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Full text of "Project Physics Resource Book Discoveries in Physics"

,m 




The Project Physics Course 



Resource Book 



B 



A Supplemental Unit 



Discoveries in Physics 




Resource Book 

Supplemental Unit B 



Discoveries in Physics 

by 



David L. Anderson 

Oberlin College 



Published by 
A Component of the (YflX) '^^'-"^' R'NEHART AND WINSTON, Inc. 
Project Physics Course [nt) 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 Resource Book is one of the many in- 
structional materials developed for the Project 
Physics Course. These materials include Texts, 
Handbooks, Resource Books, Readers, Tests, 
Programmed Instruction Booklets, Film Loops, 
Transparencies, 16mm films and laboratory 
equipment. Development of the course has 
profited from the help of many colleagues listed 
in the text units. 



Copyright (r) 1973, Project Physics 

All Rights Reserved 

ISBN 0-03-089481-6 

34567 005 987654321 

Project Physics is a registered trademark 



Table of Contents 



NOTES ON THE TEXT 



CHAPTER 1 


2 


EXPERIMENT 


2 


CHAPTER 2 


4 


CHAPTER 3 


5 


CHAPTER 4 


5 



ANSWERS TO END-OF-CHAPTER QUESTIONS 



CHAPTER 1 
CHAPTER 2 
CHAPTER 3 
CHAPTER 4 



6 

8 

11 

13 



NOTES ON THE TEXT 



PROLOGUE 

How do scientific discoveries occur? How do 
scientists go about solving problems? The four 
examples in this unit are quite different. Their 
careful study should lessen any faith in a naive 
idea that there is THE scientific method. Note 



the questions raised in the text about the condi- 
tions and timing of scientific discoveries. Class 
discussions centering on these questions will 
emphasize the major points in this unit. 



Notes on Chapter 1 

CHAPTER 1 

The film loop "Kepler's Laws" and the 
transparencies T-17, "Orbit Parameters," and 
T-18, "Motion Under a Central Force" may be 
useful for a review of planetary motion. 

Page 6. Notice that Herschel was engaged in 
a systematic count of the stars visible in his 
telescope. Also, he was alert to unusual objects 
that moved into his field of view. 

Page 7. Notice also that Johann Bode, whose 
name appears later for another reason, used the 
orbit computed by Lexell as the basis for 
searching old records that did contain earlier 
positions observed for Uranus. Often careful 
records can be searched for results unantici- 
pated by the recorder. 

Page 8. A variety of possible explanations 
were postulated to account for the scandalous 
deviations of Uranus' position from those pre- 
dicted by Bouvard. Discussion of these possi- 
bilities, and others that students may propose, 
illustrate the initial qualitative screening of ideas 
and proposals within scientific work. Only after 
the possibility of an outer perturbing planet was 
fairly well accepted would anyone undertake the 
difficult task of trying to predict its position. 



Page 12. The offering of a prize by the Uni- 
versity of Gottingen was a fairly common means 
of attracting able men to work on a problem. 
Now such prizes are rarely, if ever, offered; 
they are not needed. 

Page 12. Despite the prize for a mathematical 
prediction of the planet's position, both Adams 
and Leverrier had difficulties getting anyone to 
search near their predicted positions. Galle, 
having at hand the unpublished star map of that 
region, had an advantage over the British ob- 
servers. The systematic approach used by the 
British observers would have been, indeed had 
already been, successful; but was costly in 
terms of time for observing and reducing the 
records. 



Page 14. Bode's law for the spacing of the 
planetary orbits deserves a note here. Like 
Kepler, Bode sought a pattern among the orbits. 
Despite the "forced fit" for Mercury, Bode's 
pattern fits fairly well. Since neither the 
mass nor solar distance of the suspected 
planet was known, both Adams and Leverrier 
assumed a solar distance by extrapolating 
Bode's law. As appears later, neither Neptune 
nor Pluto are near the solar distances 
predicted by Bode's law. 



NOTES ON THE EXPERIMENT, PAGE 22 



The method of graphical iteration, used by 
Newton in Proposition 1 of the Principia and 
reproduced as Article 10 in Reader 2, was used 
in Experiment 21 (Experiment 11-9 in the revised 
Student Handbook) to develop an orbit for a 
"comet." If your students have not done Experi- 
ment 21, sufficient details are given here so 
they can proceed on this more complex analysis. 
The approach uses the idea of repeated blows 
toward a center of force at regular intervals. By 
vector addition the continued inertial motion in 
a straight line is combined with the effects of the 
accelerations to yield a new velocity vector and 
displacement for the next iteration interval. If 
two large masses are simultaneously attracting 



a small body in motion, as in this problem, the 
two attractions can be combined by vector 
addition, as in Figures lb, 2a, and 2b of the text. 

The initial conditions of the masses: their 
relative positions and their velocities, are arbi- 
trary. However, for this experiment, which must 
yield quantities which can be graphed by a 
student, the initial conditions are rather critical. 
Many trial conditions resulted In orbits which 
threw the small planet out of the planetary 
system. 

The scale of the diagram is important. If it 
is too small, the vector additions are very diffi- 



Notes on Experiment 



cult to make accurately. If it is too large, the 
graph becomes unwieldy. Since the large planet 
is for convenience put initially into a circular 
orbit at 4 AU from the sun, it moves at a uniform 
rate in the circular orbit unperturbed by the 
small planet. The data for the two initial orbits 
are: 

Planet 
Large Small 



4.0 



3.1 



0.0301 



Orbital radius, R, in AU 
Period, T, in days 

(365 XR 3/2) 2920.0 1990.0 

60/T. fractional period 

per iteration interval 0.0205 

Degrees per 60 days 

(360 X 60/T) 7.40 10.84 

Speed in AU/60 days 0.516 0.586 

Scaled speed/60 days 1.29 inches 1.47 

3.28 cm 3.72 



doing the experiment as outlined in the text, 
they may make a second analysis with different 
starting conditions. Twenty iteration steps are 
recommended because that carries the small 
planet through sizable orbital changes to a 
point where the perturbations of the large planet 
become negligible. The remainder of the new 
orbit can be approximated from the positions 
given for S 21, S 25, S 28, S 29, and the 
approximate positions of perihelion and 
aphelion. Note that the angles to these positions 
are to be laid off clockwise from the sun-small 
planet line through the starting position, S 1. 

Our plot gave the following answers to the 
questions at the end of the experiment: 

1. Average distance of the small planet 
from sun (the semi-major axis of the new orbit) 
as 2.25 AU. 



The graphs for the values of the displace- 
ment as a function of R should be drawn with 
some care. By assuming a mass for the large 
planet of 1/100 of the sun's mass, the relation 
between the two accelerating effects at the same 
distance are 1:10; 



planet 



/?2 



M. 



M,' ^'"""^^ = 100' 

S 



F. 100 ft: M. 



WhenFp = F„10flp = fl,. 

Values for these graphs are given in inches and 
centimeters for graphing the R ws F curves in 
either set of units. Graph paper subdivided in 
1/20 inch or 1/10 cm units is easy to use and 
leads to higher accuracy. 

Predicted unperturbed positions for the 
small planet are important to emphasize the 
effects of the perturbations caused by the large 
planet. Selection of the starting places, as 
indicated in Figure 4 of the text is important. 
However, some brave students may wish to 
choose other starting places; or, if they enjoy 



2. The new period is 3.35 years (2.25^ -). 

3. The eccentricity is about 0.45; 
e = c/a = 1/2.25. 

4. This is a temporary orbit for the small 
planet. The large planet will continue to attract 
it and intermittently change its orbit. