvious that a two-year span of observations does 
not give one very much to go on. (See Fig. 1.6 for a scale drawing in- 
dicating the path of Uranus in a two-year period.) It is a tribute to the 
precision with which the observations were made that tolerably 
useful calculations of the elements of the orbit could be made at all. 

A German astronomer, Johann Bode (1747-1826), soon thought of 
a possible way around this difficulty of having observations covering 
only a short span of time. It occurred to him that astronomers in ear- 
Uer years might have observed Uranus while compiling catalogs of 
stars and, assuming it to be a star, included it in their catalogs. He 
used the orbit to calculate where Uranus had been in the sky at earUer 
times. Then he looked to see whether any stars situated near the ex- 
pected path of Uranus had been recorded in one catalog but not in 



Plane of orbit 



Plane of ecliptic 




Fig. 1-4 An orbit in its plane 
compared to the plane of the earth's 
orbit (the ecliptic plane). 



To specify the size, shape, and orien- 
tation of an elliptical orbit in the solar 
system, we need to know six quan- 
tities or elements. Five of these quan- 
tities are indicated in Fig. 1-1 by the 
symbols, /, il, o*, a and c. The angles 
/, il, and CO specify the tilt of the plane 
of the orbit and the direction of the 
major axis of the ellipse. The dis- 
tances a and c define the shape and 
size of the ellipse. The angle / is the 
inclination of the object's orbit rela- 
tive to the plane of the earth's orbit. 
The angle il is the angle between the 
line of intersection of these two 
planes (called the lines of nodes) and 
a line drawn from the sun toward the 
vernal equinox. (The vernal equinox 
is the point at which the sun crosses 
the celestial equator from south to 
north about March 21. See Unit 2 Sec- 
tion 5.1 of the Project Physics Text.) 
The angle <»> is the angle between the 
major axis of the ellipse and the line 
of nodes. The distance a is half the 
major axis of the ellipse; c is the dis- 
tance from the sun at a focus of the 
ellipse to the center of the ellipse. 
The shape of an elliptical orbit is 
often specified as the eccentricity, 
e = c/a. (See Unit 2 Section 7.3 of the 
Project Physics Text.) The sixth or- 
bital element, a date when the object 
passed its perihelion point, is 
needed for the computation of a time- 
table of past and future positions. 



8 New Findings in the Heavens — Uranus, Neptune, and Pluto 

others compiled at different times. He found that such a "star" had 
been observed on December 23, 1690, and another on September 25, 
1756. Later, observations recorded in 1764 and in 1769 were found. 
Using these positions observed in the past, together with the contem- 
porary ones, the French astronomer Delambre in 1790 derived new 
elements for the orbit of Uranus. 

Thus, within a decade of its accidental discovery by Herschel, 
Uranus seemed to be a perfectly well-behaved member of the sun's 
family of planets, with accurately known elements. 



1.3 The strange motion of Uranus 

There was no doubt, then, that Uranus was one of the sun's planets; 
but by 1820 there were hints that it was not so well-behaved after all. 
The French scientist Alexis Bouvard (1767-1843) found that an orbit 
computed from observations made during the four decades since 
Herschel's discovery in 1781 could not be made to fit the old data that 
had been found in star catalogs by Bode and others. Bouvard assumed 
that the old observations had been less precise than had generally 
been believed. As time went on, however, it became clear that Bou- 
vard's orbit (1820) and his explanation of the discrepancies were 
inadequate. As new observations of the positions of Uranus were 
made they disagreed more and more with the positions predicted by 
Bouvard's elements — the elements that had been based on the 
1781-1820 observations. In other words, unhke aU other planets, 
Uranus was not moving "properly" along a reasonable orbit on a 
predicted timetable, even if the old, pre- 1 78 1 observations were dis- 
counted. The differences between observed and predicted positions 
increased to more than one minute of arc — considered a scandalous 
amount! 

Several hypotheses were put forward to explain the strange 
behavior of Uranus. One suggestion was that space might be filled 
with a very subtle fluid which could interact with planets. However, 
no known frictional or other force between such a fluid and Uranus 
could account for the observed oddities in the motion of Uranus. 
Besides, one would have to ask why the effects of such a fluid had not 
been noticed with other planets. 

Another suggestion was that Uranus might have a massive but 
undiscovered satellite. If so, the motion of Uranus and its satellite 
around each other would account for the irregular speeding up and 
slowing down of the visible planet which differed from its predicted 
orbital motion. However, it was difficult to imagine that such a mas- 
sive satellite would be invisible; in any event, its period would be too 
short to account for the observed slow variation in the motion of 
Uranus. 

Yet another suggestion was that shortly before Herschel's discov- 



Section 1.3 



-100 



-50 



+ 50 



100 



+ 150" 



1690 

~y 


171! 

■(719 


' ^ 

^ 




















Conjunction 

1 1 1 








- 


- 






V 


"^v Ahead 

\ 
\ 






178- 




..*-.• 


^••^^.-.... 


• 
• 


Leverrier's ' 


'Best Orbit" 


- 








B« 


lind ^ 


X '54 
1750"* 


55 


^''^ 














\ 
\ 

• 


from A. Bouvard (1846) 


- 






























• 
• 
• 

• 






- 


- 
































•1846 




- 



-100 



-50 



+ 50 



+100 



60 100 140 180 220 260 300 340 20 60 100 140 180 220 260 300 340 20 60 100 140 

X Heliocentric longitude 

Fig. 1-5 Differences between observed positions of Uranus (heliocentric 
longitudes) and those predicted by Leverrier from the "best orbit." 



+ 150 



ery in 1781 Uranus might have changed its orbit by a collision with a 
comet. Such a change of path would give one set of elements for the 
pre-1781 orbit and another set for the later orbit. Such a collision, 
although possible, would have been a remarkable coincidence. It 
seemed less and less plausible because even the revised observations 
began to disagree more and more with the calculations based on 
recent observation. 

A fourth proposal was that perhaps Newton's law of gravitation 
was not quite correct at that distance from the sun. Maybe in the 



equation Fgrav = G 



R' 



the exponent of the distance in the denomi- 



nator was sHghtly different from 2, or maybe there were some addi- 
tional terms which were functions of the distance and which were 
negligible except for very large distances. However, because of the 
success of the simple inverse-square law for gravitation in dealing 
with a large number of phenomena, most astronomers and physicists 
did not take very seriously this idea that the force might not vary ex- 
actly with the inverse square of the distance (F ~ 1/i?-). 

From about 1835 onward, a growing number of scientists won- 
dered whether the pecuhar motion of Uranus might possibly be due to 
attraction by some undiscovered planet in an orbit beyond that of 
Uranus. Such a planet would be faint and visible only through a tele- 
scope because of its great distance. Finding it among the myriad of 
stars along the ecliptic would be a virtually hopeless task. Some at- 
tempts were made to search for it, but without success. What was 
needed was a prediction of the planet's position, so that astronomers 
would know where to look for it. 



10 



New Findings in the Heavens — Uranus, Neptune, and Pluto 



1.4 Perturbations 

Newton deduced that a planet acted on by an inverse- square gravita- 
tional force directed toward the sun will move in an elliptical orbit 
with the sun at one focus. Furthermore, the speed of the planet will 
vary in the way described by Kepler's Law of Areas. If we observe the 
motion of any planet in precise detail, we will find, however, that it 
does not follow exactly an elliptical orbit; or a time-table based on the 
law of areas. 

Is there something wrong with the Law of Gravitation? Not at all; 
there is something wrong with the way we used it. We forgot that 
gravitation is a universal phenomenon. A planet is pulled not only by 
the sun as we assumed for the sake of simpUcity ; it is pulled also by all 
the other planets — and by their moons and by comets and by stars. 

Because it has such a tremendous mass and is relatively close, the 
sun exerts the most significant force on any planet. Sister planets and 
moons may be closer, but their masses are small; stars may be very 
massive, but they are very far away. For this reason a planet moves 
very nearly in the way we predict when we assumed that only the sun 
pulls on it. Gravitational pulls by other planets result only in small 
deviations from the expected motion. The small deviations are called 
perturbations of the motion. Since all the planets are moving, the per- 
turbing forces on any one planet are constantly changing in magni- 
tude and direction. 

Uranus, then, is perturbed by its sister planets, particularly by the 
neighboring (and especially massive) Saturn and Jupiter. Consider 
Uranus, Saturn, and Jupiter when they happen to be arranged in their 
orbits with respect to the sun as shown in Fig. 1.8(a). Knowing the 



Jupiter 



Saturn 



Uranus 



(a) 



Saturn 



Jupiter 







Uranus 



Fig. 1-6 Positions of Sun, Jupiter, 
and Saturn creating maximum (top) 
and minimum (bottom) 
gravitational attractions on Uranus. 



masses and the positions of the four objects, we can calculate the total 
attraction of the three bodies on Uranus. If the gravitational attrac- 
tion of the sun on Uranus is taken as 1000 units, then that of Jupiter 
on Uranus will be 1.5 units and that of Saturn about 1.1 units. The 
total force on Uranus toward the sun wUl be about 1002.6 units. 



Section 1.5 11 

However, when Jupiter and Saturn are on the far side of the sun 
from Uranus, as in Fig. 1.8(b), the forces they exert on Uranus will 
have magnitudes of about 0.6 units and 0.13 units, respectively. 
Under these circumstances the total force on Uranus wiU be about 
1000.6 units. Uranus, Saturn, and Jupiter are, of course, seldom ar- 
ranged as in the diagrams. Ordinarily the planetary perturbing forces 
have components perpendicular to the line of the sun's force on 
Uranus, as weU as along that Une. AU of these perturbing forces are 
very small; their sum is never more than 0.26% of the sun's force, but 
their cumulative effects distort the motion of Uranus from the perfect 
eUipse and time-table it would foUow if the sun and Uranus were 
alone in the universe. 

It is an interesting coincidence that Bouvard computed his ele- 
ments for the orbit of Uranus in 1820, only about two years before the 
conjunction in 1822 of Uranus and the still-to-be-discovered Neptune. 
For many years before 1822, Uranus was "behind" Neptune, so the 
gravitational force exerted by Neptune was increasing the speed of 
Uranus in its orbit. Observations of Uranus from 1781 to 1820 there- 
fore could be reasonably weU fitted by an orbit (Bouvard's) which took 

noaccountof unknown perturbations due to Neptune. After the con- ^ . . ..... 

^ Two planets are in conjunction when 

junction of 1822, Uranus was "ahead" of Neptune and hence was ^^^^y ^^^ ^y^^ ^^^ ^^^ 5^ 3 straight 

slowed down shghtly so the differences between its actual motion and \\ne. 

those predicted by Bouvard's 1820 calculations became increasingly 

noticeable. 



1.5 The discovery of Neptune 

Attraction by Jupiter and Saturn could account for part of the ob- 
served variations in the motion of Uranus. But there were some resid- 
ual differences between observations and computations still to be 
explained. Could these residual variations be due to the presence of an 
undiscovered planet? 

A planet that is perturbed by its sister planets perturbs them in 
turn, and they, from their perturbed positions, again perturb their per- 
turbed perturber. It is not hard to see that the theory of perturbations 
is comphcated. In fact, it is impossible to find an exact solution to the 
general problem of the motion of a given planet, except for the case 
where there are only two bodies involved: the sun and one planet. For 
the many-body problem there is in general only an approximate solu- 
tion. Fortunately, because the planets perturb one another only 
shghtly, approximate methods can yield sufficiently accurate predic- 
tions. 

To use the small residual variations in the motion of Uranus to 
deduce the position of an undiscovered planet is a difficult task. While 
we might assume that the unknown planet is following a nearly 
circular orbit, we do not know anything else about the distance, posi- 




Fig. 1-7 Urbain Jean Joseph 
Leverrier (1811-1877) who, like 
John Couch Adams, predicted the 
position of Neptune. 



12 New Findings in the Heavens- Uranus, Neptune, and Pluto 

tion, or mass of the undiscovered planet. It is one thing to use the 
theory of perturbations to calculate the motion of a planet perturbed 
by other planets whose positions and masses are known. It is quite 
another thing to turn the process around and, from the small residual 
perturbations in the motion of Uranus, calculate where the unknown 
planet must be. Hence, in 1842, the Royal Academy of Sciences of Got- 
tingen offered a prize for an adequate discussion of the motion of 
Uranus. 

Within a few years the solution was obtained and, amazingly 
enough, not just once, but simultaneously by two young scientists who 
did not know of each other's work. One was John Couch Adams of 
Cambridge University in England. The other was Urbain Jean Joseph 
Leverrier of the Ecole Polytechnique in Paris. Adams was in his late 
twenties and Leverrier in his early thirties. Both had had splendid 
training in mathematics and physics, and Leverrier was already well 
known for his brilliant work in applying the Law of Gravitation to the 
complex interactions between planets and to the motion of comets. 
Adams had begun to think about Uranus while still an undergraduate 
in 1831, but he did not begin his calculations in earnest until 1842. 

By the middle of 1845, both Adams and Leverrier separately 
solved the inverse perturbation problem; that is by the use of 
Newton's Law of Gravitation, they computed the probable mass, loca- 
tion, and motion of the hypothetical planet. Both men made essen- 
tially the same predictions about this new planet. Both men also ran 
into difficulties in persuading astronomers to search the sky in the 
region where their calculations indicated that a new planet should be 
visible with a large telescope. 



Fig. 1 -8 Trail of an asteroid which 
moved during the time-exposure 
while the telescope followed the 
motion of the stars. 




Section 1.5 



13 



Adams tried for months to get British astronomers to look for his 
planet. He finally succeeded, for the Cambridge observatory began a 
long and tedious program of mapping faint stars in the predicted 
region of the sky. The chief observer ignored Adams' suggestion that 
he simply look for a faint object that had an observable (although very 
small) disc-shaped image rather than the point-image typical of stars. 
The observatory authorities planned instead to make successive ob- 
servations of the positions of all the stars in the region. Then, if any 
one of them moved along the ecliptic between observations, it would 
probably be the new planet. Such a program would require several 
years to carry out. 

Leverrier too had trouble generating enthusiasm for observations. 
Although he was highly honored for his brilliant mathematical inge- 
nuity in showing how the residual perturbations of Uranus could be 
accounted for by the hypothetical planet, no one wanted to spend the 
time and effort needed to look for it. Finally he wrote to a young as- 
tronomer in Berlin, Johann Galle, describing his calculations and 
asked Galle to look for the planet in a specified small region of the sky. 
Galle received the letter on September 23, 1846, and obtained permis- 
sion to use the nine-inch-diameter telescope of the Berlin observatory 
that very night. A preliminary search showed no disc-shaped image, 
but, after consulting a star map of the region recently completed at 
Berlin but not yet pubhshed, Galle noted that one "star" he could see 
was not shown on the map. Later observations made it clear that this 
body was moving as predicted by Leverrier, and under higher magni- 
fying power it displayed a disc-shaped image very close to the pre- 
dicted size. The "star" was indeed the missing planet. 



Photography was then in its very 
early infancy. Modern astronomers, 
thanks to photographic plates, have 
two methods for detecting objects 
which are not fixed stars. If a plate is 
exposed for a period of time in a tele- 
scope which is moved by a clockwork 
or motor to compensate very preci- 
sely for the rotation of the earth, then 
the stars in the area of view will ap- 
pear as sharp dots on the plate. If 
there is some object such as a comet, 
asteroid, or planet in the area, its 
image will be a line or a trail, rather 
than a sharp dot. This assumes, of 
course, that the object moves a no- 
ticeable distance across the field of 
fixed stars during the exposure time. 
Another method is useful for more 
distant and slow-moving objects. 
Two photographs are made of the 
area of interest in the sky several 
days, weeks, or months apart. They 
are mounted in a special viewer, 
called a blink comparator, so that the 
two photographs are viewed, ap- 
parently in the same position, in rapid 
alternation. If an object is visible in 
one photograph but not the other, it 
will then "blink" on and off, and it can 
be quickly noticed in the midst of 
hundreds of thousands of fixed 
stars. 




Fig. 1-9 Neptune (greatly 
overexposed) and its two satellites. 
Triton, discovered by Lexell in 1846, is 
below and to the left in the glare from 
Neptune. Nereid, discovered in 1949, 
is marked with an arrow. 



OfWL 



14 New Findings in the Heavens- Uranus. Neptune, and Pluto 

The news spread quickly, and Leverrier was justly honored for his 
impressive accomplishment. There was great chagrin in England, 
particularly on the part of the Astronomer Royal. George .■Vin.-. who 
had delayed the search for months in spite of the urging of Adams and 
others. Actually the Cambridge obsen atorys tedious sur\ey had in 
fact included observations of the planet before September 23. but it 
had not been recognized for what it was. 

In due course both Leverrier and Adams were equally honored for 
their achievement in predicting the location of the planet, which was 
named Neptune. 

1.6 The orbit of Neptune 

In order to do their calculations at all, both Adams and Leverrier had 
An Astronomical unn is tne lengtn ot ^q make some assumptions about the size of the orbit of the unknown 
tttc seroi-maior axis of the earth's planet. To predict the radius of the orbit, they used what was known as 

Bode's Law. Johann Bode, whom we have mentioned earlier, had dis- 
covered an empirical formula for the average radius of a planetary 
orbit, -\lthough no physical basis of this formula is known, it repre- 
sents fairly accurately the relative radii of the orbits of the six planets 
known in Bode's time. The formula, called Bodes Law. states that the 
average radius. R, in astronomical units, of the orbit of the nth 
planet from the sun is given by R = 0.4 -^ (0.3 x 2""^. 

The orbit of Mercury, for which n^l. is an exception: for it the 
quantity in parentheses must be set equal to zero for a correct predic- 
tion of its orbital radius. At the time Bode announced his formula, 
there seemed to be another defect: the radii of the orbits of Jupiter and 
Saturn, the fifth and sixth planets from the sun. were given correctly 
only if values for n of 6 and 7. instead of 5 and 6. were inserted into the 
formula. Bode beheved that this indicated the existence of an undis- 
covered fifth planet in the space between Mars and Jupiter. VMien. 
beginning in 1801. a number of small asteroids were discovered at 
the predicted distance. Bode's Law received important support 

Table 1 . 1 compares the observed radii of the planets' orbits with 
those predicted by Bodes Law. 

TABLE 1.1 



Ptanetary OrtMts: Observed and Predicted from Bode's law. 
Planet n Observed R Predicted R 



Mercury 


1 


a39 


0.4 


Venus 


2 


a72 


0.7 


Earth 


3 


1.0 


1.0 


Mars 


4 


1.5 


1.6 


Asteroids 


5 


2.8 


28 


Jupiter 


6 


5.2 


5.2 


Satuin 


7 


9.5 


10.0 


Uranus 


8 


192 


196 



Section 1.6 15 

When Uranus was discovered it was found that the radius of its 
ortut agreed within 2% with that predicted by Bode's Law with n = 8. It 
aqppeais that Bode's Law fairly well describes the spacing of the 
planets— at least as far out as Uranus; we will see that it is less accu- 
rate for more distant planets. 

According to Bode's Law, the orbit of the next planet after 
Uranus, with n = 9, would have an average radius of 38.8 astronomi- 
cal units and a period of 242 years. Both Adams and Leverrier as- 
sumed this figiire for the orbit of Neptune. 

With a period of revolution around the stm of nearly two and a 
half centuries, it would obviously be many years before Neptune would 
move over a large enough arc of its orbit for the elements of the orbit 
to be calculated accurately from observations, rather than inferred 
from the residual perturbations of Uranus. However, in 1847, an 
American astronomer. Sears Walker, found in a star catalog of 1 795 
the recorded position for a telescopicaUy observed "star" which was 
no longer visible in that position. The "star" was shown to have been 
Neptune. As had happened with pre-discovery records of Uranus, the 
catalogued position of Neptune nearly fifty years earher, together 
with the small amount of data obtained since its discovery, enabled 
Walker to calculate a reasonably reliable orbit for Neptune. Everyone 
was surprised to find that the elements of the orbit calculated by 
Walker differed considerably from those predicted by Adams and 
Leverrier. In particular, the orbit radius was only about 30 astronomi- 
cal units instead of nearly 40, and the corresponding period was only 
about 160 years instead of 242. With Neptune closer to Uranus than 
had been predicted by Adams and Leverrier. its mass must be less 
than predicted in order to produce no more than the observed residual 
perturbations. The mass of Neptune turned out to be about half that 
predicted by Adiuns and Leverrier. 

So we must ask: was Galle's discovery of Neptune — a discovery 
guided by Leverrier's predictions — nothing more than a gigantic piece 
of good luck? The question does not have a simple answer. 

Scientists are often confronted with problems involving many 
variables for some of which they may not have accurate values. 
They may be forced to make intelligent guesses about the probable 
size of those they do not know. If they are wise — or lucky, those 
vaiiables will be ones for which a moderate error in the guess will 
not greatly affect the final result. 

This is what happened in the case of the calculations of Adams 
and Leverrier. It turns out that their results are not very sensitive to 
the value they assumed for the radius of the orbit of Neptune. In a 
smse, they were wise to use Bode's Law ; in fact, there was no other 
way that they could have obtained a value for the radius so that they 
could start the calculations. Furthermore, they had no reason to 
beheve that Bode's Law would not give the correct value. In another 
sense they were lucky, for even though Bode's Law failed for the orbit 
of Neptune, it did not fail badly enough to invalidate their final predic- 
tions. 



Why Adams and Leverrier were successful 



Why the distance of the hypothetical planet 
from the sun makes little difference in the solution 
of the problem can be seen from Fig. 1 .13. Let us 
assume that all the planets are moving around the 
sun in circular orbits. Uranus is known to be 19 
AU from the sun and to have a period of 84 years. 
The real Neptune is 30 AU from the sun and has a 
period of 1 60 years. The hypothetical planet was 
assumed to be 39 AU from the sun and therefore 
to have a period of 242 years. We also know, now, 



1832 



1812 




1781 



Fig. 1-10 Relative positions of Uranus, Neptune and the 
assumed planet from 1781 to 1846. 



that Uranus, Neptune, and the sun were in line in 
1822. The rapid build-up of discrepancy in the 
position of Uranus as shown in Fig. 1 .5 makes 
clear that about 1 820 the attractions on Uranus 
changed significantly. As Table 1 .2 shows, we can 
work backward or forward to find approximate 
positions for all three planets at any date. 

As you can see from the diagram, in 1 781 
Uranus would be pulled forward in almost the 
same direction by either the real Neptune or the 
assumed planet. The amount of the acceleration 
would depend upon the mass and distance of the 
perturbing planet. A smaller planet nearer could 
have the same effect as a large distant planet. By 
1812 the force would be larger with components 
moving Uranus ahead in its motion and also out- 
ward from the sun. After conjunction in 1822 the 
force on Uranus would slow its orbital motion and 
even as late as 1846 the retardation would be con- 
siderable. It is remarkable that Bouvard computed 
his orbit in 1820 just before the direction of the 
perturbations changed from acceleration to de- 
celeration along the orbit. No wonder his orbit 
showed large errors after 1822. See Table 1.2 
below. 

All planets and the sun were in line in 1822. 
Uranus with a period of 84 yrs. moves around sun 
about 4°/yr. Neptune, period 160 years, moves 
around sun about 27yr. Planet, period 242 years, 
moves around sun about 1.57yr. 



TABLE 1.2 



Approximate positions of Uranus, Neptune and the 
assumed planet before and after 1822 





Interval 
to 1822 


Angular motion 


around sun during i 


nterval 




Uranus (47yr) 


Neptune (27yr) 


Planet (1.5°/yr.) 


1781 


41 yrs. 


164° 


82° 


63° 


1812 


10 


40 


20 


15 


1822 





all planets and sun in line 




1832 


10 


40 


20 


15 


1846 


24 


96 


48 


36 



Section 1.7 



17 



As years went by, and Neptune's mass was determined from the mo- 
tion of its large satellite, and the elements of its orbit were more 
precisely calculated from the accumulating observations, the suspi- 
cion grew that the gravitational forces exerted by Neptune on Uranus 
could not quite account for all the residual perturbations of the motion 
of Uranus. Could there be still another planet beyond Neptune? Sev- 
eral persons tried to repeat the achievement of Adams and Lever- 
rier, but they met with httle success because the remaining residual 
variations in Neptune's motion were so small that accurate predic- 
tions of the location of the hypothetical planet were all but im- 
possible. 

In 1919, W. H. Pickering, at the Harvard College Observatory, 
specified an area of the sky in which he predicted that the new planet 
might be observed. He based his prediction on the residual perturba- 
tions of both Uranus and Neptune. A search of photographs which 
had been made at Mt. Wilson Observatory of that region of the sky did 
not show any indication of the planet. 

The most persistent seeker of the new planet was the amateur 
astronomer Percival Lowell. In 1915 Lowell had completed calcula- 
tions, based on the small residual perturbations of Uranus, which 
suggested that the new planet would be found in one of two places in 
the sky, one of which agreed with the position predicted by Pickering. 
Lowell, who was independently wealthy, had founded an observatory 
at Flagstaff, Arizona, designed primarily for solar system research. He 
died in 1916, keenly disappointed that "his" planet had not been 
found. The search went on, however, especially as more suitable pho- 
tographic telescopes became available in the 1920's. 

In 1930, a planet was finally discovered by Clyde Tombaugh, of 
the Lowell Observatory, near the position which Lowell and Pickering 
had predicted. Tombaugh used a blink comparator to compare a vast 
numberof plates. He later wrote, " . . . on the afternoon of February 
18, 1930, I suddenly came upon the images of Pluto! The experi- 
ence was an intense thrill, because the nature of the object was appar- 
ent at first sight. . . . In all of the two million stars examined thus far, 

nothing had been found that was as promising as this object " 

No pubhc announcement was made until the planet's existence was 
confirmed by further observations. The announcement was made, 
appropriately enough, on Lowell's birthday, March 13, a little over 
three weeks after Tombaugh's first observation. The planet was given 
the name Pluto, after the god of the underworld, as befits a distant 
planet moving endlessly in stygian darkness and cold. Percival Lowell 
is commemorated in the astronomers' symbol for Pluto, E, a com- 
bination of the initials P and L. 

Pluto turned out to be much closer to the sun than was expected, 
and to have a mass and size smaller than those of the earth. If the 




Fig. 1-11 Percival Lowell 
(1855-1916), amateur astronomer 
who created the Lowell Observatory, 
and predicted the position for Pluto. 




Fig. 1-12 Clyde Tombaugh in 1930 
when he discovered Pluto. 



18 



New Findings in the Heavens — Uranus, Neptune, and Pluto 



residual perturbations of the motions of Uranus and Neptune are real 
(and not, as many astronomers now believe, simply very small obser- 
vational inaccuracies), it is doubtful that Pluto is massive enough to 
account for them. Was there, then, an element of good luck in the dis- 
covery of Pluto? If there was, there was also an element of bad luck: 
Pluto had been recorded on the 1919 Mt. Wilson photographs, but it 
had been overlooked because it was so much fainter than had been 
expected. 

One would be tempted to say that the actual finding of Pluto near 
the predicted position was simply a matter of luck, since Pluto turned 
out to be too small to have caused significant perturbations. Yet 
Lowell's and Pickering's predictions did agree, and they were based on 
independent calculations. There is some evidence that a passage of 
Uranus between the sun and Pluto in the year 1710 might have 
provided just enough of a perturbation of Uranus' orbit to give the 
results that Lowell and Pickering achieved. If so, then the luck 
resulted from that unknown passage, and not the sort of luck that is 
implied in the suggestion that Tombaugh's plates only accidentally 
caught an image of Pluto. 




Fig. 1-13 Discovery photographs of Pluto showing displacement during six-day interval in 1930. 



1.1 In what sense was the discovery of Uranus an 
accident? Discuss also the accidental aspects of the 
discoveries of Neptune and Pluto. 

1-2 There have been many instances in science of 
two or more men making the same discovery, in- 
dependently of each other, at about the same time. 
The work of Adams and of Leverrier is one such in- 
stance. In what way or ways was the time ripe for 
their work? 

1 .3 The sun's mass is 329,300 times that of the 
earth. Jupiter's mass is 318 times that of the earth, 
Saturn's 95.2 times, Uranus' 14.6 times, and Nep- 
tune's 17.6 times. The average distance from the sun 
to Jupiter is 5.2 astronomical units; to Saturn, 9.6 
AU, to Uranus, 19.1 AU, and to Neptune, 30.1 AU. 



What is the ratio of the maximum force Neptune can 
exert on Uranus to the maximum force exerted on 
Uranus by Jupiter and by Saturn? These ratios wUl 
give you a rough way to compare the perturbations of 
Uranus' orbit produced by Neptune with those pro- 
duced by Jupiter and by Saturn. 



1 .4 The Figure below shows the distribution of the 
periods of the asteroids, which move inside the orbit 
of Jupiter like the small planet in the laboratory 
activity. Note the absence of certain orbital periods 
among the asteroids, known as "Kirkwood's gaps," 
at periods exactly 1/2, 1/3, 2/5, 1/4, 1/5, 3/5, and 3/7 
the period of Jupiter. What explanation do you 
propose for the existence of these "gaps" in the 
distribution of asteroid periods? 



80 



70 



60 



50 



40 



30 



20 



10 



I III ■ 



2 3 
5 7 



3 2 3 

5 3 * Jupiter 



Asteroid periods compared to Jupiter's period 

Fig. 1-14 This chart gives information which may be used to answer question 1.4 of the Study Guide above. 



19 



STUDY GUIDE 



1 . 5 Given the relative sizes and distances of the 
planets, it is possible to make a rough estimate of 
their relative brightnesses. In the following table six 
planets are listed, together with their diameters 
(compared with the Earth's diameter) and their dis- 
tances from the sun, in AU. Each planet will receive 
an amount of light from the sun proportional to the 
planet's area and inversely proportional to the square 



1.6 Neptune has a diameter of about 28,000 miles. 
It is 30.1 astronomical units from the Sun. One astro- 
nomical unit is 93,000,000 miles. From these data 
compute the apparent angular diameter of Neptune 
as viewed from the most advantageous position 
along the earth's orbit. You may give your result in 
radians and/or degrees or minutes or seconds of arc. 



(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7) 




Relative 


Dist. from 


(Diam)'^ = 




(Area) 


Relative 


Planet 


diameter 


sun, AU 


rel. area 


(Dist)2 


(Dist)2 


brightness 


Mars 


0.52 


1.52 










Jupiter 


10.97 


5.2 










Saturn 


9.03 


9.6 










Uranus 


3.72 


19.6 










Neptune 


3.38 


30.1 










Pluto 


0.45 ? 


39.5 











of its distance from the sun. Why? The planet's area 
is proportional to the square of its diameter. Fill in 
the values for the columns (4) and (5), headed "Area" 
and (Dist)-. (Use no more than three significant fig- 
ures). Then compute for each planet (Area)/(Dist)-, 
(col. 6), which will be proportional to the light it 
receives from the sun. Of that light, a certain frac- 
tion will be reflected outward. An observer on the 
earth will perceive a brightness which will be propor- 
tional to the numbers in column 6, divided by the 
square of the distance from the earth to the planet? 
(Why?). Each planet will appear brightest when its 
distance from the earth is smallest — that is, when it 
is at a distance equal to its distance from the sun (in 
AU) minus one, when (in other words) the planet and 
earth are in conjunction. FUl in column 7. 

The numbers in column 7 provide a rough esti- 
mate of the relative brightnesses of the six planets to 
an observer on earth. A rough estimate, because the 
actual fraction of light reflected by each planet is 
not the same. It ranges from about 15% for Mars 
to about 60% for Jupiter, Saturn, Uranus, and 
Neptune. 

Uranus is just barely visible to the naked eye. 
The numbers in Column 7 should suggest why Nep- 
tune was not known to the ancients, and why Pluto 
was hard to find even with large telescopes. 



1 • 7 There have been several examples in science 
of brilliant ideas or discoveries which have not been 
taken seriously for some time after they were origi- 
nally produced or observed. Both Adams and Lever- 
rier had difiiculties in getting anyone to search for 
the theoretically "discovered" planet. How can one 
decide whether or not to take such "discoveries" 
seriously, particularly when taking them seriously 
requires considerable work and time to be taken 
away from other important work? For example, any 
college or university physics department gets mail 
every week or so from persons who claim to have in- 
vented a new theory of atomic structure, or a new 
theory of gravitation, or a disproof of Einstein's 
theory of relativity. One has little, if any, time to 
give to the writers' requests that one "check my 
calculations" or "teach my theory to your students,' 
or "help me get this published." On the other hand, 
one does not want to be laughed at for several dec- 
ades as was the stuff'y Astronomer Royal who re- 
fused to pay attention to the relatively unknown 
John Couch Adams. What criteria can one use, 
if any, to "filter out" from the deluge of so called 
"crank letters" the potentially important one 
or two? 



20 



STUDY GUIDE 



Suggestions for Further Reading 

Armitage, Angus, A Century of Astronomy. London: 
Low, Marston and Co., Ltd., 1950. An introduction to 
the developments in astronomy from 1850 to 1950, 
including the discoveries of Uranus, Neptune and 
Pluto. 

Gingerich, Ov(^en, "The Solar System Beyond Nep- 
tune," Scientific American, Vol. 200, No. 4 (April 
1959). Recounts the discovery of Pluto. 

Grosser, Morton, The Discovery of Neptune. 
Cambridge: Harvard University Press, 1962. A de- 
tailed account of the discovery of Neptune. 

Rawlins, Dennis, "The Mysterious Case of the Planet 
Pluto," Sky and Telescope (March 1968). Reviews 
the coincidences in Tombaugh's discovery and dis- 
cusses current evidence for the mass of Pluto and 
the possibilities for finding an improved value for its 



Tombaugh, Clyde W., "The Discovery of Pluto," 
Source Book in Astronomy, 1900-1950. Harlow 
Shapley, editor. Cambridge: Harvard University 
Press, 1960. The author's account of his work. 

Tombaugh, "The Trans-Neptunian Planet Search," 
The Solar System, Gerard P. Kuiper and Barbara M. 
Middlehurst, editors. Vol. 3, University of Chicago 
Press, 1961. Details of the photograph search that 
led to the discovery of Pluto. The author also de- 
scribes subsequent work and discusses the dif- 
ficulties of extending the search to fainter objects. 

Watson, Fletcher, Between the Planets, Garden City: 
Doubleday, 1962. Treats the origins, orbits, and com- 
position of comets, asteroids, meteors, and meteor- 
ites. 



180 




I 



270° 



Fig. 1-15 Final orbits for trans-Neptunian planet predicted by Lowell in 1914, and Pickering in 1928. compared to orbit of 
Pluto. 



21 



22 



EXPERIMENT 

In this chapter you have read about the way in which deviations from 
the expected motion of Uranus were interpreted as resulting from the 
gravitational attraction of an outer and undiscovered planet. This lab- 
oratory experience will allow you to get a feel for the perturbations of 
a small planet by a large planet. To get first hand experience with 
such perturbations, we can use the method of graphical iteration. 
Imagine a body under uniform motion. A dry ice disc moving 
on a horizontal surface could be one example. In Fig. 1-16, let xy 
represent in magnitude and direction the velocity of the body for a 
short interval of time. 



Fig. 1-16 




Fig. 1-17 




Fig. 1-18 



Q 1. Where would you locate the position of the body at the end of the 
second interval of time? Now assume that at y the body is sub- 
jected to two forces acting simultaneously for a short and equal 
interval of time pulling the body in the directions represented in 
Figure 1-17 by the arrows a and b. The length of the arrows are 
proportional to the changes in velocities produced by the respec- 
tive forces during the very short interval of time. 

Q 2. In what direction will the body move from the point y? 

Q 3. Would the speed of the body change? If it does, would it increase 
or decrease? 

Construction of a vector diagram, showing the direction and mag- 
nitude of the motion of the body during the second interval of time, 
may help you to answer the two previous questions more accurately. 
(This is the same analysis used by Newton.) You need to add two sepa- 
rate vectors. First find the resultant of the vectors a and b (Figure 1-18 
left) and call this resultant r. Then extend xy an equal length to 
point y'. Had there been no forces acting on the body at y, it would 
have reached y' at the end of the second interval. (Remember the 
body was moving uniformly. (To find the new position we must 
add the resultant r and xy' (Figure 1-18 right) which gives the 
magnitude and direction of the velocity of the body. 

If you can perform these vector additions without any difficulty, 
you are ready to plot the perturbed orbit of the small planet. 

Initial Conditions 

First we must decide what starting conditions to choose and the 
magnitude of the gravitational forces acting. Let us take a small 
planet of negligible mass, Hke an asteroid, initially moving in a 
circular orbit 3. 1 AU from the sun. For the large planet let us take a 
body with 1/100 the mass of the sun moving in a circular orbit at 4 AU. 
Since the mass of the large planet is far more than that of the small 
one, we assume that the gravitational attraction of the small planet 



Experiment 23 

will not modify the motion of the large planet; but the gravitational at- 
traction of the large planet will modify the orbit of the small planet 
when they are near. 

Thus the small planet in orbit has two continuous forces acting on 
it when it is near conjunction with the large planet; the gravitational 
attractions of the sun and of the large planet. As the small planet 
moves, the magnitude and direction of these two forces change. 
Determination of the exact orbit of the small planet under the influ- 
ence of these continually changing forces is exceedingly complicated. 
However, you can get a reasonable approximation to the orbit by 
breaking the continuous attractions into many small steps, in which 
the two forces act as two sharp 'pulls', one toward the sun and the 
other toward the large planet, once every sixty days. The magnitude of 
each brief pull is assumed to equal the total effect of the continuous 
attraction of the large planet or the sun throughout a 60-day interval. 
Thus the continually changing complex motion of the planet has been 
made to look as simple as the motion of the uniformly moving body we 
saw in our thought experiment at the beginning. All that we need to 
know to plot the orbit are the initial velocity of the planet and the 
magnitude and direction of the puUs (vectors a and b). 

Scale 

We can adopt the same scale for plotting as we did in Experiment 
21 of Unit 2 in which 2.5 inches or 6.35 cms represent 1 AU. 

Because the small planet does not perturb the large planet, you 
can step off its positions in its circular orbit at 60-day intervals. If the 
mean distance of the large planet from the sun is 4 AU, what is its 
period in days? What fraction of the period is 60 days? How many 
degrees around the sun will the large planet move in each 60-day in- 
terval? What is the speed of the large planet in AU/60 days? Expressed 
in the scale of your plot (inches or cms), what is this speed? 

If there were no large planet, what would be the period of the 
small planet moving in circular orbit about the sun at 3.1 AU? What 
fraction of its period is 60 days? How many degrees around the sun 
will it move in each 60-day interval? What is the speed of the small 
planet in AU/60-days? What is this speed expressed in the scale of 
your plot (inches or cms)? 

Effect of the force of attraction 

From Newton's second law you know that the gravitational force 
will cause the small planet to accelerate toward the center of the 
source of attraction. If a force F acts for a time interval At on a body of 
mass m, you know that 

^ -^ At?" 
F = ma = m— 

and therefore 

-. r 

^v = — At 

m 



24 



Experiment 



In the last equation the mass m and the change in time At are 
constant. Therefore the change in velocity is proportional to the gravi- 
tiational attraction. 

Computing Av 

On the scale and with the 60 day iteration interval chosen, the 
force field of the sun is such that the Ai^ given by the pull when the 
small planet is 1 AU from the sun is 1 AU/60 days. 

To avoid computing At; for each position of the small planet we 
can plot Av against the distance R on a graph. Then for any value of R 
you can find the value of At^. 

Table 1 gives the values of R in AU and in inches and cms to fit the 
scale of your orbit plot. The table also gives for each value of R the cor- 
responding value of At; in AU/60-days, and in inches and cms to fit the 
scale of your orbit plot. 



TABLE 1 



Effects of the Sun's Attraction 



Distance from Sun, R 



Change in speed, Iv 



AU 



inches 



cm 



AU/60days 


inches 


cm 


1.76 


4.40 


11.3 


1.57 


3.92 


9.97 


1.23 


3.07 


7.80 


1.00 


2.50 


6.35 


0.69 


1.72 


4.37 


0.44 


1.10 


2.80 


0.25 


0.62 


1.57 


0.16 


0.40 


1.02 


0.11 


0.28 


0.71 


0.08 


0.20 


0.51 


0.06 


0.15 


0.38 



0.75 


1.87 


4.75 


0.8 


2.00 


5.08 


0.9 


2.25 


5.72 


1.0 


2.50 


6.35 


1.2 


3.0 


7.62 


1.5 


3.75 


9.52 


2.0 


5.0 


12.7 


2.5 


6.25 


15.9 


3.0 


7.50 


19.1 


3.5 


8.75 


22.2 


4.0 


10.00 


25.4 



Since we have taken the mass of the large planet to be 1/100 that 
of the sun, at 1/10 the distance it will exert on the small planet the 
same force as the sun does. Thus replotting of the sun's efifect at 
1/10 the distance can be used for establishing the perturbing 
effects of the large planet. Table 2 gives the distance of the small 
planet from the large planet and the corresponding values of Af. It 
is convenient to plot both the graphs on the same graph paper. 



Experiment 



25 



TABLE 2 
Effects of the Large Planet's Attraction 

Distance from large planet Change in speed, Av 

AU inches cm AU/60days inches 



cm 



0.075 


0.187 


0.475 


1.76 


4.40 


11.3 


0.08 


0.200 


0.508 


1.57 


3.92 


9.97 


0.09 


0.225 


0.572 


1.23 


3.07 


7.80 


0.10 


0.250 


0.635 


1.00 


2.50 


6.35 


0.12 


0.30 


0.762 


0.69 


1.72 


4.37 


0.15 


0.375 


0.952 


0.44 


1.10 


2.80 


0.20 


0.50 


1.27 


0.25 


0.62 


1.57 


0.25 


0.625 


1.59 


0.16 


0.40 


1.02 


0.30 


0.750 


1.91 


0.11 


0.28 


0.71 


0.35 


0.875 


2.22 


0.08 


0.20 


0.51 


0.40 


1.00 


2.54 


0.06 


0.15 


0.38 


0.45 


1.125 


2.86 


0.049 


0.123 


0.31 


0.50 


1.25 


3.18 


0.04 


0.10 


0.254 


0.60 


1.5 


3.81 


0.028 


0.07 


0.18 


0.70 


1.75 


4.45 


0.020 


0.05 


0.13 


0.80 


2.00 


5.08 


0.016 


0.04 


0.10 


1.00 


2.50 


6.35 


0.010 


0.025 


0.064 



Z) 










c< 


\ 










\ 

Large planet's \ 
^^ effect on the \>^ 
small planet \ 


^ Sun's effect on 
the small planet 






1 \ 


y 








\^ 






V 




^-^ 











Fiq. 1-19 



1 AU 2 AU 

Distance of the small planet from the source of attraction 



3AU 



4AU 



26 



Experiment 



Starting the plot 

To start the plot we need to locate the two planets and the sun. 
Also we shall need the expected unperturbed positions of the planets 
at 60-day intervals. 

On a large sheet of graph paper ( 16" by 21") make a dot, to repre- 
sent the sun, in approximately the center as shown in Fig. 1-20. 
With this 'sun' as the center draw two concentric circles of radius 
10" (25.4 cms) for the large planet L, and 7.75" (19.7 cms) for the 
small planet S. The two circles represent the initial orbits of the 
two planets. From the 'sun' draw a straight line to intersect the 
orbits of the two planets as shown in Fig. 1-20. 




Sun 



Fig. 1-20 



Along the orbit of the large planet, from the point of intersection 
step off the positions of the large planet at 60-day intervals. Similarly 
locate unperturbed positions at 60-day intervals along the orbit of the 
small planet. These are the positions at which it would have been if 
there had been no perturbation by the large planet. See Fig. 1-20. 

Let us assume that at the beginning of our observation the large 
planet is in one position or 60 days ahead of the small planet, which 
therefore is being pulled forward. Mark the starting positions of the 
small and the large planets S, and L, respectively. See Fig. 1-21. 

It is important for us to start the small planet moving properly in 
its circular ortbit. To do this, draw a Une from the point S, to the sec- 
ond point (call it Sa), which it would reach after 60 days. This line S1S2 
is the initial velocity vector. Extend SiSj an equal length to a point 
marked C to which the small planet would move if it were not at- 
tracted toward the sun or the large planet. 




Fig. 1-21 




Fig. 1-22 



28 



Experiment 



The small planet moves from S, to S2 with its initial velocity. At 
point S2 we apply vectorially the total effects of the continuous attrac- 
tions of the sun and the large planet throughout the 60 day interval as 
two puUs, one toward the sun and the other toward the large planet at 
its second position L2. The vector addition of these two pulls will deter- 
mine how the velocity of the small planet is changed. Use the graphi- 
cal plotter to derive the effective pull toward the sun. (If you have 
forgotten, see Figures 1-1 7a and b). Then use the plotter to determine 
the effective pull toward the large planet at its second orbital position 
L2. Plot the change in velocity vector toward the sun and then 
graphically add the velocity vector toward the large planet to obtain 
the resultant effect. 

Apply the resultant (R) of these two attractions to the small 
planet's vector at point C and locate the new position S3 on its orbit. 

Extend the line S2S3 for an equal length to point D. Find for 
point S3 the effective puUs towards the sun and toward the large 
planet, at its third position L3. Add the vectors and apply the 
resultant to D to establish S4. 




Fig. 1-23 
Continue the above process for at least twenty steps. 



How to use the Graphic Computer 

Cut off the bottom margin of the graph paper, or fold it under 
along the R axis. Lay this edge on the orbit plot with zero at the sun, 
then move along R to distance from the sun to the small planet. With a 



Experiment 



29 



pair of dividers pick off the value of At* corresponding to this R from 
the curve showing the sun's effect on the small planet. Lay off this dis- 
tance along the radial line toward the sun. 




Similarly place the zero point at the small planet and, for the dis- 
tance to the large planet, find the Ax* corresponding to this distance 
from the large planet curve. Lay off this distance along the line 
joining the corresponding positions of the two planets. (Why doesn't it 
matter whether you put the zero point at the large planet or the small 
planet?) 



Fig. 1-24 Useof graphical plot to 
give gravitational effect of sun on 
small planet. 




Fig. 1-25 Useof graphical plot to 
give gravitational effect of large 
planet on small planet. 



30 



Experiment 



As you can see from the graphical computer, the perturbmg effect 
of the large planet becomes Insigificant when the distance between 
the two planets becomes greater than 1 AU. Thus if you want to carry 
the orbit of the small planet beyond its 21st position and make one 
complete trip around the sun, you will only have to take into consider- 
ation the gravitational attraction of the sun. 

If you do not develop the orbit past point 21, you can get some idea 
of the total orbit by plotting the following approximate points: All 
angles are measured in a clockwise direction from the line passing 
through the sun and point Sj. 




Position 


Dist. from Sun 


Angle from S, 


S21 


3.25 AU 


215° 


S.5 


2.30 


174 


S28 


1.36 


98 


S29 


1.27 


48 


Perihelion 


1.25 


63 


Aphelion 


3.25 


241 



Fig. 1-26 



Q 1. What is the average distance of the small planet from the sun in 

the new orbit? 
Q 2. What is the new period in years? 
Q 3. What is the eccentricity of the new orbit? 
Q 4. Would you expect the small planet to follow this new orbit for as 

long as 100 years? Why? 
Q 5. Within how many years will the small planet and the large 

planet again come fairly near together? 

Q 6. Suppose that you were at the sun and could not for some 

reason, see the large planet. You knew of the small planet and 
expected it to move uniformly in the circular orbit. What unex- 
pected results would you observe in its motion across the sky 
after it passed through the point S3? 

Q 7. Consider the orbit you constructed in three sections: From S, to 
S4, from S4 to Si5, and beyond S,5. In a few words describe the 
differences you observe in the motion of the small planet in 
each of these three sections. 




Fig. 1-27 The English astronomer, William Herschel, the discoverer of the planet Uranus, built this giant but unwieldy 
40-foot reflecting telescope which had a 4-foot mirror. 



2.1 The discovery of cathode rays 33 

2.2 The wave theory of cathode rays 34 

2.3 A particle theory is proposed 35 

2.4 Properties of the particles: Schuster's calculations 36 

2.5 Hertz's experiments in support of the wave theory 38 

2.6 The wave theory collapses: the experiments of Thomson 39 

2.7 Enter the electron 41 




J.C.McClellon^ CChilcL. KLongcvitu. Prof.J.J.t\u>msot\.. J.Z^l^nu. K^Villotus. H-A-U'tl^on.. J.touynsenA^ 

Professor J. J. Thomson in 1898 with research students who contributed to many discoveries, including the electron. 



CHAPTER TWO 



Cathode Rays and the Discovery 
of the Electron 



2.1 The discovery of cathode rays 

The discovery- that cathode rays could be produced under certain cir- For a quick review, see Unit 5, Sec- 

cumstances occurred in 1858. ver>- soon after the technolo^- of vac- ^'O" ^^-^ °^ ^^^ Project Physics Text 

uum pumps had been greatly improved. The controversy that soon 

arose as to the nature of cathode rays, in contrast, took many 

years to settle. This chapter \%'ill be concerned primarily \\*ith that 

controversy. 

First, however, we must consider the initial discover\- of the rays 
themselves. As far back as 1 748. scientists had carried out experi- 
ments to find out what happens to an electric spark when the pressure 
of the surrounding air is reduced. Air pumps were rather primitive, 
but by 1800 the pressure in a glass tube could be reduced sufficiently 
for a current to pass between electrodes at the two ends of the tube, as 
a glow that filled the tube rather than as a thin streak, or spark. (Such 
tubes were the predecessors of the modem neon sign tubes.) Then in 
1855 a new kind of vacuum pump was invented which used a column 
of mercury as a piston to avoid the use of leaky pistons. With these 
new pumps the pressure could be decreased to one-thousandth of the 
normal atmospheric pressure, or even less. 



fo 


(Bj 




— + 


fii=. 


r~^^r^ 


,a 


/ ^^ 



Fig. 2-2 A schematic diagram of a Plijcker tube used to study electric currents 
conducted through gases at low pressures. 

A German physicist. Julius Pliicker. and his student Hittorf used 
such a pump to evacuate a glass tube fitted with sealed electrodes at 
each end, as shown in Fig. 2-2. When the electrodes were connected to 

33 



34 Cathode Rays and the Discovery of the Electron 

a source of high electrical potential, such as an induction coil, Plucker 
and Hittorf found that the usual reddish glow of the gas, visible when 
the air pressure in the tube was moderately low, all but disappeared 
when the pressure was made as low as possible by the new pumps. 
However, the glass at the end of the tube opposite the negative elec- 
trode glowed with a strange greenish fluorescence. By further experi- 
menting they found that this fluorescence was caused by rays of some 
sort coming from the negative electrode, or cathode - hence the name 
cathode ray. They also found that the rays traveled in straight lines, 
and were deflected by magnetic fields. This was a new type of phe- 
nomenon that caused considerable excitement. 

Other physicists began studying the rays. Goldstein, another 
German physicist, pubhshed in 1871 reports of a series of experiments 
that showed that the rays are emitted perpendicularly from the sur- 
face of the cathode. This meant that the rays could be concentrated or 
focused by use of cathodes with a concave shape. Goldstein also found 
that the properties of the rays did not seem to depend on the chemical 
nature of the cathode material; the rays behaved the same way for all 
sorts of cathodes. He also found that the rays could produce chemical 
reactions similar to the photochemical reactions produced by ultravio- 
let light. 



2.2 The wave theory of cathode rays 

What was the nature of these rays? As often happens, two types of 
explanations were proposed. One group thought that the rays were 
beams of electromagnetic radiation. James C. Maxwell, a British 
physicist, had just been brilhantly successful in showing that all the 
known properties of hght waves could be described in terms of elec- 
tromagnetic waves. Maxwell's equations were based on the assump- 
tion that electric currents were continuous — that is, smoothly vari- 
able, without granularity. 

This assumption did not automatically rule out the possibihty that 
there might be some exceedingly fine granularity to electricity, any 
more than the equations of hydrodynamics (which describe, for ex- 
ample, the flow of water in a pipe) rule out the possibility that water is 
composed of molecules. But since there was then no experimental evi- 
dence for any granular structure of electrical charge, and since Max- 
well's equations were so successful in describing a vast array of elec- 
trical, magnetic, and optical phenomena, an explanation in terms of 
electromagnetic waves was appealing. Furthermore, most of the ob- 
servable properties of cathode rays were certainly also the observable 
properties of beams of light. Although beams of light were not bent 
by magnetic fields as cathode ray beams were, this bending was the 
only property in which light rays and cathode rays seemed to diff"er 
significandy. 



I 



Section 2.3 



35 



But even then, it was known that magnetic fields do have some ef- 
fect on the transmission of light beams. If you send a beam of 
polarized light through certain materials within a magnetic field, the 
plane of polarization will be shifted when the field is changed. Thus 
the proponents of the wave theory thought that perhaps cathode 
rays could be some new and pecuUar form of electromagnetic waves 
that could be deflected by magnetic fields. 



2.3 A particle theory is proposed 

In 1879, Sir William Crookes, one of the leaders of a group of Enghsh 
physicists, showed that cathode rays could heat up thin foils and could 
exert enough force to move thin vanes. (Light can do the same things.) 
Crookes, unlike many of his colleagues, beheved that these cathode 
rays were streams of negatively charged particles -negatively 
charged because of the way the rays were deflected in a magnetic 
field. He went on to suggest a possible mechanism by which the rays 
might be formed. He suggested that molecules of the residual gas in 
the tube, upon hitting the cathode, might pick up a negative charge. 
They would then be strongly repelled by the cathode. These molecules 
might behave in the same way as small bits of paper, originally elec- 
trically neutral, are sometimes attracted to a negatively charged 
plastic rod (or pocket comb) and then suddenly repelled vigorously 
when they have acquired some of the negative charge. The cathode 
ray beam, Crookes thought, might well be composed, as he put it, of a 
"torrent" of negatively charged molecules. Such an hypothesis could 
account for many of the known properties of the rays. Thus the two al- 
ternate explanations: electromagnetic waves or particles, developed. 

But opponents of the particle theory quickly thought of an objec- 
tion to Crookes' idea. Goldstein pointed out that the mean free path of 
a molecule, charged or uncharged, in Crookes' cathode ray tubes 
would be about 0.6 cm - about 1 /4 inch, far less than the length of the 
tubes. If we know the pressure and density of a gas and the diameter 
of the gas molecules, we can calculate the mean free path of the mol- 
ecules. Even with the good vacuums Crookes was able to achieve, 
enough residual gas molecules remained for their mean free path to 
be only slightly more than half a centimeter. Thus Crookes' hypotheti- 
cal negatively charged molecules would have approximately 150 
collisions before hitting the glass at the far end of the tube from the 
cathode. The observed straight-line travel of the beam, under such 
circumstances, was clearly impossible. Crookes replied that perhaps 
the torrent of molecules simply pushed the other, randomly moving 
molecules out of the way. One might think, for example, of a squad of 
rapidly moving soldiers pushing a milling mob of onlookers off to the 
side. 

But another argument against Crookes' hypothesis was provided 
by the faint glow emitted from the beam itself. If the glow came from 




Fig. 2-3 William Crookes (1832- 
1919) the English radiologist. This 
photograph was taken around 1910. 



The mean free path of a particle in a 
gas is the average distance a particle 
travels between collisions with other 
particles. The mean free path running 
the 100-yard dash is usually more 
than 100 yards. The mean free path of 
a blindfolded person trying to run 
across New York's Times Square at 
midnight on New Year's Eve would be 
perhaps two feet. 

At ordinary temperatures and pres- 
sures, the mean free path of a mole- 
cule in air is about 1/100,000 of a cen- 
timeter. 

Notice the argument by analogy. 

In modern tubes one sees little, if 
any, such glow. But in the 1870's vac- 
uum pumps were less effective, and 
a glow due to the residual gas was 
quite common. 



36 Cathode Rays and the Discovery of the Electron 

For a review of the Doppler shift, see Crookes' "torrent of molecules," the wavelength of spectral lines, ob- 
Section 12.11 in Unit 3 of the Project served when light from that glow was sent through a spectroscope, 

p K u c j ^ o T^ y t 

' ' should be shifted by the Doppler effect as shown in Fig. 2-4. How- 

ever, no such shifts were observed in the spectral lines of the light 
from the cathode ray glow. Actually this argument against the "tor- 
rent" model is relevant only if the glow is assumed to be produced 
by the particles moving in the torrent. We now know that the 
glow is produced by ordinary gas molecules, which just happened to 
be standing around, as it were, in the path of the beam. 





Fig. 2-4 (1) When a source of waves is stationary, the waves emitted in all 
directions have the same wavelength. (2) However, when the source of waves is 
moving, the wavelengths ahead of the source become shorter and those behind 
become longer. Such a Doppler shift for a moving source occurs for electro- 
magnetic waves as well as for sound waves. 



2.4 Properties of the particles: Schuster's calculations 

By 1884, another EngUshman, Arthur Schuster, had carried out some 
experiments which supported the particle model. Schuster suggested 
that the cathode ray beams might not be composed of whole mole- 
cules that had acquired a negative charge at the cathode, but rather of 
negatively charged fragments of molecules that had broken up on hit- 
ting the cathode. Schuster further pointed out that the observable 
bending of the beam in a magnetic field could be turned into a quanti- 
tative experiment which would give information about the particles. 
In a magnetic field, B, perpendicular to their line of motion, charged 
particles of a given speed will move in a path which is part of a circle 
of radius R. (R can be determined by observation of a faint glow along 
the beam, if some gas is present, or by observing the endpoint of the 
beam as it hits a fluorescent screen.) If we assume that gravita- 
tion and other forces may be neglected, the centripetal force which 
bends each particle into a circular path must be provided by the 
magnetic force of the field on the moving particle. By equating the 
centripetal force to the magnetic force, we may write 



= Feen. (2.1) 



Bqv - —5- (2.2) 



Section 2.4 37 

in which m is the mass of the particle, q its charge, and v its speed. 
Equation (2.2) can be rearranged to give 

X = JL (2.3) 

m BR 

This equation says, then, that the ratio qlm of the charge to the 
mass of the beam particles (presumably an intrinsic characteristic 
of the particles) can be expressed in terms of B and R and of v, the 
speed of the particles. Both R and B could be measured; the difficulty 
was in determining or estimating the value of v. 

By 1890 Schuster had established upper and lower limits for the 
magnitude of qlm. By assuming that all the energy, V„ acquired by 
the charged particles from the electric field between the cathode 
and the anode (of potential difference V) is turned into kinetic energy 
of the particles, \l2mv\ he could write another relationship: 

Vq = imv'- (2.4) 

Since some of the energy provided by the electric field might be lost in 
coUisions or other processes, Schuster could be sure that the original 
energy of the charged particles equalled or exceeded their final 
kinetic energy, or 

Vq^hmv^ (2.5) 

This second relationship between qlm and v could be used si- 
multaneously with Eq. (2.3) to find numerical values of qlm. and v, 
in terms of measurable quantities. In this way, Schuster was able 
to conclude that qlm. was not greater than about 10'" 
coulombs/kilogram (coul/kg). 

To determine a lower limit for qlm., Schuster assumed that the 
speed of the beam particles would surely be greater than that of the 
residual gas molecules. The average speed of such molecules could be 
computed by use of the kinetic theory of gases and is about 1000 m/sec 
for hydrogen molecules at room temperature. This value for v, in- 
serted in Eq. (2.3), gives 5 x IC* coul/kg as a lower limit for 
q/m. Admittedly, it is not completely satisfying merely to know that an 
important physical characteristic of the particles — their ratio of 
charge to mass — is between two values so far apart as 5 x 10® and 
10'" coul/kg. However, even such limited knowledge is better than 
no knowledge at all. Schuster pointed out that by electrolysis the 
ratio of charge to mass for hydrogen atoms had been found to be 
about 10** coul/kg, which is in the middle of his range of possible 
values for the qlm. ratio for cathode ray particles. Hence the idea 
that cathode ray particles were charged molecules, or fragments 
of molecules, is to some extent supported by his results. 



38 



Cathode Rays and the Discovery of the Electron 



2.5 Hertz' experiments in support of the wave theory 




Fig. 2-5 A sketch showing an 
arrangement of the cathode-anode 
terminals for an experiment of the 
type conducted by Hertz to 
demonstrate the electromagnetic 
characteristics of cathode rays. 



The German physicists, being firm behevers in the wave theory of 
cathode rays, began a brilliant series of experiments designed to con- 
tradict the particle theory and to support the idea that the rays carried 
no charge and were in fact some form of electromagnetic ray. 

In 1877 Heinrich Hertz had succeeded in demonstrating the exis- 
tence of the electromagnetic waves that Maxwell had predicted would 
be emitted by oscillating electric charges, and in showing that these 
waves had the properties predicted by Maxwell. Beginning in 1883, he 
and his colleagues carried out several experiments with cathode rays. 
In one experiment, Hertz used a cathode ray "tube" consisting of two 
flat glass plates about 1 cm apart and 12 cm square. In one arrange- 
ment of such a tube, the cathode and anode were situated as shown in 
Fig. 2-6. By measuring the magnetic field (presumably due to the 
flow of electrical charge from C to A) outside the tube. Hertz found 
that the current followed the curved paths between cathode and 
anode indicated by sohd lines in the diagram. From the location of 
the fluorescence on the glass he concluded that the cathode rays 
moved along the straight lines indicated by the dotted path. This 
experiment seemed to show quite conclusively that the flow of 
electricity was unrelated to the direction of the cathode ray beam. 

Hertz did another expermiment, this one designed to detect the 
charge, if any, carried by the cathode ray beam. He designed a tube 
with the cathode and anode at the same end (what we would now call 
a cathode ray gun), arranged, as in Fig. 2-7, to project a beam of 
cathode rays down toward the other end of the tube. The end of the 
tube could be inserted into a shielded metal container inside which 
was an insulated metal can or collector electrode connected to a sensi- 




SOURCE. 

Fig. 2-6 A sketch of another arrangement of anode-cathode placement used by 
Hertz to show that a cathode ray beam carried no electric charge. 



tive electrometer. (An electrometer is a charge-detecting and mea- 
suring device.) 

Hertz reasoned along these lines: if the cathode rays convey neg- 
ative charge, then the inside of the glass cathode ray tube should 



I 



Section 2.6 



39 



become coated with negative charge. These charges will attract posi- 
tive charges from the electrometer to the insulated can and cause the 
electrometer to deflect. To test the equipment he removed the cath- 
ode ray tube and inserted a very, very small amount of negative 
charge into the collector can; the electrometer responded strongly. 
Then when he inserted the cathode ray tube and sent cathode ray 
beams down the tube, the electrometer responded only feebly, except 
for a transient response when the cathode ray was first turned on. 
These results, Uke his earlier results with the bent discharge, certainly 
seemed to suggest that the cathode ray beam carried no electrical 
charge. 

Hertz did still other experiments. In one of them he tried to 
detect bending of a cathode ray beam in a transverse electric field. 
If the beam consisted of charged particles, surely it would be 
deflected by an electric field as well as by a magnetic field. He found 
no deflection. 

By 1891, Hertz and his pupil Lenard had shown that cathode ray 
beams could penetrate very thin metaUic films. Such films were 
moderately transparent to visible Ught — to electromagnetic waves, 
in other words — but were too thick to let atoms through. The conclu- 
sion seemed inescapable that the cathode rays could not be 
particles, because the rays could go through thin foils which stopped 
even the smallest known particles. 



2.6 The wave theory collapses: the experiments of Thomson 

Yet by 1896 virtually the whole scientific world agreed that Hertz, 
Lenard, and the other proponents of the electromagnetic wave theory 
of cathode rays had been wrong, and that the rays were, indeed, 
negatively charged particles. 

First, Jean Perrin in France and then J. J. Thomson in England 
repeated Hertz's experiment to detect the charge carried by the 
beams. But instead of putting the collector electrode outside the 
cathode ray tubes, they put it inside. Any charge carried by the beam 
could be conveyed by a wire connection through the glass tube to the 
electrometer. Perrin found that when the beam was on, the elec- 
trometer did register a negative charge. Thomson's version of the 
same experiment used a collector electrode displaced from the 
straight-line path of the cathode ray beam. By bending the beam 
with a magnetic field the beam could be directed onto the collecting 
electrode. The results revealed that the negative charge carried by 
the beam was in fact also responsible for the bending of the beam 
in a magnetic field. 

Why had Hertz's experimental results been so misleading? The 
explanation is easy to see now, but it was by no means obvious at the 
time the experiments were being done. At the time the results fitted in 




Fig. 2-7 Sir Joseph John Thomson 
(1856-1940), one of the greatest 
British physicists, attended Owens 
College in Manchester, England, and 
then Cambridge University. He 
worked on the conduction of 
electricity through gases, on the 
relation between electricity and 
matter, and on atomic models. His 
greatest single contribution was the 
discovery of the electron. He was the 
head of the famous Cavendish 
Laboratory at Cambridge University, 
where one of his students was Ernest 
Rutherford. 



40 Cathode Rays and the Discovery of the Electron 

so nicely with what Hertz and his colleagues thought ought to 
happen. In the tube shown in Fig. 2.3 the cathode rays probably 
represented a very small fraction of the total current in the tube. In 
comparison with the magnetic field produced by the current con- 
ducted along the curved path, the magnetic field due to the cathode 
rays was too small to be detected by Hertz. 

Similarly, the electrometer experiment (Fig. 2.4) failed to detect 
any charge deposited on the wall of the tube because most of the 
charges carried by the beam moved along the inner glass walls of the 
tube so that very few charges accumulated on the outside walls 
within the electrometer can. When the electrometer was connected to 
a collecting electrode inside the cathode ray tube, as Perrin and 
Thomson did, quite different results and conclusions were reached. 

Hertz's inability to detect any deflection of a cathode ray beam by 
means of an electric field occurred because his fields were not strong 
enough. (In Hertz's defense it should be said that he was sabotaged, as 
it were, by the unsuspected conductivity of the residual gas, which 
kept the potential diff'erences across his electric-field-producing plates 
from being as high as he believed they were.) 

Thomson succeeded in producing a deflection of the beam by 
means of electric fields. In an apparatus somewhat like that shown in 
Fig. 2-5 the beam traversed a region, between the two flat plates, in 
which a strong electric field, E, could be created by a potential dif- 
ference, V, across the plates. If the plate separation, d, is small com- 
pared to the length and width of the plates, then E = VId. 
By providing a magnetic field, B, in the same region in which there 
was an electric field, Thomson could carry out the following sequence 
of operations: 

(a) After arranging the directions of E and B appropriately, he could 
adjust their magnitudes until no net deflection of the beam 
occurred. Under those circumstances, for each particle, 

•T elec -r mag (2.6) 

or Eq = Bqv 



which may be rearranged to give 



E 



^ = J (2.7) 

Thus the velocity, v, of a given beam could be determined. 
(b) By changing either the electric field or the magnetic field alone, he 
could then find qlm. For example, when he used the magnetic field 
alone and observed the deflection which gave the radius of cur- 
vature of the path R of the beam, he could use Eq. (2.3) to find 
qlm, since 

a V 
m BR 



Section 2.7 41 

You will recall that Arthur Schuster had proposed that the value 
of qlm was expected to lie in the range between 5 x 10*^ and 10'" 
coulombs per kilogram. However, Thomson's first experiment gave 
the value of qlm as approximately 10" coul/kg, and later refine- 
ments in the apparatus gave results much closer to 1.76 x 10" coul/kg. 
It is difficult to tell from Schuster's papers why even his maximum 
value turned out to be only a tenth as much. 

The value that Thomson ultimately obtained for qlm is 1840 
times the value of the charge-to-mass ratio for hydrogen ions in elec- 
trolysis. There are three possible ways to account for the larger value 
of qlm. for electrons. Perhaps the charge on the cathode ray particle 
is 1840 times the charge on a hydrogen ion. Or perhaps the charges 
are the same, but the mass of the cathode ray particle is 1/1840 the 
mass of a hydrogen ion; or perhaps both the charge and the mass 
differ from those of the hydrogen ion. Thomson suggested that the 
mean free path argument, originally used against the Crookes hy- 
pothesis, and Lenard's experiments, in which cathode rays 
penetrated thin foils, were both evidence that the size (and pre- 
sumably the mass) of the cathode ray particle must be very small. 
He therefore favored the second of the above possibilities, and 
suggested that cathode ray particles, or electrons, as they came to be 
known, were in fact constituents of all atoms. 

2.7 Enter the electron 

In the two decades before Thomson's experiments of 1895 and 1896, 
other scientists had discovered that negative particles were emitted 
by metals in apparatus other than cathode ray tubes. Edison had 
found that white-hot metals, such as incandescent lamp filaments, 
gave off negatively charged particles. Hertz had discovered, while 
showing that Maxwell's electromagnetic waves were emitted by 
accelerating electric charges, that light could knock negatively 
charged particles out of certain metals. This was the photoelectric 
effect. Thomson was able to show that the negative particles from 
hot filaments and those produced in the photoelectric effect had 
the same ratio of charge to mass as did his cathode ray particles. 

In late 1895 and early 1896 Wilhelm Rontgen, in Wiirzburg, Ger- 
many, discovered x rays while performing experiments with a cathode 
ray tube. Later in 1896, Henri Becquerel, in Paris, while investigating 
X rays, accidentally discovered radioactivity. Soon thereafter, radio- 
active materials were found to emit one or more of three different 
sorts of rays. One of these, called the beta ray, was found to be com- 
posed of negatively charged particles. These, too, were found to have 
the same ratio of charge to mass as cathode ray electrons had. 

Another intriguing experiment involving charge-to-mass ratios of 
charged particles was also made in 1896, clearly a vintage year of im- 



Thomson's q/m Experiment 



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





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




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




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

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




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



Section 2.7 43 

portant discoveries. A Dutch physicist, Zeeman, asked whether the 
spectra emitted by atoms in gases were influenced by the presence of 
a magnetic field. Zeeman put gas discharge tubes (tubes containing 
gas, at low pressure, through which electricity was flowing) in a 
strong magnetic field. Light from the tubes was examined through a 
spectroscope. Zeeman found that the spectral lines were slightly 
broader when the magnetic field was turned on than when it was 
off. With better spectroscopes of higher resolving power, both 
Zeeman and Crookes found that the apparent broadening of the 
lines was really a spUtting of the lines into doublets (close pairs) or 
triplets and were polarized. Zeeman and another Dutch physicist, 
Lorentz, soon worked out a theory to explain this eff'ect. If one assumes 
that atoms emit hght by means of oscillations of charged particles 
having a certain ratio of charge to mass, then the theory predicts 
that in the presence of a strong magnetic field the wavelengths of 
the emitted polarized hght are shifted in such a way as to show the 
observed sphtting of the lines. The ratio of charge to mass neces- 
sary to fit the observed amount of splitting turned out to be the 
same as qlm already found for cathode ray electrons. 

All these experiments, then, supported Thomson's idea that elec- 
trons were parts of atoms and that all electrons have the same ratio of See Film Loop entitled "Thomson 
charge to mass, no matter from what sort of atoms they were emitted. Model of the Atom", 
and no matter what physical process was used to break them loose 
from the atoms. Zeeman's experiment was, in addition, convincing 
evidence that electrons existed within atoms and played a crucial role 
in the emission of light. The arguments were over; cathode ray beams 
were undoubtedly composed of a stream of very small, negatively 
charged particles, and these particles were constituents of atoms. 

It was some years before the actual role of electrons in atoms was 
satisfactorily understood. Thomson thought that perhaps they were 
distributed within some sort of positively charged cloud, as (to use his 
analogy) raisins are distributed in a raisin cake. Such a model was not 
very satisfactory; it was hard to understand how atoms with such a 
structure could be stable, or how they could emit line spectra. Experi- 
ments with alpha particles, conducted by Rutherford in 19 11, showed 
that atoms had very small positive nuclei. In 1913 the young Danish 
physicist Niels Bohr proposed a theory that showed how one might 
imagine hydrogen atoms to consist of a charged nucleus plus one or- 
biting electron. Bohr's atoms of hydrogen would emit and absorb light 
at the right wavelengths. More complicated but more general theories 
describing the behavior of electrons in atoms and their roles in the 
emission of hght and in chemical bonding began to be developed 
about 1926. 

With such theories came a better understanding — or at least a 
more detailed description — of electrons. Robert Millikan and others 
had developed a series of experiments by which one could show that 
electric charges were multiples of some basic and very small unit of 



44 Cathode Rays and the Discovery of the Electron 

charge, and by which one could determine that charge: 1.60 x 10~'^ 
coulomb. Bohr's theory, as well as the later more general theories, as- 
sumed electrons with that charge, and with q/m of 1.76 x 10'' 
coul/kg. These theories all contributed to the firm conviction that 
such electrons are among the basic building blocks of the universe. 

Certain experiments and theories suggested that the electron was 
not simply a tiny bit of charge and mass, but also had angular 
momentum and a magnetic moment. These properties would result if 
we thought of an electron as spinning, for a spinning charge — Uke a 
current-carrying coil — behaves hke a bar magnet. 

Two other developments should be mentioned briefly for the sake 
of completeness. One was the discovery of positively charged elec- 
trons found first as a consequence of the absorption of high-energy 
gamma rays occurring in cosmic rays and later as positive beta rays 
from certain artificially produced radioactive isotopes. The other was 
the discovery that cathode ray particles were not, after aU, simply par- 
ticles, but rather that in certain experiments a beam of cathode rays 
seemed to behave like a stream of waves! This does not mean that the 
old electromagnetic wave model for cathode rays was in any sense 
right, but simply that the particle theory was too simple. Modem phys- 
ical theory suggests that all "particles" (including locomotives and jet 
airliners) have associated with them a waveUke nature. In everyday 
experiences this wave nature is irrelevant; the wave lengths 
are much too small to have noticeable effects. But electrons 
accelerated through potential differences of a few hundred volts 
have associated wavelengths roughly comparable to the spacing 
between layers of atoms in a crystal, so beams of such electrons can 
be diffracted by such crystals. 

Cathode rays are now used in a host of devices: television cam- 
eras and picture tubes, electron microscopes, cathode ray oscillo- 
scopes, computer output displays, and many others. (In such devices 
the rays are formed by electrons emitted from hot filaments and accel- 
erated by potential differences of up to more than 30,000 volts.) Thus, 
while the development of a new technology in the 1850's (good vac- 
uum pumps) made the discovery of cathode rays possible, the discov- 
ery and understanding of cathode rays, in turn, provided the basis for 
many technical developments from 1920 onward — and not technical 
developments alone, but a new understanding of the nature of matter. 



Suggestions for Further Reading 

Anderson, David L., The Discovery of the Electron. Rays — A fourth State of Matter"; J. J. Thomson, "The 

Princeton: D. Van Nostrand Co., Ind., 1964. A full ac- Discovery of the Electron"; Robert A. MiUikan, 

count of the development of the atomic concept of "Atoms of Electricity", 
electricity. 

Boorse, Henry A., and Lloyd Motz, editors, The World Millikan, Robert A., The Electron, facsimile edition 

of the Atom. New York: Basic Books, Inc., 1966. edited by J. W. M. DuMond. University of Chicago 

These articles in Vol. 1 are concerned with the dis- Press, 1963. A detailed account of the author's own 

covery of the electron: William Crookes, "Cathode work. 



STUDY GUIDE 



2.1 Summarize the evidence that cathode rays are 
not electromagnetic waves. Indicate as clearly as 
you can how this evidence disproves the wave hy- 
pothesis. 

2.2 What experimental evidence was there, around 
1900, for saying that the electric charge of the 
cathode ray particle (the electron) was equal in size 
to the charge carried by a hydrogen ion? Did the 
experimental evidence give the size of the charge 
directly? 

2.3 In what ways was the time ripe for the discov- 
ery of the electron in the 1890's? What difficulties 
would a scientist have had testing the electron hy- 
pothesis a half century earlier? 

2.4 In Thomson's experiment on the ratio of charge 
to mass of cathode ray particles (p. 42), the following 
might have been typical values for B, V and d: with a 
magnetic field B alone, the deflection of the beam in- 
dicated a radius of curvature of the beam within the 
field of 0. 1 14 meters for B = 1 .0 x 10" ' tesla.* With the 
same magnetic field, the addition of an electric field 

in the same region (V = 200 volts, plate separation d = 
0.01 meter) made the beam go on straight through. 

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

(b) Find qlm for the cathode ray particles. 

2.5 (a) The difference in potential between the 
cathode and the anode in a certain cathode ray tube 
is 5000 volts. Given that the ratio of charge to mass 
for cathode ray particles is 1.76 x 10" coul/kg, show 
that the velocity of the particles as they emerge from 
the hole in the anode in the cathode-ray gun is 4.2 x 
10" m/sec. 

(b) The two deflecting plates in the tube are at a po- 
tential difference of 300 volts and are 1 cm apart. 
Show that the electric field strength, E between the 
plates is 3 X 10^ newtons/coulomb. 

(c) Given that the charge on an electron is 1.6 x 10"'^ 
coulomb, find the force on an electron in the cathode 
ray beam between the plates. 

(d) Given the mass of the electron (9.1 x 10"" kg), 
find the vertical acceleration of the electron while it 
is between the plates. 

(e) How long does it take the electron to travel hori- 
zontally through the region between the plates which 
are 5 cm long. 

(f ) What vertical component of velocity wiU the elec- 
tron acquire during that time? 

(g) Show that it will "drop" 0.375 cm while between 
the plates and therefore will not hit the plate toward 
which it is deflected. 

(h) After the electron emerges from the region 
between the plates, it will have both its original hori- 
zontal component of velocity (why?) and its newly 
acquired vertical component of velocity. The elec- 
tron will hit a fluorescent screen, located 30 cm from 
the point at which it emerges from the plates. What 
is the distance of that impact point from the point 
where the electron would have hit had there been no 
electric field between the plates? 
(i) Suppose one had wished to counteract the effect 
* The MKSA unit for B is N/amp ■ m and is now called 
the tesla, after the electrical engineer Nikola Tesla. 



of the electric field by superimposing, in the same 
region, a magnetic field of strength B. What direction 
and magnitude for B would one need? 

2.6 In one of Lenard's experiments in which he sent 
cathode rays through very thin metaUic foils, he used 
an aluminum foil 0.003 millimeter thick. 

(a) How does this thickness compare with that of a 
typical sheet of paper? (Hint: how thick is a ream of 
typing paper or a 100-page section of a book?) 

(b) One cubic centimeter of aluminum has a mass of 
about 2.7 grams. The atomic weight of aluminum is 
27. What is the volume of a gram-atom of aluminum 
(i.e. of 27 grams of aluminum)? How many atoms 
does that volume contain? How much volume is oc- 
cupied by an average aluminum atom? If this vol- 
ume is cubical, how long is one edge of such a 
cubical volume? 

(c) About how many layers of aluminum atoms did 
the cathode rays penetrate in Lenard's experiment? 

2.7 Consider a cathode ray tube 90 cm long, in 
which the air pressure is such that the mean free 
path for molecules is 0.60 cm; therefore the tube is 
150 mean free paths long. A large number of cathode 
ray particles start out from the cathode, //they are 
electrically charged molecules (as Crookes originally 
thought), then half of them will have suffered colli- 
sions and have been deflected in the first 0.60 cm. 
Half of the remaining ones would have been de- 
flected in the next 0.60 cm. About what fraction 
would survive for a total straight-line path of 90 cm? 
(Note: this is a rather crude argument which would 
need to be modified to take into account the motions 
of the other air molecules and other complicating 
factors. But the answer will be a rough estimate, 
good enough to show why many physicists did not 
beheve Crookes' idea.) 

2.8 A cathode ray tube is connected to an induction 
coil which provides 40 pulses per second. During 
each pulse the anode is at 20,000 volts positive with 
respect to the cathode. The average current to the 
cathode, as measured by a milliammeter, is 0.50 
miUiamps. Each pulse lasts approximately 0.001 sec. 
Calculate: 

(a) the actual charge conveyed by the beam during 
each pulse; 

(b) the number of electrons per pulse; 

(c) the energy that the beam of cathode rays could 
give, per second, to a thin foil. Assume that the 
cathode is cup-shaped, so that all the rays from the 
cathode hit the foil. Does your result indicate that the 
foil might be noticeably heated? (Hint: think about 
smaU light bulbs.) 

2.9 In what ways were the discovery of electrons 
dependent upon prior technical developments? 

2. 10 Sketch or diagram the arguments and evi- 
dence used to support the proposals that cathode rays 
were (a) waves, (b) particles. 

2. 1 1 Trace the history of the determination of the 
mass and charge of the electron from the work of 
Schuster through that of MiUikan. Separate the 
arguments and conclusions from the experimental 
results. 



45 



3.1 Introduction 47 

3.2 Bombarding nuclei with neutrons 48 

3.3 The special problem of uranium 48 

3.4 The search for transuranic elements 49 

3.5 A discovery missed 50 

3.6 Alpha particles and another near-discovery 51 

3.7 The discovery is made 53 

3.8 The study of nuclear fission begins 55 

3.9 The chain reaction 56 

3.10 The wrar intervenes 57 

3.11 Some thoughts for our models of discovery 58 




Enrico Fermi and an assistant testing the first atomic pile at the University of Chicago in 1942. 



CHAPTER THREE 



Nuclear Fission 



3.1 Introduction 



The discovery of nuclear fission was a fascinating drama with many 
participants and many misleading developments. Furthermore, the 
results have shaped human history with a suddenness and a profun- 
dity almost unique in the history of science and technology. This dis- 
covery could have happened at any time between 1934 and 1939, and 
one might even say that it was a discovery that went around rapping 
at many laboratory doors, only to be ignored again and again because 
no one was expecting it. Indeed, when one scientist did suggest, in 
1934, that certain unusual experimental results could be explained by 
assuming that uranium nuclei could spht apart, no one paid any atten- 
tion. The possibility that a nucleus could be spht into two nearly equal 
parts by the addition of a neutron went against all previous experience 
with nuclear disintegrations. The most massive particle known to be 
ejected from a nucleus was an alpha particle, with less than two per 
cent of the mass of the uranium nucleus. Because the alpha particle is 
a uniquely stable composite of two neutrons and two protons, it was 
understandable that this particular combination was emitted from 
nuclei. But all the existing theories of the nucleus indicated that no 
other combination of nuclear particles could hang together during the 
process of nuclear disintegration. 

It is only natural to try to explain or understand unusual experi- 
mental results or observations in terms of the best theories and ideas 
already available, rather than by changing theories. Science grows by 
building upon the current body of knowledge and existing accomphsh- 
ments. Its development is analogous to the slow evolution of an 
animal species, which continuously produces organisms that are the 
direct results of their antecedents. But biologic evolution also leaves 
behind a fossil trail of trials that failed, and science too must discard 
its unfit or outworn products in favor of new evolving, dominantly 
useful concepts and theories. 



For a brief review, see Project Phys- 
ics Text, Unit 6 Sections on Nuclear 
Fission and on Chain Reactions. 



47 



48 



Nuclear Fission 



3.2 Bombarding nuclei with neutrons 




Fig. 3-2 Enrico Fermi, 1901-1954. 



The discovery of the neutron had taken only about two years, from the 
first finding of a strange new kind of "ray" by Bothe and Becker in 
1930, to its identification by Chadwick in 1932 as an electrically neu- 
tral particle of mass very nearly equal to that of the proton. Neutrons 
are normal constituents of all nuclei (except that of ordinary hy- 
drogen, the nucleus of which is simply a proton). Since neutrons are 
uncharged, they are not repelled, as protons are, when they approach 
a nucleus. Soon after their discovery it therefore became clear that 
neutrons could be used to bombard stable nuclei, with very interesting 
results. Experiments showed that a neutron captured by a nucleus 
may cause the nucleus to react in various ways by emitting a proton, 
an alpha particle, one or two other neutrons, or a gamma ray. The 
actual outcome depends on the energy of the incoming neutron and on 
the nature of the bombarded nucleus. In any event, after emitting the 
particle or particles, the remaining nucleus is often left with an 
excess of energy in what is called an "excited state." Such a nucleus 
can settle down to a stable state by emitting a beta ray or a gamma ray 
or both. 

If the bombarding neutron has Uttle kinetic energy, its capture is 
very likely to result only in the emission of a gamma ray, leaving a 
nucleus with the same charge as before, but with one more mass unit. 
Such a nucleus is often unstable and decays, with a half-Ufe charac- 
teristic of the particular isotope, by emitting a negative beta ray. The 
nucleus (called the "daughter") which remains after the beta emis- 
sion has one additional positive charge and so is displaced in the peri- 
odic table by one atomic number — that is, it is chemically one position 
higher in the periodic table. The daughter products in such cases are 
almost invariably stable. 



3.3 The special problem of uranium 

Beginning in 1933 a young and vigorous group of Itahan physicists, 
among them Enrico Fermi, began using neutrons to bombard samples 
of all the known elements. In doing so, they produced many previously 
unknown radioactive elements, and measured for many elements the 
relative chance that a neutron would be captured by an atom. This 
chance of capture is described as a target area having a certain "cross 
section." When Fermi and his collaborators began bombarding ura- 
nium with neutrons, an interesting question arose. Would isotopes be 
produced (by the beta decay process described above) which would be 
a step higher than uranium in the periodic table? No such transuranic 
elements were known to exist in nature, presumably because their 
nuclear structure would make them unstable. If such isotopes existed, 
they would be exceptions to the generalization that the daughters 



Section 3.4 



49 



resulting from neutron bombardment products are usually stable. 
Sure enough, when Fermi and his collaborators bombarded uranium 
with neutrons, they found that they produced a radioactive material 
that was not just a single radioactive isotope with a single half -life. It 
behaved as a mixture of isotopes, with at least four (and probably 
more) half-lives. Since there were only three isotopes in the uranium 
that was bombarded, it seemed odd that at least four isotopes were 
produced. At least one of them might be a transuranic element: ele- 
ment number 93. Such an element would be chemically rather like 
manganese (element 25), technetium (element 43), and rhenium (ele- 
ment 75). When some manganese was added to the solution con- 
taining the bombarded uranium, and then precipitated out as MnOa, it 
carried with it some of the radioactivity. This and other chemical tests 
showed that one or more of the radioactive isotopes was chemically 
similar to manganese and could be presumed to be an isotope of ele- 
ment 93. 

Fermi's work aroused considerable interest, but not everyone was 
convinced that his group had really produced a transuranic element. 
A German chemist, Ida Noddack, suggested that Fermi had not actu- 
ally ruled out, by chemical tests, the possibihty that the radioactive 
isotopes that he had produced were elements in the middle of the peri- 
odic table. She suggested, in fact, that perhaps uranium nuclei were 
somehow broken into large fragments when bombarded with neu- 
trons, and that these fragments were radioactive. Literally no one took 
this suggestion seriously. There was no experimental evidence that 
such fragmentation could happen, and there were good theoretical 
reasons for believing that a bombarded nucleus could emit nothing 
larger than an alpha particle. But Miss Noddack insisted that for 
Fermi to be sure that the radioactivity was due to a transuranic ele- 
ment, he would have to perform chemical analyses that would rule 
out all other chemical elements, not just those in the immediate 
neighborhood of uranium. No one took her advice. 



'-^ 



®- 





u^^czt) 




Fig. 3-3 



3.4 The search for transuranic elements 



Several other physicists and chemists did, however, try experiments 
designed to find how the several radioactive products by neutron bom- 
bardment of uranium and thorium were related, if at all, to each other. 
Otto Hahn and Lise Meitner, in Berlin, found that certain "activities" 
produced by neutron bombardment of thorium were chemically hke 
radium. One of them, with a half-life of one minute, seemed to decay 
into an actinium-hke isotope with a half-Ufe of 3.5 hours. 

In 1936 and 1937 Hahn, Meitner, and Fritz Strassmann carried 
out in Germany an extended series of experiments which seemed to 
show quite conclusively that neutron bombardment of uranium (U-"*) 
produced a whole collection of transuranic elements — including 



Such an "activity" in some radioac- 
tive isotope is specified in terms of its 
half-life. 



Nuclear isomers have the same 
charge and mass, but differing half- 
lives. 



50 



Nuclear Fission 




Fig. 3-4 



three different isotopes of element 93, which then decayed by beta 
emission into three different isotopes of element 94, which in turn 
beta-decayed into isotopes of element 95, and so on. This was indeed 
puzzling, for ordinarily one would not expect a single material, pre- 
sumably element 93 with mass number 239, to have three isomers. 
In ordinary artificially-produced radioactive isotopes, isomers do occa- 
sionally occur. For example, indium' ^*^, made by bombarding the most 
abundant stable isotope of indium, In"\ with slow neutrons, exists 
in two isomeric states having different activities. Both decay by 
emitting beta particles, one with a half-life of 54 minutes, the other 
with a half life of 13 seconds. Both decay into Tin"**, which is stable. 

Some cases of triple isomerism are now known, but in 1937 triple 
isomers seemed strange. Even stranger was the apparent inheri- 
tability of this triple isomerism — that is, the apparent existence of 
chains of successive decays. Expressed in another way, it was sur- 
prising that a single neutron put into a relatively stable uranium 
nucleus could produce such a disturbance that as many as five suc- 
cessive emissions of beta rays were necessary before the nucleus be- 
came stable. 



3.5 A discovery missed 



A substance, like lanthanum in this 
experiment, used to provide an ade- 
quate quantity of material to permit 
the manipulation of radioactive iso- 
topes, is called a carrier. 



®— I 



Fig. 3-5 




C=^l 




/^' 



Half-life 
3.5 hours 



Chemically 
like La, 
perhaps a 
form of 
actinium, 
element 89. 



In 1937 and 1938 Irene Joliet-Curie and Paul Savitch, in Paris, carried 
out extensive investigations of the activities produced by neutron 
bombardment of uranium. When they added the nonradioactive ele- 
ment lanthanum to the bombarded uranium, dissolved the mixture, 
and chemically separated out the lanthanum by precipitating it, they 
found that a substance with a half-hfe of 3.5 hours was carried along 
with the lanthanum. Since actinium was the heaviest element with 
chemical properties like those of lanthanum, they assumed that this 
activity was a form of actinium, the 89th element in the periodic table. 
They did notice that this activity was chemically more hke lanthanum 
(the 57th element in the table) than hke actinium, but they thought 
that they had been able to separate it from lanthanum. 

As we shall see later, what they were dealing with was not ac- 
tinium (an element close to uranium in the periodic table), but actu- 
aUy an isotope of lanthanum 35 elements away from uranium. If they 
had correctly identified this activity, they would have established that 
uranium does break up into pieces with one of the fragments (lan- 
thanum) having about two-thirds the mass of uranium. They failed 
to make the correct identification because they believed that they 
had proved they had actinium by chemically separating the activity 
from lanthanum. In retrospect it seems likely that among the prod- 
ucts of the bombarded uranium was still another fission product in 
the same chemical family as lanthanum and actinium, an isotope of 
yttrium, element 39, with a half-hfe of about 3.6 hours, very close to 



Section 3.6 



51 



the half-life of the lanthanum isotope. If this surmise is correct, they 
were the victims of an unfortunate coincidence. Otherwise they 
surely would have been driven to accept their other chemical evi- 
dence that the 3.5-hour activity really was an isotope of lanthanum 
which must have resulted from a major fragmentation of the ura- 
nium nucleus, not the emission of a few particles. (The nuclear frag- 
ment picks up enough electrons to form a neutral atom.) The discov- 
ery of uranium fission was in their grasp, but it slipped away. 



3.6 Alpha particles and another near-discovery 

In 1938 Hahn and Strassmann repeated the work of Irene Joliot-Curie 
and Paul Savitch, this time without Lise Meitner, who had fled from 
the Nazis to Sweden. Hahn had been working with problems in the 
identification of radioactive substances since his early days as a 
student under Rutherford in England and in Montreal. He, Miss 
Meitner, and Strassmann were superbly equipped for this work by 
training and experience. From a solution of neutron-bombarded salts 
of uranium they were able to precipitate with barium carriers at least 
three activities with half-lives of 25 minutes, 110 minutes, and sev- 
eral days. From these activities they found daughter products, precipi- 
tated with lanthanum carriers, with half-Uves of 40 minutes, 4 hours, 
and 60 hours. They attributed the first set to isomers of radium-^* 
(because radium is chemically like barium) and the second set to ac- 
tinium^''' isomers, since actinium is chemically like lanthanum. They 
suggested that the Ra^^* was formed from U^^** by the emission of two 




Fig. 3-6 Professor Otto Hahn 
(center) is pictured in 1962 behind 
the laboratory equipment used for his 
experiments in 1938 on the irradiation 
of uranium with neutrons. The 
equipment is now in the German 
IVIuseum in Munich. To the left of 
Hahn is his former assistant, Fritz 
Strassmann. 



52 



Nuclear Fission 



Perhaps : 




Fig. 3-7 



alpha particles after the capture of a neutron. This would reduce the 
charge of the nucleus by four units, two for each alpha particle, and 
its mass by seven units, four for each alpha particle emitted less the 
added one for the incoming neutron, and would account for the charge 
and mass of the Ra-^'. 

These results, hke those of the group's 1936 and 1937 experi- 
ments, raised the questions of threefold isomerism and the inheri- 
tabihty of isomerism. In addition, they appeared to involve the rather 
unlikely emission of two alpha particles after bombardment by a 
single neutron. Because it is relatively hard for even a single alpha 
particle to escape from uranium-^**, its normal half-life is so long, 4.5 
billion years. But Hahn, Meitner, and Strassmann found somewhat 
similar results when thorium^^^ was bombarded by neutrons. (In the 
case of thorium, only a single alpha particle would need to be emitted 
in order to produce a radium isotope.) 

Attempts were made, beginning in 1937, to detect the alpha par- 
ticles presumably ejected when neutrons hit thorium and uranium. 
More than once, this search led scientists to the brink of discovering 
nuclear fission. 

The technique used in testing for alpha particles was to put a thin 
layer of thorium or uranium in an ionization chamber and bring a 
neutron source nearby. Any alpha particles emitted from the thorium 
or uranium into the gas in the chamber will ionize a great many mole- 
cules of the gas. The more energetic an alpha particle, the more 
ionization it produces. The ionized molecules can be collected by an 
electrically charged plate, and the pulses of current initiated by each 
alpha particle can be observed. In 1937 Braun, Preiswerk, and 



Fig. 3-8 Use Meitner and Otto Hahn, 
photographed in 1925. 




Section 3.7 



53 



Scherrer, in Germany, found in this way alpha particles with energies 
of about 9 miUion electron volts, about twice the energy commonly as- 
sociated with ordinary alpha rays from naturally radioactive materi- 
als. It is surprising, in fact, that they did not observe much larger 
pulses of current, corresponding to particle energies of the order of 
100 million electron volts, for there should have been some fission 
fragments present with energies of that order. Here again, a stu- 
pendous discovery was narrowly missed. But even if such pulses had 
been observed, they would have been extremely difficult to interpret. 
(It would be like noticing your speedometer jumping up to 100 miles 
per hour from time to time when you were inching your way along in a 
traffic jam. Since you would know that cars just do not behave that 
way, you probably would assume that something was wrong with the 
instrument.) 

Droste, in Germany in 1938, tried similar experiments, but he 
adopted a very sensible refinement. He covered his uranium and 
thorium with very thin foils, just thick enough to stop the Gow-energy) 
alpha particles due to the natural radioactivity of uranium and 
thorium. He found very few high-energy alpha particles. But neither 
did he find any high-energy pulses from fission fragments, since the 
thin foils could easily stop any heavy highly charged particles even if 
they did have a lot of kinetic energy. Once again the particular experi- 
mental design blocked a major discovery. 



One electron volt is the energy 
required to move one electronic 
charge through a potential difference 
of one volt. It is equal to 1.6x10'^ 
joule. 




To counter or 
cathode ray 
oscilloscope 



Fig. 3-9 



3.7 The discovery is made 

Since the reaction, proposed in explanation of the 1938 Hahn- 
Strassmann results. 



2U"« + on' 



.,He^ + ^He^ + ««Ra2 



with its assumption that two alpha particles are emitted, seemed 
unlikely to Hahn and Strassmann, they began a systematic chemical 
study of the "radium" products of the reaction, and of the daughter 
products. 

Hahn and Strassmann finally found themselves driven by their 
careful experiments to announce that the activities were due not to 
radium and actinium, but to barium and lanthanum. They had found 
that they could easily separate radium and actinium isotopes from 
barium and lanthanum carriers, but they simply could not separate 
the new activities from such carriers. Apparently the bombardment of 
uranium with neutrons must have produced the hghter elements 
barium and lanthanum. On January 9, 1939, they pubhshed their 
results, remarking that "On the basis of these. . . . 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 



54 



Nuclear Fission 




Fig. 3-10 Otto Frisch. 



to all existing experience of nuclear physics. After all, a series of 
strange coincidences may, perhaps, have led to these results." 

While preparing this paper for pubUcation just before Christmas 
in 1938, Hahn wrote to his former colleague, Lise Meitner. As an Aus- 
trian citizen Miss Meitner, although Jewish, had been able to work 
safely in Berlin. But in March of 1938 the Nazis had taken over Aus- 
tria, and all Austrians had been declared to be Germans. Miss Meitner 
escaped with the help of an international committee headed by Niels 
Bohr. She went first to Holland and then to Stockholm, where she took 
a research position at the Nobel Institute. Her nephew. Otto Frisch, a 
brilMant physicist, was then working in Copenhagen. They agreed to 
meet in southern Sweden during the Christmas hoUdays. Miss 
Meitner showed Frisch the letter she had received from Hahn. He 
thought there must have been some mistake in the experiments, but 
she knew that Hahn was too careful — that his results had to be taken 
seriously. They asked themselves how one could get barium out of 
uranium. It seemed ridiculous; too much energy would be needed. 

But then they began to think about some suggestions Bohr had 
made, that atomic nuclei could be thought of as "Uquid drops" in 
which various forces interacted — such forces as the mutual repulsion 
of the protons, the attractions between the nucleons (protons and neu- 
trons) at close range, and so forth. One could even consider the 
nucleons at the surface of a large nucleus to interact with each other 
in a manner similar to the way that molecules at the surface of a Uq- 
uid interact to produce surface tension. Could it be possible, they won- 
dered, for the incoming neutron to set up some sort of oscillation in the 
"liquid drop" nucleus of uranium, elongating it enough so that the 
electrostatic repulsion between the protons at one end and the protons 
at the other could overcome the nuclear attractive forces and "surface 
tension" and actually break the elongated drop into two parts? In that 
case, because of the strong electrostatic repulsion between them, the 
two parts would fly apart with enormous energy. Einstein's theory of 
relativity would require that the combined mass of the original nu- 
cleus plus the incoming neutron should be greater by an appropriate 
amount than the masses of the two product nuclei. Miss Meitner did 
some calculations on the back of Hahn's letter, and sure enough, the 
masses of uranium nuclei and of the product nuclei would differ by 
about the right amount to provide that enormous energy. 

After their two-day holiday, the aunt and nephew returned to 
Stockholm and Copenhagen. Frisch immediately informed Niels Bohr 
of this new development, just as Bohr was on his way to take a ship for 
America. By the middle of January 1939, Frisch had shown that mas- 
sive fragments with enormous energies did indeed emerge from ura- 
nium which had been bombarded by neutrons, and he immediately 
sent off a paper containing his ideas to the British journal Nature. In 
this paper he and Miss Meitner introduced the word "fission," bor- 
rowing it from biologists, who use it to describe the splitting of cells. 



Section 3.8 55 

Meanwhile, Hahn and Strassmann were similarly convincing 
themselves that the barium and lanthanum activities really were due 
to radioactive isotopes of those elements and were the result of an 
actual break-up of uranium nuclei. They correctly deduced that other 
fragments must exist and quickly identified strontium and yttrium. 
Also they found evidence of the radioactive noble gases, xenon and 
krypton, among what we may now call the fission products. As soon as 
the Frisch-Meitner interpretation became pubUc, Frederick Johot 
(husband of Irene Joliot-Curie) and several Americans almost simul- 
taneously confirmed that fission was indeed occurring when neutrons 
hit uranium or thorium. 



3.8 The study of nuclear fission begins 

Attention to the work of Meitner and Frisch's interpretation of Hahn 
and Strassmann's experiments was world-wide in a few days. Frisch 
had told Bohr of their ideas as Bohr was hurrying to catch a ship for 
New York. On the transatlantic voyage, Bohr discussed the new dis- 
covery with Rosenfeld, a young colleague from Copenhagen. When 
the liner arrived in New York on January 16, 1939, Bohr and Rosen- 
feld were met by John Wheeler of the Princeton University physics 
department and by Enrico and Laura Fermi, who had recently fled 
from Fascist Italy to Columbia University in New York. That night 
Rosenfeld discussed fission at a meeting of physicists at Princeton. 
The next day Bohr became alarmed that this informal communication 
of the news would result in publications about fission before Frisch 
and Meitner's account would be pubUshed in Europe, so he and Rosen- 
feld quickly prepared a short report, giving Meitner, Frisch, Hahn, and 
Strassmann full credit, and sent it off" to Nature shortly after Frisch 
had sent his own paper from Denmark to the same journal. 

A few days later, on January 26th, at the Fifth Washington (D.C.) 
Conference on Theoretical Physics, a reporter showed Bohr a copy of 
Hahn and Strassmann's first publication of their research. Bohr then 
felt free to report to the Conference both the work of Hahn and 
Strassmann and the ideas of Meitner and Frisch. Within a few hours 
physicists in Washington, New York, Princeton, and many other 
places were setting up experiments on fission. In many of these exper- 
iments, ionization chambers were used to show that the fission frag- 
ments did have large amounts of kinetic energy. Others used cloud 
chambers to show the heavy tracks of the fission particles. Ingenious 
experiments showed that the fragments were indeed radioactive 
when separated from the uranium foil in which they were formed by 
the fission process. 

Another set of experiments confirmed the chemical identifica- 
tions of the fission products by means of the x rays emitted by some of 
them. Certain radioactive decay processes (capture of an electron by 



56 



Nuclear Fission 



the nucleus from the inner electron orbits, or the knocking of such an 
electron out of its orbit by a gamma ray emerging from the nucleus) 
leave an electron vacancy in the inner orbits of the atom. As electrons 
"fall" into that vacancy, x rays are emitted which have wavelengths 
characteristic of the element. Abelson, in America, had in fact already 
measured some of these wavelengths for fission products before 
January of 1939, that is, when they were still thought of as trans- 
uranic elements or as radium isotopes and their decay products. He 
had interpreted his results, quite naturally, as appropriate for x rays 
emitted in transitions to the second set of orbits (the L orbits) of heavy 
elements. After fission was recognized, he reahzed very quickly that 
his measured wavelengths could be much better understood as due to 
transitions to the first set of orbits (the K orbits) of elements such as 
iodine and tellurium — that is, of fission products. Here again, a scien- 
tist had been very close to an important discovery, but he interpreted 
his data in a way consistent with the accepted ideas of his time. It is 
unhkely that Abelson even considered the possibihty that the x rays 
could be due to elements in the middle of the periodic table. 



3.9 The chain reaction 




("K-^ 



Fig. 3-11 



Once the discovery of fission was announced, many investigators con- 
tinued the work of Hahn, Strassmann, Meitner, Abelson, and others in 
attempts to sort out the bewildering array of possible fission products. 
AH of these products would have had, presumably, an excess of neu- 
trons in their nuclei, since aU^^'^nucleus — while it lasted — would have 
about 1.6 neutrons in it for every proton, whereas the stable elements 
in the middle of the periodic table are known to have about 1.3 neu- 
trons per proton. The fragments or fission products, then, probably 
have too many neutrons and are highly radioactive. They can turn into 
stable nuclei most easily by successive emissions of electrons (nega- 
tive beta rays), that is, by turning some of their neutrons into protons 
and electrons and emitting the electrons. But a few physicists began 
to wonder whether a few free neutrons might not also emerge during 
the fission process. In France, von Halban, the JoUot-Curies, and 
Kowarski were able to show that possibly as many as three or four 
neutrons were emitted, on the average, for each neutron-induced fis- 
sion. Similar experiments were carried out in America by Anderson, 
Fermi, and Hanstein. 

The discovery that neutrons are emitted when fission occurs 
immediately raised an intriguing question: could a self-sustaining 
chain reaction occur? It was quickly recognized that such a reaction 
would be possible if, on the average, at least one of the neutrons 
emitted during fission could hit another uranium nucleus and cause 
that nucleus to split. Since neutrons could also escape to the sur- 
roundings, or be absorbed in non-fission-producing ways, it was not at 



Section 3.10 



57 



all obvious that a chain reaction would be possible. In 1939 and 1940 
many papers appeared discussing the relative probabiUties for such 
events. More and more physicists in all parts of the world became con- 
vinced that a chain reaction, with production of an enormous amount 
of energy, might well be possible. 



3.10 The war intervenes 



Early in 1939 many of these physicists became concerned that a 
weapon using nuclear fission might be developed by Nazi Germany. 
As World War II came closer, efforts were made to interest the United 
States government in supporting research in this area. By early 1940 
there was a voluntary agreement among most physicists in America 
to stop publication of significant results. (In this connection, it is inter- 
esting to look at the list of papers quoted in L. A. Turner's comprehen- 
sive review of the discovery of uranium fission, in the January 1940 
issue of Reviews of Modern Physics. In his review Turner hsts three 
papers published in 1934, two by Fermi and his group and one by their 
critic, Ida Noddack. In 1935, there were seven; in 1936, five; in 1937, 
five; in 1938, nine; and then, in 1939, there were 117. By the end of 
1940 the number of papers being published had dropped virtually to 
zero. There have been other discoveries or new ideas in science which 
have caused a sudden explosion of pubhshed papers — the discovery, 
in 1958, of the Mossbauer effect, for example, or the invention of 
masers and lasers, but one cannot think of any other case in which 
the papers suddenly stopped appearing.) 

By the time the pubUcation of fission research stopped, the basic 
problems were clear. Bohr and Wheeler had worked out a good theory 
of the process by which fission occurs. In terms of that theory, it could 
be understood why some nuclei (the abundant U^^*, for example) un- 
dergo fission only when hit by a very fast-moving neutron, while 
others (the rare isotope U-^', for instance) would be more hkely to un- 
dergo fission when hit by a relatively slow neutron. By the end of 1939 
the basic questions had been asked, and many of them had been 
answered. 

The subsequent development of nuclear bombs and of peaceful 
appHcations of nuclear energy is a fascinating story, well told now in 
many books. It is a story interesting from many standpoints, especially 
because it makes us think about the interaction between science and 
technology and between science and government. The technological 
developments stemming from nuclear fission confronted all states- 
men with inescapable problems and raised many issues — which 
are by no means settled — about the role of scientists in a modem state. 
If you are interested in these issues, you will want to read some of the 
books and articles listed in the bibhography at the end of this 
chapter. 




58 Nuclear Fission 

3.11 Some thoughts for our models of discovery 

The discovery of nuclear fission does not fit very well any of the 
models of scientific discovery suggested in the introductory section. It 
was not a single event in history, Uke the discovery of Pike's Peak or 
the Victoria Falls. It was not a jigsaw puzzle in the usual sense, 
although there were certainly many puzzling pieces. The murder 
novel model is fairly close; there were many clues, and an "obvious" 
solution which ended up being wrong, as well as a surprising burst of 
activity at the end of the story. But there were accidents which 
delayed the solution; if similar accidents had happened in a detective 
story, impatient readers would accuse the author of padding the plot 
merely to prolong the story. 

What were some of those accidents? One accident occurred when 
Droste used thin foils to cut down background in a search for alpha 
particles, and thereby stopped the fission fragments from reaching the 
ionization chamber. Another was the possible presence of the 3.6-hour 
yttrium fission products mixed with the 3.5-hour lanthanum discov- 
ered by Joliot-Curie and Savitch. The yttrium made the radioactive 
material seem slightly different from lanthanum in the chemical sep- 
arations. Sometimes scientists are helped by fortunate accidents, but 
occasionally chance occurrences hinder them. 

A more important lesson to be learned is that it is often terribly dif- 
ficult for a new scientific idea to be bom. As Conant, Holton, Kuhn, 
Barber, and many others have pointed out, scientists do not leap to an 
unusual explanation for some newly observed phenomena if there is 
an ordinary explanation handy. When Fermi and his colleagues found 
the radioactive by-products of neutron bombardment of uranium to be 
unlike the chemical elements just below uranium in the periodic 
table, the only obvious answer was that transuranic elements had 
been produced. Ida Noddack pointed out the flaws in this logic, but to 
follow her suggestions would have meant taking at least two steps 
that seemed unacceptable: exhaustive chemical tests would have had 
to be made for all 92 elements, and scientists would have had to sus- 
pend their rehance on some of the most productive and valuable ex- 
isting theories on the behavior of nuclei. There are those who say that 
"the scientific method" requires that any theory be tossed out the 
moment a single contradictory experimental fact comes along. Scien- 
tists, however, know that a single contradictory experimental fact 
may be an experimental mistake, or if not, then possibly the old theory 
can be changed to include the new fact. The apparent triple inheri- 
table isomerism of the "radium" and the "actinium" activities was 
rather extraordinary, but not nearly so extraordinary as nuclear fis- 
sion would have seemed. 

The final understanding of nuclear fission came about through 
the work of many persons in many countries. Crucial roles were 
played in Italy, Germany, France, Denmark, Sweden, and America. 
Scientists of many countries and nationalities were involved. This is 



Section 3.11 



59 



not to say that there was not intense competition for priorities. A sci- 
entist, like anyone else, enjoys the fame of being the first to make an 
important observation or to have an important idea. But the competi- 
tion was embedded in a context of cooperation. 

The international scientific community was, of course, divided by 
World War II. One of the great ironies of history is that American tech- 
nology and science, especially the study of nuclear energy, were so 
much advanced by the distinguished scientists who fled the tyrannies 
of Hitler and Mussolini. 

A minor irony in the history of science is that the discovery of 
nuclear fission did not, after all, require any convulsive revision of 
older concepts of atomic and nuclear structure. Once scientists got 
used to the idea of what for five years had been dismissed as impos- 
sible—nuclear fission — it turned out to be quite understandable, after 
all, in terms of the theories of nuclear structure that had been devel- 
oped by Bohr and others during those same five years. But then, 
"Monday morning quarterbacking" has always been easy. 



160 




1900 



1925 



1950 



1975 



2000 



Fig. 3-13 



3.1 List the experiments performed after 1930 that 
you consider of critical importance in the discovery 
of nuclear fission. Indicate the part played by each 
experiment in preparing for this discovery. 
3 2 Prepare a brief glossary of the terms used in 
this chapter for someone who had not studied Unit 5 
or Unit 6. Include at least the following terms: cross 
section, carrier, activity, half-life, transuranic ele- 
ment, fission, alpha particle, neutron. 
3.3 How do you think the world would be different if 
nuclear fission had been discovered in 1930? Not 
until 1950? 

3 4 To what extent do you think the date of a signif- 
icant discovery, such as the discovery of nuclear fis- 
sion, is influenced by deliberate human decisions? 
What changes in society might have accelerated the 
discovery by 10 years? Delayed the discovery by 10 
years? 

3.5 Give examples of discoveries in which the dis- 
coverer had a conviction that he would find what he, 
in fact, did find. Also give examples in which the dis- 
covery was unexpected and surprising. In which cat- 
egory do you place the discovery of nuclear fission? 
Of Neptune? Of the electron? Why? 

3.6 Find the answer to problem 24. 16, Unit 6, or to 
the modified version of that problem presented 
here. The end products in one particular mode of 
fission of U^^^ when that nucleus is bombarded with 
slow neutrons are sjLa'^** and 42Mo"\ This mode 
may be described by the equation 



^V^^' + on' 



^La"'"' + 42Mo«5 + 2on' + T-.e" 



The mass of syLa^-'is 138.9061 atomic mass units 
(amu), that of 42Mo''^ is 94.9057. How much energy is 
released per atom in this particular fission mode? 
The mass of the seven electrons may be neglected. 
The mass of a U"^ nucleus is 235.04393 amu, and 
that of a neutron is 1.00867 amu. According to Ein- 
stein's relativistic mass-energy relationship, AE = 
Amc ', the energy equivalent of one amu is 931 mil- 
lion electron volts. 

3.7 One way in which a U^*'^ nucleus hit by a neu- 
tron may undergo fission is by splitting into two 
radioactive nuclei, 54Xe'"* and .^gSr"', plus three neu- 
trons. Suppose we could somehow see the two daugh- 
ter nuclei just after the split has occurred. We would 
see two charged objects very close to each other. Ac- 
cording to Coulomb's law, there would exist a strong 
force pushing them apart. As the two objects fly 
apart, the force will, of course, diminish rapidly, but 
we can calculate the electrical potential energy that 



will be converted to mechanical kinetic energy of the 
particles in the process. By use of Coulomb's law, one 
can show that the work required to bring a charge Q, 
up to a distance R from a charge Q2 is given by 
kQiQJR. This same amount of work can be done, 
then, by two charges that find themselves a distance 
R apart. (You will recall from Unit 4 that k is about 9 
X 10" newton-metersVcoulomb-.) Suppose that, just 
after the fission, the above fission fragments are 
approximately 2x10"'^ meters apart, and virtuaUy at 
rest. Find the sum of their kinetic energies after they 
have flown apart, in joules and in electron volts. 
(Note: the electronic charge is 1.6 x 10"'" coulomb 
and 1 electron volt = 1.6 x 10" '"joule.) Probably your 
answers in of the same order of magnitude as your an- 
swer to problem 3.6. Why isn't it exactly the same? 

3.8 Calculate approximately how the total kinetic 
energy will be shared by the two fission fragments. 
(Hint: use conservation of momentum to find the 
ratio of their velocities.) 

3.9 When an alpha particle goes through the gas in 
an ionization chamber, it loses an average of about 
30 electron volts of energy each time it produces an 
ion pair by disrupting neutral atoms and molecules. 
An alpha particle of total energy 4 MeV would come 
to rest after producing about how many ion pairs? 
How many ion pairs would be produced by a 
100-MeV fission fragment? If all the ions are singly 
charged, about how much negative charge would be 
coUected by the positive plate of the ionization 
chamber from ion pairs caused by a fission frag- 
ment? 

In a certain ionization chamber the collection of the 
ions by the positive plate might take on the order of 
1/1000 second. What is the average current in the 
pulse that would flow from the positive plate to the 
power supply as a result of the collection of the ions' 
charge? How might this pulse be detected? 

3.10 In order for radium to be produced by neutron 
bombardment of uranium, two alpha particles would 
have to be emitted by the bombarded nuclei. The 
chemical evidence, until the end of 1938, seemed to 
indicate that radium isotopes were produced in this 
way. 

(a) What sorts of chemical evidence were used? 

(b) What was the prevailing opinion among physi- 
cists about twofold emission of alpha particles under 
such circumstances? 

(c) Was there any other reason for hesitation among 
physicists in accepting the chemical evidence for 
the radium-actinium isomers? 



60 



Suggestions for Further Reading 



Fermi, Laura, Atoms in the Family. University of 
Chicago Press, 1954. (Now in paperback.) A good 
biography of Enrico Fermi by his wife, with an ex- 
cellent account of the early work on fission. 

Graetzer, H. G. and Anderson, D. L., The Discovery of 
Nuclear Fission. New York: Van Nostrand-Reinhold 
Company, a Momentum Paperback, 1971. A docu- 
mentary history of the discovery of nuclear fission, 
including many of the original papers, translated 
(when necessary) into Enghsh. 

Grodzins and Rabinowitch, Editors, The Atomic Age. 
New York: Basic Books, Inc., 1963. Essays from 
"The Bulletin of the Atomic Scientists", 1945-1962, 
by a wide variety of important scientists such as 



Bethe, Bom, Oppenheimer, Goudsmit, Teller, and 
Bertrand RusseU. 

Lang, Daniel, From Hiroshim.a to the Moon. New 
York: Dell Laurel Edition LXI34, 1961. A collection 
of essays on various aspects of the making of the 
atomic bomb. 

Moore, Ruth, Niels Bohr. New York: A. A. Knopf, 
1966. A popular biography of Bohr; especially good 
as a portrait of a truly great man and a great sci- 
entist. 

Turner, L. A., in "Reviews of Modem Physics" Vol. 
12, January, 1940, conveys something of the excite- 
ment of the early months of fission research. 



61 



4.1 Introduction 63 

4.2 Products of radioactive decay 63 

4.3 Beta decay seems to violate conservation laws 65 

4.4 The neutrino is "invented" 67 

4.5 The problem of experimental detection 68 

4.6 The Reines-Cowan experiment 69 

4.7 Neutrinos conserve linear momentum 71 

4.8 The antineutrino 72 

4.9 The muon's neutrino and antineutrino 74 

4.10 Questions the neutrino may help answer 78 

4.11 Some themes in scientific discovery 80 
Epilogue 84 




Scintillation counter detector used by Hemes and Cowan in theirfirst neutrino expemnent at Hanford, Washington, in 1953. 
The counter, which weighed ten tons, is the cylindrical object at the bottom of the pit. 



CHAPTER FOUR 



The Neutrino 



4.1 Introduction 

The planet Neptune was discovered because astronomers took 
seriously Newton's Law of Gravitation and his Laws of Motion. If one 
accepted Newton's laws, then one consistent way to account for the 
very slight deviations of Uranus from its expected orbit was to postu- 
late the existence of a planet beyond that orbit. If one were to give up 
the inverse square law of gravitation and see whether some other 
exponent for the distance might account for the deviations, it would 
mean modifying physical laws which by 1840 had been abundantly 
verified in countless physical situations. 

Nearly 200 years after the discovery of Neptune, the neutrino was 
discovered because physicists took seriously two other physical princi- 
ples — conservation of energy and conservation of angular mo- 
mentum. Experimental nuclear physicists found evidence of an 
apparent violation of these principles. In order to save the principles, a 
new particle was invented. We say "invented" because for many years 
there was no direct experimental evidence for the properties or even 
the existence of the particle. It was as though Neptune had been "in- 
vented" by Leverrier and Adams to save Newton's laws in the face of 
the pecuhar behavior of Uranus — and had then turned out to be totally 
invisible for many years. 



4.2 Products of radioactive decay 



Not long after the discovery in 1896 of radioactivity, radioactive mate- 
rials such as radium and uranium were found to emit three different 
sorts of rays. Those with shortest range were called alpha rays and in 
due course were identified as helium nuclei with kinetic energies of 
up to several million electron volts. The second group, beta rays, could 
penetrate thicker layers of absorbers; these were found to be negative 



See Unit 6, Chapter 21 , of the Project 
Physics Text for the story of the dis- 
covery of radioactivity and the iden- 
tification of the products of radioac- 
tive decay. 



63 



64 



The Neutrino 




Photographic plate 



Magnetic field 

perpendicular 

to paper 

Vacuum 
chamber 

Radioactive 
materials 

Fig. 4-2 A diagrammatic represen- 
tation of the behavior of a, p, and y 
radiation in a magnetic field. 



electrons with energies comparable to those of alpha rays. A third 
group, gamma rays, could penetrate even further; they were found to 
be, like x rays, electromagnetic radiation, but they usually had shorter 
wavelength and higher energies than typical x rays. 

Many experiments were devised to measure the relative intensity 
at various wavelengths of the gamma rays emitted and the relative 
numbers at various energies of the alpha or beta particles emitted. 
These experiments describe the spectrum of each of the rays emitted 
by radioactive nuclei, much as the experiments of Fraunhofer and 
others described the spectrum of the light emitted by excited atoms. 
Radioactive isotopes were found to emit line spectra of alpha or 
gamma rays, with different isotopes emitting different spectra. All the 
alpha rays emitted by polonium 218, for example, have a kinetic 
energy of 6.11 million electron volts. Polonium 212 emits gamma rays 
at a number of different wavelengths, the most intense correspond to 
energies of 1.80 MeV, 1.6 MeV, 1.51 MeV, 0.953 MeV, and 
0.785 MeV. 



RdTh, 5.42 Mev 



Fig. 4-3 Theenergy distribution of 
radiations from various heavy nuclei. 



1000 
900 
800 
700 
600 
500 
400 
300 
200 
100 



^ 




ThX 

. 5.68 

Mev 


































































• Tn 




.ThA 




















1 








Me 


1 i«-^ 

llMev 


























The, 1 

e nc 1 




























Mev J 




























/ 




N 


















— AThC,^ 






/ 
























/I 8.78 

# 1 Uau 






1 




, 


i 


1 
















^\i 












\J 




V. 














J 


> 


^ 


>• 



7 10 15 20 25 



30 35 40 45 50 55 60 65 
Channel number (a function of energy) 



70 75 80 



The observation that radioactive nuclei emit line spectra in- 
dicated that these nuclei can assume only certain definite energies, 
just as the existence of spectral lines in the optical spectrum of 
hydrogen and other atoms indicates that their electrons and nuclei 
can assume only certain definite energies. In the same way 
that a study of optical spectra led to the development of much of our 
modem theory of atomic and molecular structure, so a study of the 
energy spectra of alpha, beta, and gamma rays has contributed to the 
development of nuclear theory. The emission of line spectra by both 
nuclei and atoms indicated that the quantum ideas useful for under- 
standing the behavior of atoms would be important for understanding 
nuclei. 



Section 4.3 



65 



4.3 Beta decay seems to violate conservation laws 

Beta ray spectra produced a puzzle. As early as 1919, James Chad- 
wick, a young English physicist, showed that, unlike alpha and 
gamma ray spectra, the typical beta ray spectrum was continuous; 
beta rays of all energies from zero up to some maximum energy, £„,, 
appeared as shown in Fig. 4-4. Some beta ray spectra showed addi- 
tional sharp lines at definite energies. These were soon found to be 
not electrons emitted from the nucleus, but orbital electrons from 
outside the nucleus and will not concern us further here. The beta rays 
which produce a continuous spectrum come from the nucleus itself. 



>" 


r^ 






















f 




\ 




















4 






\ 
























> 


V 
























\ 


V. 
























\ 


k 
























\ 


^ 




Enc 


point 

\ 


















N 


V 




\ 




















X 


^K 




\ 



0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 
Kinetic energy of the beta-particles, r(MeV) 



Fig. 4-4 The energy spectrum of the 
beta particle. 



Since the evidence from alpha and gamma ray emission shows 
that nuclei exist in states with a definite energy, any change that 
occurs in a nucleus should result in a change in energy equal to the 
difference between the energy of the original and that of the final 
state. Specifically, when nuclei in a given state change to a lower 
energy state by emitting beta rays, each of the nuclei should lose the 
same energy. Therefore we would expect that each of the beta rays 
would be emitted with the same energy. The beta rays should show 
line spectra, but they don't. However, the difference in energy 
between the parent and daughter nuclei is equal to the maximum 
beta ray energy, Em, and that, on the average, the energy carried off 
by a beta ray was considerably less than that. 

For example, consider the isotope 84P02'**, which occurs in nature 
as one of the isotopes in the decay chain which includes U^^^ and 
Ra^^^ Most Po^*** nuclei emit an alpha particle of energy 6.1 1 MeV, be- 
coming 82Pb^'^, which in turn sooner or later emits a beta ray, so that 
it becomes sjBi-'^. The beta ray spectrum has an E^ of 1.03 MeV. The 
total difference in energy between Po-'** and Bi-'^ is therefore 6.1 1 + 



66 The Neutrino 

1.03 or 7.14 MeV. But how can we account for those beta rays emitted 
by Pb^'^ with less than the maximum energy of 1.03 MeV? Since the 
sum of the energies of the alpha particle and the beta ray now is less 
than 7.14 MeV, it appears that some energy has been lost. One pos- 
sible answer is that the Bi-'^ has more than one energy state, so that, 
depending on which state the Bi-^^ is produced in, the beta rays will 
have different energies. 

The existence of another mode of decay of Po-'** indicates that this 
is probably not the case. About two out of every 10,000 Po-'** nuclei 
decay by emitting a beta ray first. The resulting nucleus, soAt-'*, then 
emits an alpha particle, becoming gsBi-^^. The maximum beta ray 
energy here is E^ = 0.39 MeV, and the alpha particle energy is 6.75 
MeV; the energy difference between the Po-^** and the Bi-'^ is 0.39 + 
6.75 or 7.14 MeV, the same as before. 

This makes it apparent that the decays occur from one specific, 
well-defined energy state of Po-'** to one specific well-defined energy 
state of Bi^'*. In both modes of decay, when the beta ray is emitted 
with less than the maximum energy, some energy seems to be lost. 
Furthermore, this "lost energy" can have any value up to 1.03 MeV. 

In the 1920's many guesses were made as to what might be hap- 
pening to the missing energy. Some physicists thought that it might be 
carried off by unnoticed gamma rays, but careful searches failed to 
detect them. Another possibihty was that not all beta rays are aUke; 
the missing energy might be accounted for by having different masses 
of beta rays. Much experimentation, however, had shown that all beta 
rays had the same ratio of charge to mass. To believe in a variety of 
masses would require a behef in a variety of electric charges — and 
there was strong experimental evidence against that idea. Finally, one 
might beheve that the principle of conservation of energy simply does 
not hold for nuclei when they are emitting beta rays. To give up this 
principle would be an appalling idea; it would shake the very founda- 
tions of physics. We shall see that physicists were prepared to go to 
considerable lengths to preserve the principle of conservation of 
energy in beta decay. 

The study of beta ray spectra also posed a threat to a second con- 
servation principle, the conservation of angular momentum. In your 
previous work in physics you have used the principle of conservation 
of linear momentum, which has been a powerful tool for scientists in 
understanding motion and especially in understanding coUision pro- 
cesses. You may also have studied rotational motion and learned that 
for any system of particles one can define a quantity, angular mo- 
mentum, which remains constant provided no external torque acts 
upon the system. A ballet dancer or figure skater can change her rate 
of rotation by moving her arms in and out — the position of her arms 
changing the distribution of her mass, one factor in her total angular 
momentum. If she brings her arms close to her body, her angular 
momentum remains constant, but her rate of rotation increases. 



Section 4.4 67 

Theory and experiment in the 1920's had indicated that atoms 
and subatomic particles, including electrons and nuclei, possessed 
angular momentum. Just as the electron in a hydrogen atom can have 
only certain amounts of angular momentum, so nuclei and nuclear 
particles can have only certain amounts of angular momentum. But 
there was a difficulty in the beta decay of a typical isotope: the total 
angular momentum carried by the beta ray and daughter nucleus 
together after the emission was different from the angular mo- 
mentum of the parent nucleus before the emission. Therefore, what 
became of the "missing" energy and also the "missing" angular 
momentum? 



4.4 The neutrino is "invented" 

In the early 1930's Wolfgang Pauli, an Austrian theoretical physicist, 
suggested that in order to save the principles of conservation of 
energy and of conservation of angular momentum, one would have to 
assume the existence of a new particle that would be emitted along 
with the beta ray. This particle would have no electric charge and 
would have Uttle or no mass, but it would be capable of carrying 
energy and angular momentum. 

Enrico Fermi took Pauh's suggestion and worked out its imphca- 
tions. In a sense, Fermi did for the neutrino (he gave it the Italian 
diminutive for neutron) what Adams and Leverrier had done for Nep- 
tune. The question Fermi asked and answered was essentially, "Can 
modem theoretical quantum mechanics account for the shape of the 
beta ray spectrum and the half -life of a given isotope, if we assume 
that neutrinos exist and have the properties proposed by PauU?" The 
analogous question for Adams and Leverrier was, "Assuming that a 
hypothetical planet beyond Uranus exists, can it account for the ob- 
servable behavior of Uranus?" The problem faced by Adams and 
Leverrier required the appUcation of classical Newtonian mechanics 
and the law of gravitation. The problem faced by Fermi required the 
use of the then newly developed quantum mechanics and certain as- 
sumptions about the interactions between nuclear particles, beta par- 
ticles and neutrinos. 

Fermi succeeded. He showed that if one assumed that a neutrino 
was emitted along with a beta ray and that the neutrino had the char- 
acteristics suggested by Pauli, then the predicted shape of the beta ray 
spectrum would agree with what was observed experimentally. Fur- 
ther, his theory gave physicists some understanding of how the half- 
life of a given isotope should be expected to be related to the max- 
imum energy, £„,, of the beta spectrum and to certain other character- 
istics of the parent and daughter nuclei. 

Fermi's work made the neutrino respectable. From 1934 onward, 
the neutrino was accepted as real on two theoretical grounds: it 



68 The Neutrino 

preserved the laws of conservation of energy and angular momentum, 
and a theory based on its existence predicted the right shape for beta 
ray spectra. However, all other known particles — protons, neutrons, 
electrons, positrons, and photons — could be experimentally detected 
in one way or another. The neutrino, by virtue of its pecuUar charac- 
teristics, was, it seemed, undetectable. 



4.5 The problem of experimental detection 

Detecting a particle means observing its influence on a medium 
through which it travels. This is easiest if the particle is charged, for 
then it can exert electric forces on the molecules or atoms or nuclei in 
its surroundings. For example, a charged alpha particle ionizes the 
gas along its path in a cloud chamber, and the condensation of water 
vapor on the ions reveals its path. A charged proton ionizes the gas in 
a Geiger counter, and the ions, accelerated by the electric field in the 
counter, produce more ions by collision, which in turn produce still 
more ions; the ensuing avalanche of ions constitutes a large enough 
pulse of charge to be detected electrically. 

Uncharged particles are detected more indirectly. A neutron shot 
into paraffin can knock protons forward. The moving proton, being 
charged, can then be detected in a number of ways, and its detection 
implies the presence of the neutron which hit it. 

With no electric charge and essentially no mass, the neutrino 
cannot directly affect molecules or atoms. It is, according to the 
theories of Pauli and Fermi, immune to the nuclear force, and there- 
fore it cannot affect protons as the neutron does. Since it has httle or 
no mass, even if it did interact with another particle, the other particle 
would be virtually unaffected; it is the virtually undetectable neutrino 
which would be deflected — like a ping pong ball thrown at an ele- 
phant. 

Since it interacts almost not at all with other particles, the range 
of motion for the neutrino is huge. We now know that before in- 
teracting with another particle, a typical neutrino from a beta decay 
would travel about 100 light years in a material hke hquid hy- 
drogen—that is, about 11/2 miUion round trips to the sun: 

Such a peculiar particle was, of course, a challenge to the experi- 
mental physicist. Surely there must be some way to detect it! And 
eventually there was — but it had to wait a good many years for cer- 
tain technological developments. From time to time in science a good 
theory will have to wait, sometimes years, before technology has 
developed enough to provide the tools needed for an experimental test. 
To understand what technology had to develop, let us go back and look 
at the reactions in which neutrinos are produced. A typical beta ray 
decay process might be 

f Is the Greek letter nu. ssPb"' »• saBi^'^ + _ie" -I- oi^"(-) (4.1) 



Section 4.5 



69 



in which -jC" represents the negative beta ray, and ovX—) represents 
the neutrino. The minus sign in parenthesis is not the neutrino's 
charge (it is uncharged); it is to remind us that the neutrino was 
formed in a negative beta decay — an important reminder, as we shall 
see. 

One can think of the decay process represented in Eq. (4.1) as in- 
volving the conversion of a neutron, within the Pb-'^ nucleus, into a 
proton. Such conversions occur, in fact, with free neutrons: 



on' 



iP' + _,e« + o^-(-) 



(4.2) 



Fermi's theory suggested that a converse reaction might occur: a neu- 
trino and a proton might combine to produce a neutron and a positron 

(.ie«). 



iP' + 01^%-) 



on' 



(4.3) 



One could estimate from Fermi's theory, and from the characteristics 
of free neutron decay, that what physicists call the cross section for 
the process indicated in Eq. (4.3) would be about 10"^^ cm-. In Sec- 
tion 3.3 we said that the cross section for a process is a measure of 
the probabihty that the process will occur under given circumstances. 
In the case of a target particle being hit by an incoming particle, the 
cross section for the event is the effective area of the target particle as 
seen from the direction of the incoming particle. (If the target were a 
large object, this would be equivalent to the area of its shadow on a 
wall immediately behind it.) The cross section depends on the process 
as well as the target. The cross section for scoring with a basketball is 
smaller than the cross section merely for hitting some part of the 
basket, just as the cross section for blowing out a candle with a puff of 
air is smaller than the cross section for making it fhcker. The cross 
section of a proton for interacting with a relatively slow-moving neu- 
tron is of the order of 10"-^ cm-. 

To observe the reaction described by Eq. (4.3), then, one would 
need to have a very large number of protons, and a huge number of 
neutrinos flowing among the protons, because the cross-section is so 
small. The large number of protons requires a large volume. A large 
volume means long distances between the events and the detectors, 
and hence some very sensitive detecting devices (scintillation 
counters) are needed to detect the reaction products. Neither the 
large flux of neutrinos nor the very sensitive scintillation detectors 
became available until after World War II. Finally, in 1956, 
Frederick Reines and Clyde Cowan, than at the Los Alamos labora- 
tory, were able to announce that they had actually "found" some 
neutrinos reacting as in Eq. (4.3). 



When a high energy particle (such as 
a beta particle or a gamma ray 
photon) is absorbed in certain liquids 
or solids, some of the energy of the 
particle is converted into a very weak 
flash of light, or scintillation. Some of 
the early research in radioactivity 
was carried out by observing and 
counting these scintillations with no 
tools but the human eye and brain. 
Modern apparatus observes the scin- 
tillations by use of very sensitive 
photoelectric cells. 



4.6 The Reines-Cowan experiment 



To obtain a large flux of neutrinos, Reines and Cowan needed enor- 
mous numbers of beta decays going on. These were produced by one of 



70 



The Neutrino 



the nuclear reactors that were a development of nuclear fission re- 
search during World War II. Fission products, as we saw in Chapter 3, 
are strongly radioactive. When a huge nuclear reactor is turned on and 
off, the amount of beta activity in the reactor goes up and down. It 
does not disappear immediately when the reactor is turned off, be- 
cause, as in all decay processes, a time constant is involved. But the 
intensity of the neutrino flux is strongly dependent upon the power 
level at which the reactor is working — which, of course, is directly 
related to the number of fission processes per unit time. 

The experiment carried out by Reines and Cowan, using the large 
reactor at Savannah River as a neutrino source, was designed to de- 
tect events described by Eq. (4.3). The reactor provided a large flux of 
neutrinos (about 1.3 x 10'7cm-/sec as calculated from the fission reac- 
tion rate). The detector consisted of a tank containing 1400 liters 
(about 370 gallons) of an organic liquid which included 8.3 x 10^* pro- 
tons and a small amount of a cadmium compound. The detector also 
included counters to record the scintillations produced by the gamma 
rays released upon the creation of a neutron and a positron — the prod- 
ucts of the hoped-for reaction. 



Fig. 4-5 Schematic example of 
neutrino reaction in a scintillation 
tank. 




Fig. 4.5 shows a sequence of events in which a neutrino interacts 
according to Eq. (4.3) with a proton in the scintillation tank. The posi- 
tron, /3+ or +ie", moves off a short distance, but slows down very 
rapidly and meets an orbital (negative) electron. The positron and the 
electron annihilate each other, and their energy emerges in the form 
of two gamma rays, yi and y^, each with an energy of approximately 
0.5 MeV. These gamma rays are absorbed by the scintillator liquid, 
and a flash of light appears in the tank — the intensity of the flash 
depending upon the gamma ray energy. This flash is detected by two 
banks of large photomultiplier cells. If both banks "see" the light 
flash, and if the flash is within the expected range of gamma-ray 
energies, then a signal is accepted which alerts the logic circuits of 
the associated equipment. Meanwhile, the neutron on' loses energy as 
it bounces from proton to proton. Eventually (and that means, on the 



Section 4.7 71 

average, after 5 to 20 microseconds) the neutron will be going slowly 
enough to be absorbed by a cadmium nucleus. A group of gamma rays, 
represented by y^, y^, 75, and ye in Fig. 4-5, are emitted during the ab- 
sorption process. These, in turn, are absorbed by the scintillator hquid, 
with each producing a flash detected by the photocells. The alerted 
logic circuits then register an "event" when a neutron-absorption-by- 
cadmium pulse is received in an appropriate time interval (from 0.75 
to 30 microseconds) after an electron-positron annihilation pulse. 
Another big scintillation tank, with associated photocells and circuits, 
is used to screen out, or prevent the counting of, spurious events 
caused by highly energetic cosmic rays coming through the appara- 
tus. Such devices, plus careful shielding, reduced the number of 
spurious events counted. 

When the reactor was operating, Reines and Cowan found that 
there were 36 ± 4 events per hour more than when the reactor was not 
running. By taking into account the size of the flux and the number of 
protons in the target tank, they concluded that the cross section for the 
reaction was (1.1 ± .26) x 10""cm-, as predicted by the theory. This 
cross-section is about 10-" times smaller than that for ordinary nuclear 
reactions. 

This experiment provided the first relatively direct experimental 
evidence that neutrinos exist and are produced during beta decay of 
radioactive materials. One says "relatively" direct because, of course, 
one could not see, hear, or feel the neutrinos directly. But then we do 
not see, hear, or feel electrons or protons or neutrons, either. Of course, 
in the case of these more famihar particles, the experimental and con- 
ceptual steps which lead us to say, "These observable phenomena are 
surely due to such-and-such a particle," are rather more straight- 
forward. But Reines, Cowan, and their colleagues at least succeeded 
in clothing the neutrino with a reahty beyond that provided only by 
faith in the conservation laws and a theoretical prediction. In addi- 
tion, the cross section they measured was more than just an impres- 
sively small number. It was useful in helping physicists to decide 
between two opposing theories which had developed as to the basic 
nature of the neutrino. 



4.7 Neutrinos conserve linear momentum 

There had been other attempts to demonstrate the existence of 
neutrinos by experiment. Beginning in 1936, a series of experiments 
by many people, had been carried out to show that neutrinos carry 
away linear momentum as well as energy and angular momentum. 
The idea behind such experiments is simple. If a nucleus emits a beta 
ray and a neutrino, then the beta ray track should be detectable, as in 
a cloud chamber, going in one direction and the recoiling daughter 
nucleus in another. If there were no neutrino, or if it carried no linear 



72 



The Neutrino 





Nucleus 



(a) (b) 

Momentum diagrams 



momentum, then the law of conservation of Unear momentum would 
require that the beta ray and the nucleus go in opposite directions and 
that the vector sum of their momenta be zero. If there is an unde- 
tectable neutrino emitted along with the beta ray, the beta ray track 
and the recoil nucleus track would go off at some angle less than 
180° from each other, and the vector sum of their momenta would 
be opposite to the momentum of the neutrino. 

Even simpler in theory are those cases in which an isotope decays 
not by beta ray emission, but by the capture of one of the inner orbital 
electrons into the nucleus. The net effect is much hke emission of a 
positive beta ray, so presumably a neutrino is emitted in the process. 
The observable recoil momentum of the atom after the event in one 
direction is numerically equal to the momentum of the neutrino in the 
other. In this case, since all captured electrons had a definite 
energy, the neutrinos will also have a definite fixed energy and form a 
line-spectrum rather than a continuous spectrum as in ordinary beta 
decay. If recoil atoms could be observed, and if all of them (for a given 
isotope) were found to have a definite momentum, this would confirm 
the idea held by most physicists that only one neutrino is emitted 
during a decay process. 

Experiments designed to detect such recoils are difficult because 
such a recoiling nucleus has a small amount of energy. Each one, 
therefore, travels only a short distance through the gas of a cloud 
chamber. (The energy can be calculated from the conservation laws, 
as in any coUision or two-body explosion problem.) The recoil energies 
come out to be of the order of 100 electron volts or less, compared with, 
for example, energies of 4000 times that much for the recoil energy 
accompanying the emission of a typical alpha particle. 

By 1948 a variety of experiments had shown that recoils could be 
observed. Such observations confirmed what people expected — that 
the neutrino would obey the law of conservation of linear momentum 
as well as those of conservation of energy and angular momentum. All 
of these experiments, of course, dealt with the emission of neutrinos. 
The experiments of Reines and Cowan were first to show unam- 
biguously an effect due to the absorption of a neutrino. 



4.8 The antineutrino 

In 1955 Raymond Davis, of the Brookhaven National Laboratory, 
reported a different sort of experiment in which he had attempted to 
find reactions caused by neutrinos. More exactly, his experiment had 
best be thought of as an attempt to rule out a certain kind of reaction. 
It was known that an isotope of argon, A^^ decays with a half-life of 
34 days, by orbital electron capture, to become an isotope of chlorine 
and, it was thought, emit a neutrino. Such a reaction may be repre- 
sented by the equation 



sA'-'" + -,e"' 



.7CI' 



01^%+) 



(4.4) 



Section 4.8 73 

One writes o»'"(+) because the neutrino thought to be produced in this 
reaction would be the same sort of neutrino as is produced in pos- 
itron (+ie*) emission. 

Neutrinos ought to be able to produce the converse reaction: 

i^CP^ + ou%+) > isA" + _,e« (4.5) 

But meanwhile theoretical physicists had suggested that there were 
probably two kinds of neutrinos — those emitted during decays pro- 
ducing negative electrons and those emitted during decays producing 
positrons — and that one would not be able to make A^" from Cl^' with 
i^(— ) neutrinos, the wrong neutrinos for this process. Davis' experi- 
ments, then, were an attempt to show that an intense flux of p(—) neu- 
trinos (from a uranium reactor) would have Uttle or no eff'ect in going 
through large amounts of CP'. First at Brookhaven, and then later 
with two 500-gallon tanks of chlorine-rich carbon tetrachloride at the 
Savannah River reactor, Davis first bubbled very pure heUum through 
to pick up and carry off" any argon already in the tanks from reactions 
produced by cosmic rays or other contaminants. Then after the tank 
had been irradiated for several weeks by the neutrino flux from the 
reactor, a small amount — about 0.1 cm^— of pure (nonradioactive) 
argon (A^°) was introduced as a carrier for any radioactive argon 
nuclei that had been formed by the reaction described in Eq. (4.5). The 
argon was then flushed out with helium, purified, and then inserted 
into a small Geiger counter. (Quite HteraUy "into" — that is, the argon 
was added to the gases already inside the counter itself.) Careful 
shielding of the counter was provided to limit the background 
counting rate. Davis' results showed that, within the limits imposed 
by his very small background counting rates, there was no measur- 
able activity that would indicate the presence of argon 37 produced 
from the chlorine. He could express his results numericaUy by saying 
that the cross section for the reaction given by Eq. (4.5) rewritten for 
v(—) was less than 0.9 x 10"^' cm which is about a factor of 100 smaller 
than the cross section for the reaction of these neutrinos with 
protons. 

Davis, then, provided experimental confirmation for the idea that 
there really are two different sorts of neutrinos. We have called them 
!'(+) and v(--), but the generally accepted usage now is to call p(+) the 
neutrino and i'(— ) the antineutrino. The symbols for the neutrino and 
the antineutrino are v and v respectively. 

Like most fundamental particles, neutrinos and antineutrinos 
possess angular momentum; they can be pictured as spinning on an 
axis. The difference between neutrinos and antineutrinos is their 
direction of spin. If you could see a neutrino moving away from you, 
you would see it spin around the axis of its direction of travel in a 
clockwise sense, whereas you would see an antineutrino spin around 
the axis of its direction of travel in a counterclockwise sense. 



74 The Neutrino 

We have seen, so far, that the neutrino provided us with a good ex- 
ample of the sort of scientific discovery that came about because 
experimental observations (in this case, the beta ray spectrum) con- 
tradicted what was expected on the basis of well-estabhshed princi- 
ples (in this case the principles of conservation of energy and of an- 
gular momentum). The particle "invented" by Pauli in order to avoid 
giving up these laws then turned out to be useful in Fermi's theory of 
beta ray emission. The theory prompted other experiments, particu- 
larly the nuclear recoil experiments, that gave results which strength- 
ened belief in the particle. But not until twenty years had elapsed — 
and a whole new technology had developed — was it possible 
to detect neutrinos by their interactions with matter. Meanwhile, 
theory had suggested that there might be two sorts of neutrinos - neu- 
trinos and antineutrinos, a suggestion confirmed by experiments such 
as those by Davis. 



4.9 The muon's neutrino and antineutrino 

The story does not stop there. The neutrino has turned out to be both 
useful and intriguing in many areas of physical research. And it has 
turned out that there are not just two kinds of neutrinos, but at least 
four. This discovery owes itself to a number of developments that 
have taken place in particle physics since the neutrino was "in- 
vented." 

After World War II there were spectacular advances in the devel- 
opment both of accelerators to produce high-energy particles and of 
methods for observing the behavior of particles. In the postwar years, 
cyclotrons and other accelerators were built with higher and higher 
output energies — first with tens of millions of electron volts, then with 
hundreds, then, in the mid-1950's, with a billion electron volts or 
more, and on up to 20 and 30 biUion electron volts in the mid-1960's. 
Meanwhile, in addition to Geiger counters and ionization chambers, 
new devices such as scintillation counters, photographic emulsions, 
bubble chambers, spark chambers, and highly complex electronic 
control circuits were developed. 

One result of these developments was that many new particles 
were discovered. As early as the middle of the 1930's, particles with 
masses between the mass of the electron and that of the proton had 
been found in cosmic rays. Originally they were called mesotrons 
(meaning intermediate-mass particles) and later mesons. When more 
and more such particles were discovered as increasingly effective 
equipment became available after World War II, it became apparent 
that the so-called mu-mesons, which were the lightest members of 
the family (with masses about 200 times that of the electron) were 
not members of the meson family at all. They were much more 



Section 4.9 75 

closely related to electrons. They are now called muons. Muons, it 
was found, decayed into positive or negative electrons. A typical muon 
decay could be written as 

/x~ » +ie" + energy + momentum (4.6) 

Cloud chamber and other observations indicated that the energy 
and momentum from a muon decay probably would have to be carried 
away, not by one, but by two neutral particles. One of them would no 
doubt be a neutrino associated with the production of the .je", while 
the other was thought to be an antineutrino associated with the disap- 
pearance of the /A^. But the theory of such interactions predicted that 
if both neutrinos were of the same sort (although one of them an an- 
tineutrino), then on at least some occasions the muon decay process 
ought to produce a gamma ray. But such gamma rays were not found. 
So here again theory suggested a new kind of neutrino, which we shall 
denote by v^, and its antiparticle, denoted by F^. 

In 1962 Gordon Danby, Leon Lederman, and their collaborators at 
Brookhaven carried out an experiment suggested by other physicists 
to check this hypothesis. The accelerator at Brookhaven was used to 
produce a beam of protons with an energy of 15 biUion electron volts. 
These protons, upon hitting a suitable target, produced a fairly intense 
beam of pi-mesons, which are particles somewhat heavier than 
muons. In traveling about 20 meters (in a few hundredths of a 
microsecond), some of the pi-mesons decayed into muons and high- 
energy neutrinos. The remaining pi-mesons and the muons were 
stopped in steel shielding forty feet thick. Few neutrinos would be ab- 
sorbed by this shielding. (The steel was armor plate from a dismantled 
battleship. If prophets in an older culture dreamed of turning swords 
into plowshares, it is pleasing to know that in our day battleships can 
be turned into apparatus for scientific research.) The neutrinos — all 
but a very few — went right on through. 

What the experimentaUsts were trying to detect were reactions 
between the neutrinos and some protons. If the neutrinos from the pi- 
mesons were the same as the beta-ray-produced neutrinos, then a neu- 
trino-proton collision should produce high-energy electrons. 

v^ + V ^ e (4.7) 

If they were not, then the neutrino-proton coUisions should pro- 
duce high-energy muons. 

t'e + P * M (4.8) 

(In its search for neutrino-proton collisions, the experiment was 
Uke the Reines-Cowan experiment, with high-energy acceler- 
ator-produced neutrinos, rather than relatively low-energy, nu- 
clear-reactor-produced neutrinos.) 



On these pages are shown some of 
the important nuclear research 
laboratories where American and 
Russian physicists are probing the 
basic structure of matter. The 
photograph at the right shows the 
bending magnets in a section of the 
National Accelerator Laboratory 
located in Illinois. The aerial view 
below gives some idea of the area 
occupied by this enormous particle 
accelerator, 1 .24 miles in diameter, 
and with a circumference of four 
miles. Within this giant ring, protons 
are accelerated to energies which are 
expected to reach 500 BeV. 




.^^Lf^ 









Russian nuclear physicists are doing 
important research at the two 
installations shown on this page. 
Above, is the 10 BeV capacity proton 
synchrotron accelerator located at 
the Dubna Joint Nuclear Research 
Institute. Below, is the proton 
synchrotron at Serpukhov which 
began operation in 1968. Its capacity 
is rated at 70 BeV. 



78 The Neutrino 

How did they detect the reactions? Behind the shielding was a 
spark chamber containing 90 aluminum plates, each an inch thick 
and four feet square, and spaced 3/8 inch apart. The space between 
plates was filled with neon gas. When a charged particle goes through 
the plates of a spark chamber, it leaves many free electrons and ions 
in its path in the gas between each plate. The alternate plates can be 
charged quickly to a high potential difference, which makes a visible 
spark jump just where the electrons and ions were. Stereo pho- 
tographs can then be made to record the path of the original high- 
energy charged particle. 

Elaborate precautions had to be taken to avoid photographing 
thousands of useless tracks made by muons from cosmic rays and by 
other background phenomena. The spark chamber, for example, was 
made to be sensitive only during beam pulses, which occurred every 
1.2 seconds and which lasted for only 3 microseconds each. The exper- 
iment continued for some eight months, for a total of about two 
million pulses — so the equipment was actually sensitive for a total of 
only about six seconds during the eight months. But as many as 10 
million neutrinos passed through the spark chamber for every pulse, 
and about 10'^ traversed it during the whole run. About 50 of them in- 
teracted with protons within the spark chamber, and produced muon 
tracks. If the pi-meson-produced neutrinos were identical with the 
beta-ray-produced neutrinos, then one would have expected about 
half of the tracks to have been due to electrons. The gratifying thing, 
however, was that virtually no electron tracks were produced. (Elec- 
tron tracks are readily distinguishable from muon tracks.) Therefore, 
the reaction described, equation 4.7 does not occur, while the reaction 
described by equation 4.8 is confirmed. The experiment, which in 
more recent years has been extended to higher energy sources, firmly 
established the idea that there were two quite different kinds of neu- 
trinos, each with its own antiparticle. The question remains as to how 
the two kinds of neutrinos are related to each other. 



4.10 Questions the neutrino may help answer 

One delightful aspect of science is that quite often the solution of one 
puzzle raises other questions. But in some cases, the solving of a 
puzzle makes it possible to understand phenomena which had been 
confusing in other areas of physics, or to verify experimentally some 
hypothesis which, until that time, could not be checked directly. It is 
thought, for example, that ordinary stars produce their heat energy by 
means of certain nuclear reactions. Such reactions must produce 
large numbers of neutrinos and antineutrinos. It would be nice to be 
able to test the hypothesis by detecting the neutrino flux from the sun. 
Frederick Reines has designed a detector, with a mass of about a 
thousand tons, as a step toward the detection of neutrinos from the 
sun. 



Section 4.10 



79 




On a more speculative level, astrophysicists have recently been 
considering reactions that might take place in the interiors of large 
stars with exceptionally high interior temperatures — temperatures of 
the order of a biUion degrees Kelvin or more. The very short- 
wavelength photons inside such stars would produce large numbers 
of electron-positron pairs. It has recently been suggested that under 
such circumstances many of these electrons and positrons can sud- 
denly recombine, or annihilate each other, not only by the usual 
process in which two gamma rays (i.e., high-energy photons) are 
produced, but by producing two neutrinos. Gamma rays, which in- 
teract with stellar material easily, would only slowly transfer their 
energy up to the surface of the star and beyond. The neutrinos, how- 
ever, interact so rarely that most of them would escape from the 
star, traveling with the speed of hght. 

Thus it would be possible for a star, once it achieves such a high 
interior temperature, to lose vast amounts of energy almost instanta- 
neously by emitting neutrinos. Such a star would shrink, and the 
gravitational energy associated with the collapse would cause — at 
least temporarily — the production of even higher interior tempera- 
tures. Such a theory may account for at least some of the behavior of 
supemovae. H. Y. Chiu has calculated that a supernova 1000 light 
years away would give off enough neutrinos in such a process that 



Fig. 4-8 Left, a spark chamber at the 
Bevatron, Berkeley, California. Right, 
particle tracks photographed in a 
spark chamber. 



80 The Neutrino 

about ten of them might be detected on our planet, in a time span of 
from 100 to 1000 seconds, by a detector containing some 10,000 tons 
of sensitive material. 



4.11 Some themes in scientific discovery 

The "invention" and the detection of the neutrino have illustrated for 
us, then, several themes that are common in scientific discovery. One 
theme is the interaction among theory, physical experiment, and tech- 
nology. Two well-estabhshed physical laws are apparently violated. 
Theorists therefore hypothesized a new particle to preserve the laws. 
The particle turned out to have considerable utihty in the develop- 
ment of the theory of beta ray decay in radioactivity. Then the devel- 
opment of technological devices (in particular, large scintillation 
counters and sophisticated electronic circuits) made it possible to de- 
tect the absorption of the particle in spite of its elusiveness. Mean- 
while, the growing understanding of the role of the neutrino in the 
theory of particle interactions has raised further questions both in 
physics and in astronomy. 

A second theme we should note is that the experiments required 
tremendous resources, both in sheer bulk and consequent expense, 
and also in pushing available techniques to extremes of sensitivity. 
(In the Danby experiment with the pi-meson-produced neutrinos, the 
apparatus muons had to be selected from cosmic ray muons which ap- 
peared at a rate of about 80 per second, when the sought-after events 
were occurring at a rate of only 50 in eight months.) By no means all 
important theories in physics need experimental tests requiring such 
staggering equipment and effort — even in these days of "big science." 
But some do. 

Meanwhile, if it took you an hour to read through this chapter, 
some lO'** neutrinos from the sun's nuclear reactions streamed 
through you during this time. But even with this large number there is 
less than one chance in a hundred that a single one of these neutrinos 
interacted with one of the perhaps 10^** protons in your body. When 
such a reaction does occur it produces no detectable changes in your 
body. 



4. 1 State in your own words an argument that 
begins with the observation that atoms emit a line 
spectrum and concludes that atoms exist in states 
with a definite energy. 

4.2 How does the evidence that polonium-218 
decays to bismuth-214 by two distinct paths support 
(a) the conclusion that only one energy level of po- 
lonium and one energy level of bismuth is important, 
and (b) the conclusion that in cases of beta decay, the 
radioactive nucleus loses energy equal to the max- 
imum energy of beta rays emitted? 

4.3 In addition to accounting for the missing en- 
ergy, what other experimental findings did Fermi's 
theory of beta ray emission help explain? 

4.4 What characteristics of the neutrino made it ex- 
pecially difficult to detect? How did Reines and 
Cowan overcome these difficulties? 

4.5 Recoils were observed for atoms undergoing or- 
bital electron capture as early as 1948. Why are 
Reines and Cowan credited with being the first to de- 
tect the neutrino when these recoils indicated that 
the nucleus must have emitted a neutrino? 

4.6 List the four types of neutrinos and indicate a 
reaction for producing each one of them. What sort of 
evidence indicates that we cannot get along with 
three or fewer neutrinos? 

4.7 How might neutrinos account for stellar novae? 
What additional evidence would you want before 
concluding that neutrinos play an important role in 
stellar novae? 

4.8 Bismuth-214 (ggBi^") nuclei usually decay by 
emission of negative beta rays with a maximum 
kinetic energy of 3.26 MeV, and turn into polonium- 
214 (g^Po^'*). Polonium-214 emits an alpha particle 
almost at once (half-life 0.00016 sec), wdth a kinetic 
energy of 7.83 MeV. 

A small fraction of the Bi^'^ nuclei decay by an- 
other route, first emitting an alpha particle of energy 
5.61 MeV and turning into thaUium-210 (giTP'"). The 
Tl^'", in turn, decays by emission of a negative beta 
ray with a maximum energy of 5.48 MeV. 

Show that both decay routes lead to the same 
end product, and that the total energy available in 
going from Bi-'^ to that end product is the same for 
both routes. 

4.9 One can estimate very roughly that the average 
energy for the beta rays in the spectrum represented 
in Fig. 0.0 is about one-fourth of £„,. Making the 
rather rash assumption that the average energies of 
the beta rays for the two isotopes in Problem 4.8 are 
also one-fourth of the corresponding Em's, show that 
the two decay routes do not lead to the same energy 
state for the final product, if the average energies are 
used rather than maximum energies. (Actually you 
can show this would be the case if any reasonable 
fraction were used instead of the estimated one- 
fourth.) 

4. 10 Beryllium-7 (aBc'^ nuclei ordinarily decay by 
capturing a K-orbit electron, with a half-life of 53.4 
days, and changing into lithium-7 (sLiO- (The end 



result of a K-capture process is the conversion of a 
proton inside the nucleus into a neutron and has es- 
sentially the same effect as the emission of a positive 
beta ray from 4Be' would have had if there had been 
enough energy for that to have occurred.) When the 
electron is captured, a neutrino is emitted. A study of 
the masses of Be" and Li" indicates that the neutrino 
must take with it an energy of about 0.86 MeV. 

According to the relativity theory, the mo- 
mentum of a massless particle, such as a neutrino, 
can be calculated by dividing its energy by the speed 
of Ught. Use the conservation of linear momentum to 
show that the Li" recoU energy is about 57 electron 
volts. (Note: the recoil energy is so small that it can 
be written as ll2mv'" in which m is the mass of the 
recoihng atom and v is its velocity. Note also that the 
mass of a proton multiplied by c- is 931 MeV.) 
4.11 Assume that the beam of neutrinos that Danby 
and his collaborators used at Brookhaven had a 
cross-sectional area S. The beam went through a 
thickness, L, of aluminum plates. The volume of alu- 
minum traversed by the beam would then be V = LS. 
The mass, M, of aluminum in that volume would be 
M = DV = DLS, if D is the density of aluminum. If we 
divide this mass by the atomic weight of aluminum, 
A, we would get the number of moles of aluminum, 
n, in that volume: n = DLSIA. 

If we now multiply the number of moles by No, 
Avogadro's number, we should get the number, N, 
of aluminum atoms (and hence the number of 
aluminum nuclei) in the volume: N = DLSNJA. 
Now let us assume that each of these nuclei 
presents some very small cross section, a, to an 
incoming neutrino. The total area available for 
reactions would be N times a. If we divide this area 
by the cross- sectional area of the beam, we should 
get the probability, P, that any given neutrino would 
react with an aluminum nucleus. 

P = NalS = DLNoSalAS = DLNocr/A 

If Nr reactions occur when a total of N^ 
neutrinos go through the plates, show that 



^^m 



DLNo 



Given the dimensions of the spark chamber, the 
total number of neutrinos traversing it for a given 
number of recorded reactions, and looking up the 
density and atomic number of aluminum, and 
Avogadro's number, estimate the cross section of the 
aluminum nuclei for reactions with muon neutrinos. 

Why is it permissible to neglect consideration of 
the neon gas between the plates in doing these calcu- 
lations? 

4.12 Compare the neutrino with constructs in an- 
other field, for example with id, ego, and superego in 
psychology, or the gene, or the atom. What elements 
do the history of these concepts have in common? 
What are the important diflterences? 



81 



Activities 



1 Read the Smythe report and The German Atomic 
Bomb (see "Suggestions for Further Reading" at end 
of Chapter 3). Write an essay contrasting one or more 
of the most significant differences between the 
American and German experience. 

2 Consider the credibility of the neutrino hy- 
pothesis at four stages: (a) when first proposed by 
PauU; (b) after Fermi's theory of beta decay; (c) fol- 
lowing the discovery of recoils of atoms following 
electron capture by nuclei, and (d) following the 
experiment of Reines and Cowan. Suggest criticisms 



which might have been made of the neutrino hy- 
pothesis by philosophers of science and by scientists 
and see how these criticisms changed from one stage 
to another. Discuss the appropriateness of these criti- 
cisms. 

3 Was the costly experiment of Reines and Cowan 
worth doing? Argue either side of the case (or both 
sides, if you Uke). Consider possible outcomes as well 
as those that did occur, the extent to which the exper- 
iment was fruitful of other experiments, as well as 
the possibUity for alternative experiments. 



Suggestions for Further Reading 



AUen, James S., The Neutrino. Princeton University 
Press, 1958. A comprehensive account of what was 
known about the neutrino prior to the Reines-Cowan 
experiments. 

Asimov, Isaac, Heaven. Garden City: Doubleday and 
Co., Inc., 1966. The author raises the question of why 
it took chemists so long to discover that the noble 
gases can form compounds. 
Bernstein, Jeremy, The Elusive Neutrino. U.S. 
Atomic Energy Commission, 1969. A fine introduc- 
tion to neutrino physics, available free from 
USAEC, P.O. Box 62, Oak Ridge, Tennessee 37830. 
Cohen, I. Bernard, Science, Servant of Man. 
Boston: Little, Brown and Co., 1948. A discussion of 
the fortunate "accident" in scientific discovery and 
of the practical application of scientific knowledge. 
Conant, James B., On Understanding Science. New 
York: New American Library, Inc., 1947. An analysis 
of the processes of scientific discoveries, with case 
histories of research in gases, electricity, and com- 
bustion. 

Conant, James B., et.al., Harvard Case Histories in 
Experimental Science. Cambridge: Harvard Uni- 
versity Press, 1957 edition. A series of short paper- 
backs of case histories, including more detailed 
studies of cases in On Understanding Science. 
Crane, H. R., "Energy and Momentum Relations in 
Beta-Decay, and the Search for the Neutrino," 
Reviews of Modern Physics, Vol. 20 (January 1948). 
An article summarizing the experimental evidence 
in 1947 for the neutrino. 

Holton, Gerald (Ed.) The Twentieth-Century Sci- 
ences: Studies in the Biography of Ideas. New 
York: W. W. Norton, 1971. Includes biographical 
and autobiographical accounts of the discoveries of 
such scientists as Einstein, Bohr, Linus Pauling, F. 
Crick, E. Erikson, A. Weinberg, R. R. Wilson, et al. 
Koestler, Arthur, The Sleepwalkers. New York: 
Grosset and Dunlop, Inc., 1963. Subtitled "a history 
of man's changing vision of the universe." 
Lederman, Leon, "The Two-Neutrino Experiment," 
Scientific American, Vol. 208 (March 1963). An ac- 
count of the experiment that demonstrated that 
there are two kinds of neutrinos. 



Lederman, Leon M., "Resource Letter on History of 
the Neutrino, (Neu-1)," American Journal of Phys- 
ics, 38 (1970), pp. 129 ff. A very valuable guide to the 
whole literature, obtainable by sending a request 
with 25c and a stamped return envelope to Depart- 
ment RL, American Association of Physics Teach- 
ers, 1785 Massachusetts Ave. N.W., Washington, 
D.C. 20036. 

Morrison, Philip, "Neutrino Astronomy," Scientific 
American, Vol. 207 (August 1962). What we can 
learn about stars from a study of neutrinos striking 
the earth. 

Reines, Frederick, "Neutrinos, Old and New," Sci- 
ence, Vol. 141 (August 30, 1963). A brief article sum- 
marizing the evidence that there are four kinds of 
neutrinos. 

Reines, Frederick and Sellschop, J. P. F., "Neutrinos 
from the Atmosphere and Beyond," Scientific 
American, Vol. 214 (February 1966). Describes the 
detection of naturally occurring neutrinos. 
Romer, A., ed.. The Discovery of Radioactivity and 
Transmutation. New York: Dover Publications, Inc., 
1964. A reprinting of many fundamental papers in 
this field, with discussions. 

Shamos, Morris H., Editor, Great Experiments in 
Physics. New York: Holt, Rinehart and Winston, 
Inc., 1960. Reprints of the original papers describing 
twenty-four important experiments, edited and with 
marginal notes. 

Snow, C. P., The Search. New York: Charles 
Scribner's Sons, 1958. Sections III and V of Chapter 
6 give a fictional account of the thoughts of a young 
scientist in the process of making a discovery. 
Townes, Charles H., "Quantum Electronics, and Sur- 
prise in the Development of Technology," Science, 
Vol. 159, No. 3816 (February 16, 1968). 
Watson, James D., The Double Helix. New York: 
Atheneum Publishers, 1968. One of the discoverers 
of the DNA molecule gives an account of this impor- 
tant scientific finding. 

Wu, C. S., "The Neutrino," a chapter in Theoretical 
Physics of the Twentieth Century, Wiley-Inter- 
science, Inc., New York, 1960. A concise review at 
an advanced level. 



82 




Fig. 4-9 The first successtu, part,c,e accelerator constructed in 1929 by Cockcroft and Walton at the Cavendish Laboratory. 




84 Discoveries in Physics 

Epilogue: How Does Science Progress? 

In the Prologue we suggested that one might describe the processes of 
scientific discoveries in terms of various possible models — among them 
the voyage of discovery model, the army campaign model, the jigsaw 
puzzle model, and the murder mystery model. Let us see if any one of 
these models fits all of our four case histories. Most of us would agree that 
these scientific discoveries cannot all be fitted into any one of these 
models, but our case histories do show elements of one or another of 
them. 

For example, the initial discovery of the cathode ray beam could be 
compared to an unexpected event on a voyage of discovery. Likewise, the 
discovery of the several "transuranic" elements when Fermi first bom- 
barded uranium with neutrons was, in a sense, a product of a "let's try it 
and see what happens" approach. (Actually, of course, Fermi and his col- 
laborators weren't all that aimless-they had good reason to think that 
interesting things might turn up in their experiments, just as a voyager to a 
new country would expect to find new and interesting things.) Herschel's 
discovery of Uranus might be thought of in the same way, except that 
Herschel was. in fact, carrying out a well-planned series of observations to 
map the distribution of stars. He was not on a "voyage of discovery" at 
all - he was trying to chart in a systematic way the already well-known 
heavens. 

The neutrino, on the other hand, was by no means "found." We have 
described the process by saying that It was "invented." It was invented on 
theoretical grounds, in deference to the laws of conservation of energy 
and angular momentum. 

How about the army campaign, the strategy and tactics model? One 
might certainly describe the attempts to detect the neutrino in terms of 
such a model. Impressive resources were required, and the cooperation of 
several men. The probable characteristics of the neutrino had to be 
worked out in terms of physical theory, so that the experimentalists could 
plan their experiments within the limitations of space, time, source 
strengths, detector efficiencies, and the like. Similarly the study of elec- 
tron pair formation by very high-energy gamma rays, shown in the 
Project Physics film "People and Particles, " would also serve as a good 
example of scientific research that, in some ways, fits the army campaign 
model. (But it is also true that much research is not organized on such a 
scale. A one-man research project also involves much careful planning, 
strategy and tactics, but not in the way implied by the model.) 

Both the cathode ray controversy and the understanding of nuclear 
fission can be thought of in terms of the jigsaw puzzle model. Various 
"facts" were found by careful and clever experimentation. The "facts ' had 
to be fitted together, and finally a clear picture emerged. 

But the puzzle model suffers from oversimplicity. In a jigsaw puzzle 
the pieces are all there-you have to sort them out, but presumably you 
have them all to start with. In real-life science, you have to find the pieces, 



Epilogue 



85 



sometimes in the most unlikely places, and you have to interpret them. The 
existence of some of the experimental "facts," for example, in the cathode 
ray controversy, depended very much on certain preconceptions. 
(Lenard's experiments in which he sent the rays through thin foils and 
Hertz' experiments in which he tried to follow the flow of current are ex- 
amples.) One might say also that Droste's experimental search for the 
alpha particles thought to emerge from neutron bombardment of uranium 
was a case of failure to find a real piece of a puzzle (the ionization pulses 
due to fission fragments) while he was looking carefully for pieces that 
didn't really exist (the alpha particles). 

The murder mystery model comes closer, perhaps, to describing the 
process by which Neptune was discovered. There was a genuine mystery: 
what could be causing the strange behavior or Uranus? There were 
various possible solutions to the mystery: interaction with a comet, a pos- 
sible breakdown of the inverse-square law of gravitation, a new planet 
beyond Uranus, and possibly others. The evidence of continued perturba- 
tions continued to accumulate. The two "detectives," Adams and Lever- 
rier, had to use ingenious mathematical techniques and much hard work 
to derive the solution to the mystery. 

The understanding of nuclear fission also involved many of the ele- 
ments of a puzzling mystery. There were peculiar clues, false scents, an 
"obvious" solution too strange to believe, and other elements beloved by 
mystery writers. 

If there is no model that can fit even our four case histories, there is 
certainly none that will work fora// scientific discoveries. Still our models 
have been useful, if only to help us see that certain threads are common to 
two or more discoveries. Moreover, all of them had elements of surprise, 
of occasional confusion, and of delight. Adams and Leverrier, Fermi, Lise 
Meitner, Frisch, J. J. Thomson, Hertz, and all the others all had one thing in 
common —their minds were restless until they had found answers, until 
they could say, "So that is how it works!" 

The scientist, or the potential scientist, will probably find familiar this 
common sequence of surprise, confusion, and delight in discovery — 
either in his own work, or in the scientific work of those he knows. 
One young Nobel Prize-winning physicist was asked why he was a physi- 
cist, and he is said to have replied, "Well, if I knew of some other work that 
was more fun, then I'd do that." There is a creative satisfaction, quite apart 
from whatever usefulness the research may have. An unsolved mystery in 
science cries out to be solved. Personal fame, financial reward, usefulness 
to society— all of these and many more motivations may spur the scientist 
on. He is, after all, an ordinary human being. But there are other paths to 
fame, fortune, and usefulness, so it is the creative tension of the unsolved 
puzzle and the delight in the occasional understanding of nature that 
leads to careers in science. 

But all that is from the standpoint of the scientist, looking at his work 
and at himself. From the viewpoint of the scientific community and society 
at large, there are questions about science that our case studies may help 







86 Discoveries in Physics 

us answer. What is the value of vast and costly laboratories? How are sci- 
ence and technology related? How do scientists communicate with each 
other and with the world? What conditions favor scientific discovery? Why 
do some new discoveries take so long to get accepted? 

Let us consider, for example, this last question, about the acceptance 
of new ideas in science. Why didn't Airy, the Astronomer Royal, rush to his 
telescope to find Neptune when Adams asked him to do so? Why was Ida 
Noddack's suggestion (that uranium atoms might undergo fission) ig- 
nored by Fermi and almost every one else in 1934? Why did Hahn and 
Strassmann take so long to believe their own very impressive chemical 
evidence? 

There is no single answer to such questions. In the first place, busy 
scientists do not have time to consider seriously every idea that comes 
their way — not even every idea they have themselves, let alone those that 
turn up from others who are not in the main stream of research. Rontgen 
was surprised enough by a glowing fluorescent card near his cathode ray 
apparatus to begin to investigate it carefully, and so he discovered x rays. 
Other men before him had observed fluorescence from what must have 
been x rays, but they were busy thinking of other things. One cannot be 
distracted by every intriguing thing that turns up. Airy had the work of his 
observatory carefully scheduled, and he did not want to be interrupted by 
a young man he thought was an upstart with far-fetched ideas. (Admit- 
tedly, Airy is an extreme example. His psychological makeup was such that 
almost no interruption of his schedule was tolerable. But any scientist 
trying to get on with a carefully planned program of research cannot help 
having a certain sympathy for him.) 

But there is a second, and more important, reason why it often takes 
so long for a new idea to be accepted. If a new discovery- and especially a 
new theoretical concept — does not seem to fit into the currently ac- 
cepted patterns of scientific thought, most scientists are not eager to 
take it very seriously. Some textbook prefaces, in describing "the scien- 
tific method," insist that scientists are always very open-minded, 
always willing to discard an old theory or an old concept the very 
minute some apparently contrary observation is made. In actual fact, 
scientists are rather conservative in scientific matters. They have good 
reason to make use of the ideas that have worked well in the past. 

Consider, for example, the current scientific view of the structure of 
atoms. We think of an atom as having a very small nucleus (with a diameter 
of about 10"'- centimeter), with a certain electrical charge and a certain 
mass, surrounded by electrons distributed in orbits or "clouds" in cer- 
tain ways, to make up a total diameter of about lO"'* centimeters. Present 
physical theory can tell us, at least in principle, how the electronic clouds 
are distributed, what sort of light the atom can emit or absorb, what 
forces it can exert on nearby atoms, how it will form molecules, and, in 
certain cases, whether it is likely that the nucleus of the atom will emit an 
alpha particle or some other radiation. Our theory can also predict how 
such an atom will be affected by a magnetic field, how much energy will 



Epilogue 87 

be needed to ionize it, and many other things. In practice, the calculation 
of some of these properties would be very difficult, but in principle the 
behavior of atoms and their nuclei is quite well understood. Now sup- 
pose someone comes along with an awkward experimental observation, 
or some new theory, that does not seem to fit into this beautiful, work- 
able and satisfying picture of the atom. Must this picture be then dis- 
carded? 

The first question scientists probably would ask is, "Who claims to 
have made this discovery?" Few, if any, scientists will waste much time 
trying to check or repeat the observations if the claimant does not have 
some standing in the field. Even if a person has a good reputation in one 
area of science, any really unusual ideas he may put forth in another field 
will not be taken very seriously. When Ida Noddack criticized the logic 
Fermi had used in his original paper in which he claimed to have produced 
some transuranic elements, no one paid much attention. She was a chem- 
ist, and she pointed out flaws in the chemical argument: Fermi and his col- 
leagues had not ruled out all other elements by careful chemical tests. 
Physicists did not take her argument seriously, because they could not see 
any likely way for nuclei to split into large fragments. All previous experi- 
ments, in fact, had shown just the opposite: only very light particles (alpha 
particles, neutrons, protons, beta rays, or gamma rays) were emitted by 
disturbed nuclei. The idea that a nucleus could split into large fragments 
after the capture of a neutron simply did not fit into the prevailing nuclear 
theory. One would sooner expect that an iron cannonball would fly apart 
when hit by a small BB pellet than imagine that a nucleus would undergo 
fission when hit by a slow-moving neutron, and certainly nobody would be 
asked to perform lengthy tests to prove that a cannonball hit by a BB will 
remain intact. So Miss Noddack's argument, though sound from a chemi- 
cal standpoint, was ignored. 

On the other hand, four and a half years later, it was a different story. 
For one thing, as we have seen, mystery had piled upon mystery as more 
and more experiments were done with neutron bombardment of heavy 
nuclei. But Frisch and Meitner did not simply pronounce the magic word, 
"fission." They showed how it made sense out of all the observations, in a 
way that was in accordance with contemporary ideas about the nucleus. 
So the moment the news of Frisch's and Meitner's interpretation of Hahn's 
and Strassmann's results was made public, physicists quite literally could 
not get to their laboratories fast enough to check all sorts of implications 
of the dramatic new idea of nuclear fission. 

Otto Frisch has quoted Niels Bohr as having said, when he was told 
that Frisch and Meitner had suddenly realized how there really could be 
enough energy available for nuclear fission to occur, "Oh, what fools we 
have been! We ought to have seen that before!" But Bohr was too hard 
on himself. It is always easy to look back and see how blind one has been 
to a simple but new idea. 

The moral is not, of course, that scientists must spend all their time 
considering every unlikely idea that pops up. But clearly they must remain 



88 Discoveries in Physics 

open-minded to some degree; they must preserve their sense of curiosity. 
And yet it must be a disciplined kind of curiosity. If our four case histories 
have anything in common, aside from the joy in discovery we have already 
mentioned, perhaps it is that great discoveries and great ideas are most 
often made by men and women who are thoroughly immersed in the best 
scientific experimentation and thinking of their day. They are the ones 
who, in Pasteur's words, arepreparecf for the accidents of discoveries, for 
the hard work, and for insights that produce creative discoveries. Adams 
and Leverrier were magnificently trained in classical mechanics. Reines, 
Cowan, and the other experimentalists who finally "caught" the neutrino, 
were imaginative and creative experimentalists, well prepared to take ad- 
vantage of new technological developments to achieve breakthroughs in 
pure science. Hahn and Strassmann were known to be such impeccably 
careful radiochemists that Frisch and Meitner were able to trust their 
incredible results. 

Let us go on to consider some of the other questions raised earlier in 
this chapter that might be asked about scientific creativity, as viewed 
from that standpoint of society as a whole. What circumstances seem to 
encourage scientific creativity? One might ask, for example, the rather 
simple question of whether the most fruitful work is done in large groups 
or small. Our four case histories provide too small a sampling to give us a 
clear answer. Herschell, Adams, and Leverrier each worked alone. The 
men who made the crucial experiments in the cathode ray controversy 
worked singly or in pairs. Fermi worked with a small group of collabo- 
rators in making his initial discoveries with neutron bombardment of 
nuclei. 

When Pauli and Fermi first produced their theoretical ideas con- 
cerning the existence and nature of the neutrino, they were working indi- 
vidually. But the actual tracking down of that elusive particle experi- 
mentally was quite different — enormously complex equipment was 
needed, and the cooperation of many men. The later experiments on 
nuclear fission also involved large teams. A recent issue of the Physical 
Review Letters, a journal containing brief reports of current research, has 
an average of 3.3 authors per paper, with one paper having ten authors 
and another fifteen. But one will also still find papers with a single author, 
and many of the really important contributions are made in such papers. In 
particular, the kind of "discovery" which is, in fact, a breakthrough 
achieved by looking at old data in a new and creative way is often the cre- 
ation of one man. And while many of the exciting experiments in modern 
science require enormous amounts of equipment and many collaborators, 
it is also true that many significant experiments are thought up, and often 
carried out, by one person. 

But these scientists, whether they work alone or in groups, do not live 
in a vacuum. Almost all of them, nowadays, work in college or university 
laboratories, or in governmental institutes, or in industrial research 
laboratories. There is what might be called "intellectual cross-fertiliza- 
tion" in any good laboratory in which several scientists are working, even 



Epilogue 89 

though they are not all working on the sanne projects. And of course 
there is the wider interplay of ideas among scientists, an interplay which 
takes place by means of a very large and growing number of scientific 
journals and by means of national and international meetings, as well as 
by personal visits. 

Not only does the scientist work in collaboration, or at least in cooper- 
ation, with other scientists; he knows he is often quite dependent on engi- 
neers and other technologists. The interplay between the science and the 
technology of any period is a fascinating area of study in itself — an area we 
have been able to touch upon only briefly in our case histories. In some 
cases a newly developed technique has made a scientific discovery pos- 
sible: better vacuum pumps led directly to the discovery of cathode rays. 
In other cases the gradual development of technological resources made 
it possible to verify or to check some crucial idea. Thus fission reactors, 
scintillation counters, and modern electronic circuits made it possible to 
detect neutrinos experimentally. 

In modern scientific research it often takes time before some creative 
person recognizes that an engineering development whose application 
has so far been mainly technical might provide a new tool or instrument 
forscientific research. Photomultipliertubes were used commercially, and 
for certain research applications, for quite some time before anyone 
thought of using them to detect and measure the very faint scintillations 
caused by single particles in nuclear research. Photographic plates and 
films were available for years before anyone tried to use them to record 
particle tracks in cosmic ray or other high-energy particle research. 

Of course, the interplay between science and technology occurs on a 
two-way street. The modern oscilloscope and television tubes are direct 
descendantsof the early tubes used in cathode ray research -tubes which 
a British statesman in the 19th century described with the words, "How 
beautiful, and how useless!" Lasers, now finding applications in medicine 
and in industry, resulted from what was thought to be pure research on the 
energy levels of the electrons in certain atoms. 

To put this issue another way, one might say that no board of directors 
of a large corporation, or of a national foundation, could have said, in 
1850, "Let's subsidize the discovery of cathode rays" or, in 1895, "Let's 
get someone to discover x rays and radioactivity." The most that any such 
group can do is to decide to spend some fraction of its resources in sup- 
porting research undertaken without specific applications in mind, to 
allocate that fraction to the sort of men and women who have demon- 
strated creative abilities, and to rejoice when knowledge and under- 
standing of nature are increased. Finally, they may hope that now and then 
some useful things will come out of that increased knowledge and under- 
standing. The problem, in other words, faced by a forward-looking nation 
or a forward-looking corporation, is not whether to support pure research, 
but to decide what fraction of its resources should be used for that pur- 
pose - and then to choose the scientists to carry out that research. The 
decision as to what fraction of a nation's or a corporation's resources 



90 



Discoveries in Physics 



should be allocated to pure research is difficult; it must be settled in terms 
of economic and social goals. The choice of which scientists to support is 
even more complex. Case histories of the sort we have discussed, are 
helpful but not determinative. One method of choice is to provide support 
for those who have already shown themselves to be productive, and to 
enable them to surround themselves with younger scientists whose abili- 
ties will develop. 

We have been considering, in these past few pages, some of the ques- 
tions that our case histories might raise in the minds of outsiders, looking 
at the work of scientists. But at least some readers, looking forward to a 
scientific career, may see in these histories of past discoveries a more per- 
sonal goal. They will see that the scientific process is open-ended, and 
that there is excitement in taking part in scientific research. There are lots 
of new experiments to be done, new deductions from old theories to be 
tested, and new theories to be developed. 



Activities 



1 Read a biography of an outstanding scientist 
and categorize his major discoveries according to 
the scheme suggested in this unit. The following 
are some suggested readings: Galileo Galilei 
(Ludovico Geymonat); Sir Isaac Newton (E. N. 
Andrade); Count Rumford, Physicist Extraordi- 
nary (Sanborn C. Brown); Madame Curie (Eve 
Curie); Einstein, His Life and Times (Phihpp 
Frank); Pioneers of Science (Sir OUver Lodge); 
The Double Helix (James Watson); Atoms in the 
Family (Laura Fermi). 

2 Read a novel in which a scientific discovery 
plays an important part, such as The Search (C. P. 



Snow). How does the discovery process compare 
with those described in this unit? 
3 Read James Watson's The Double Helix, and 
then read some reviews of the book. What do the 
book and the reviews tell you about scientists' views 
of the discovery process? Here are some reviews 
written by scientists: 

Science, March 29, 1968 (Erwin Chargaff) 
Nation, March 18, 1968 (Jacob Bronowski) 
New York Review of Books, March 28, 1968 
(P. B. Medaa) 

New Yorker, April 13, 1968 (Jeremy Bernstein) 
Nature, May 18, 1968 (John Maddox) 



Note on Further Reading 



Those who, after finishing this book, wish to pursue 
further the ideas on Discoveries, may wish to con- 
sult the following additional resources: 

1 the specific references hsted at the end of each 
chapter in this volume 

2 one or more of the following books that are con- 
cerned with the process of discovery in the physical 
sciences as reported in historical cases 

3 these articles in the Project Physics Readers. 

Andrade, E. N. da C, Rutherford and the Nature of 
the Atom; Anchor Books, Doubleday and Company, 
Inc., Garden City, New York (1964) 

Armitage, Angus, The World of Copernicus; A 
Mentor Book pubhshed by The New American Li- 
brary of World Literature, Inc., New York, New 
York (1951) Pubhshed under an earlier title: Sun, 
Stand Thou Still; Henry Schuman, Inc. (1947) 



Beveridge, W. I. B., The Art of Scientific Investiga- 
tion; W. W. Norton and Company, Inc., New York 
(1957) 

Brown, Sanborn C, Count Rumford, Physicist 
Extraordinary; Anchor Books, Doubleday and 
Company, Inc., Garden City, New York (1962) 

Caspar, Max, Kepler, 1571-1630 (trans. C. Doris 
Hellman); CoUier Books, New York, New York 
(1962) 

Chalmers, T. W., Historic Researchers: Chapters 
in the History of Physical and Chemical Discov- 
ery; Morgan Brothers, London (1949) 

Cline, Barbara Lovett, Men Who Made a New Phys- 
ics; Signet Book T3745 (1969), also in an earlier 
pubhcation: The Questioners: Physicists and the 
Quantum Theory; Thomas Y. Crowell Company, 
New York (1965) 



Epilogue 



91 



Conant, J. B. and Nash, L., Harvard Case Studies 
in Experimental Science, Harvard University 
Press, Cambridge, Mass. (1957) Two volumes. 

Curie, Eve, Madame Curie: A Biography; 
Doubleday, Doran and Company, Inc., New York 
(1937) 

Eiduson, Bemice T., Scientists: Their Psycholog- 
ical World; Basic Books, Inc., New York (1962) 

Fermi, Laura, Atoms in the Family; University of 
Chicago Press, Chicago (1954) 

Frank, Philipp, Einstein: His Life and Times; 
Alfred Knopf, New York, New York (1967) 

Geymonat, Ludovico, Galileo Galilei: A Biography 
and Inquiry into his Philosophy of Science (trans. 
StiUman Drake); McGraw-Hill Book Company, 
New York (1965) 

Hadamard, Jacques, An Essay on the Psychology 
of Invention in the Mathematical Field; Dover 
Pubhcations, Inc., New York (1945) 

Hahn, Otto, Otto Hahn: A Scientific Autobio- 
graphy; Charles Scribner's Sons, New York, New 
York (1966) 

Hanson, Norwood Russell, Patterns of Discovery; 
The University Press at Cambridge, London (1958) 

Jaffe, Bernard, Michelson and the Speed of Light; 
Anchor Books, Doubleday and Company, Inc., 
Garden City, New York (1960) 

Jungk, Robert, The Big Machine (trans. Grace 
Marmor Spruch and Traude Wess); Charles 
Scribner's Sons, New York (1968) 

Koestler, Arthur, The Watershed: A Biography of 
Johannes Kepler; Anchor Books, Doubleday and 
Company, Inc., Garden City, New York (1960) 

Kuhn, Thomas S., The Structure of Scientific Rev- 
olutions; The University of Chicago Press, Chicago 
(1964) 



Manuel, Frank K., A Portrait of Isaac Newton, 
Belknap Press, Cambridge (1968) 

Moore, Ruth, Niels Bohr; Alfred Knopf, New York, 
New York (1966) 

More, Louis Trenchard, Isaac Newton; Dover Pub- 
hcations, Inc., New York, New York (1934) 

Roe, Anne, The Making of a Scientist; Dodd Mead, 
New York, New York (1953) 

Romer, Alfred, Ed., The Discovery of Radioactivity 
and Transmutation (Classics of Science Series, 
Volume II); Dover Pubhcations, Inc., New York 

Romer, Alfred, Ed., Radiochemistry and the Dis- 
covery of Isotopes (Classics of Science Series, Vol- 
ume VI); Dover Pubhcations, Inc., New York, New 
York, (1970) 

Rukeyser, Muriel, Willard Gibbs; Doubleday, Doran 
and Company, Inc., Garden City, New York, (1942) 
Segre, Emiho, Enrico Fermi: Physicist; University 
of Chicago Press, Chicago, (1970) 

Taton, R., Reason and Chance in Scientific Discov- 
ery (trans. A. J. Pomerans); Science Editions, Inc., 
New York (1962) 

Thomson, George, J. J. Thomson and the Caven- 
dish Laboratory in His Day; Doubleday and Com- 
pany, Inc., Garden City, New York (1965) 

Wertheimer, Max, Productive Thinking; Harper 
and Row, New York (1959) 

Williams, L. Pearce, Michael Faraday; Basic 
Books, Inc., New York (1965) 

Wood, Alexander, Thomas Young: Natural Philoso- 
pher; The University Press, Cambridge (1954) 



From the Project Physics Readers 



Reader 1 

How to Solve It G. Polya 
Representation of Movement 



Gyorgy Kepes 



Reader 2 

Kepler on Mars J. Kepler 
The Garden of Epicurus A. France 
The Boy Who Redeemed His Father's Name 
Terry Morris 

Reader 3 

The Law of Disorder George Gamow 
Silence, Please Arthur C. Clarke 



Reader 4 

Popular Applications of Polarized Light 

Wilham A. ShurclifF and Stanley Ballard 

The Invention of the Electric Light Matthew 

Josephson 

On the Induction of Electric Currents 

James C. Maxwell 
A Mirror for the Brain W. Grey Walter 

Reader 5 

Parable of the Surveyors 
Wheeler 



E. F. Taylor & J. A. 



Reader 6 

Some Personal Notes on the Search for the 
Neutron Sir James Chadvdck 
Success Laura Fermi 



INDEX 



Abelson, wavelengths of fission 

products, 56 
Accelerators, 76-77 
Actinium, 50-51 
Adams, John Couch, motion of 

Uranus, 12-15 
Airy, George, Neptune discovery, 14 
Alpha particle, 47, 51-53, 60 
Alpha rays, 63 
Antineutrino, 72-74 
Asteroid periods, 19 
Asteroid trail, 12 
Astronomical unit, 14 
Atom(s), electrons in, 43-44; recoil 

momentum, 72 

Barium, and nuclear fission, 53, 55 
Becker, neutron discovery, 48 
Beta ray, 63; decay, 65-67, 68-69; 

emission, 48 
Bhnk comparator, 13 
Bode, Johann, elements of Uranus 

orbit, 7-8 
Bode's Law, 14-15 
Boethe, neutron discovery, 50 
Bohr, Niels, atomic theory, 43-44; 

nuclear fission, 54-56 
Bouvard, Alexis, motion of Uranus, 

8-9, 11 

Carrier, 50 

Cathode ray(s), discovery, 1, 33-34; 

particle properties, 36-41 ; 

particle theory, 35-37, 39-41 ; 

uses; 44; wave theory, 34-35, 

38-39 
Chadwick, James, beta ray 

spectrum, 65; neutron 

discovery, 50 
Chain reaction, 56-57 
Charge-to-mass ratio, 41, 43-44 
Charged particles, 41, 43-44, 68 
Comets, orbits, 7 
Conjunction of planets, 11 
Conservation of angular 

momentum, 66-68 
Conservation of energy, 65-66 
Continuous spectrum, 65-67 
Cowan, Clyde, and Frederick 

Reines, neutrino experiment, 

62, 69-71 
Crookes, Sir WiUiam, cathode ray, 

35-36 
Cross section of process, 69 

Danby, Gordon, muons, 75, 78 
Davis, Raymond, antineutrino, 

72-74 
Doppler shift, 36 
Droste, alpha particles, 55, 60 

Einstein, theory of relativity, 56 

Electrometer, 38 

Electrons, in atoms, 43-44; as 

charged particles, 41-44 
Electron volt, 53 
EUiptical orbit(s), 7 
Energy, and beta decay, 65-68 
Excited state nucleus, 48 
Experimental detection, 68-69 

Fermi, Enrico, chain reactions, 56; 

neutrino, 67-68; uranium 

isotopes, 46, 48-49, 58 
Frisch, Otto, nuclear fission 

discovery, 54 

Galle, Johann, Neptune discovery, 

13 
Gamma rays, 54; emission, 48; 

relative intensity, 64 
Gauss, Karl Friedrich, elements of 

elhptical orbit, 7 
Graphic computer, 28-30 
Gravitation, inverse square law, 9; 

Newton's second law, 23-24; 

92 



Newton's theory of universal, 5, 
9, 12; See also Perturbations 

Hahn, Otto, isomerism, 51-53; 

nuclear fission discovery, 53-55; 

transuranium elements, 49-50 
Herschel, William, Uranus 

discovery, 6-7; telescope, 31 
Hertz, Heinrich, wave theory of 

cathode ray, 38-41 

Indium isomers, 50 
Isomerism, 51-54 
Isotopes, 48-49 

Johot-Curie, Irene, chain reactions, 
56; uranium fission, 50-51, 58 

Jupiter, orbit, 14; perturbations, 
10-11 

Kepler, Law of Areas, 10 
Kirkwood gaps, 19 
Kowarski, chain reactions, 56 
Krypton, 55 

Lanthanum, 50-51, 53, 55, 58 
Laplace, elements of elliptical 

orbit, 7 
Lederman, Leon, muons, 75, 78 
Leverrier, Urbain Jean Joseph, 

motion of Uranus, 12-15 
LexeU, elements of elliptical orbit, 7 
Line spectra, 64 
Linear momentum, conservation, 

71-72 
LoweU, Percival, search for Pluto, 

17-18 

Mean free path, 35 

Meitner, Lise, nuclear fission, 54, 

55-56; transuranic elements, 

49-50 
Mercury, orbit, 14 
Mesons, 74 
Muons, 74-75, 78 

Neptune, discovery, 1, 5, 11-14,63; 

orbit, 14-16; perturbations, 

11-14; sateUites, 13 
Neutrino, absorption experiment, 

72-74; antineutrino, 72-74; 

detection, 68-69; discovery, 63; 

emission experiments, 68-72; 

emissions from sun and stars, 

78; "invention," 67-68; Unear 

momentum conservation, 

71-72; muons, 74-75, 78; 

properties, 1 ; reactions 

producing, 68-71 
Neutron(s), bombardment, 48; 

chain reactions, 56-57; 

discovery, 48 
Nuclear bomb, 57 
Nuclear energy, peaceful uses, 57 
Nuclear equation, 53, 56 
Nuclear fission, discovery, 47, 

53-55, 58; study, 55-57 
Nuclear reaction, equation, 50, 53 
Nuclei, radioactive, 64 
Nucleus, bombardment, 48; stable, 

56; See also Atom 
Newton, second law, 23-24; theory 

of universal gravitation, 5, 9, 12 
Noddack, Ida, uranium isotopes, 

49,58 

Orbit(s), comet, 7; elhptical, 7; 
radii, 14-16 

Particle, detection, 68-69 
Particle accelerators, 76-77 
Particle theory of cathode ray, 

35-37, 39-41 
Pauh, Wolfgang, neutrino 

discovery, 67 
Perrin, Jean, cathode ray, 39 



Perturbations, 10-14; of small 

planet experiment, 22-29 
Photoelectric effect, 41 
Photographic detection of objects, 

13 
Pickering, W. H., search for Pluto, 

17-18 
Planets, conjunction, 11; diameters 

compared wdth Earth, 20; 

discovery, 1, 5-8, 11-14, 17-18; 

mass compared with Earth, 20; 

motion, 8-11, 14-16; 

perturbations of motion, 10-14; 

radii of orbits, 14-16 
Pliicker, Juhus, Plucker tube, 

33-34 
Pluto, discovery, 1, 5, 17-18 
Principia, 5 

qlm experiment, 40-42 

Radioactive decay, 55-56; products 

of, 63-64 
Radium, production, 60 
RecoU momentum of atom, 72 
Reines, Frederick and Clyde 

Cowan, neutrino experiment, 

62, 69-71 

Saturn, orbit, 14; perturbations, 

10-11 
Savitch, Paul, uranium fission, 

50-51, 58 
Schuster, Arthur, cathode ray 

particle, 36-37, 41 
Science, aspects, 2-3 
Scientific discovery, models for, 1 , 

84-90; themes in, 80 
Scintillation, 69 

Scintillation counter detector, 62 
Scintillation tank, 70-71 
Spark chamber, 78, 79 
Spectrum, beta ray, 65-68; 

continuous, 65-67; gamma ray, 

64; line, 64 
Stable nuclei, 56 
Stars, scientific models, 1 
Stellar field photographs of Pluto, 

17-18 
Strassmann, Fritz, isomerism, 

51-53; nuclear fission 

discovery, 53-55; transuranic 

elements, 49-50 
Strontium, 55 

Thomson, J. J., 32; particle theory 
of cathode ray, 39-41 ; qlm 
experiment, 42 
Thorium, bombardment, 49, 52 
Tombaugh, Clyde, Pluto discovery, 

17-18 
Trans-Neptunian planet, 21 
Transuranic elements, 48-55 

Uncharged particles, detection, 

68-69 
Uranus, discovery, 1, 5-8 
Uranium, fission, 50-51 ; isotopes, 

48-49 
Uranus, orbit, 7-14, 15-16; 

perturbating forces, 10-14; 

sateUites, 6, 9; variation in 

motion, 8-14 

von Halban, chain reactions, 56 

Walker, Sears, Neptune orbit, 15 
Wave theory of cathode rays, 34-35, 
38-39 

X rays, identification of radioactive 

fission products, 57-58 
Xenon, 55 

Yttrium, 50-51, 55, 58 

Zeeman, charged particles, 43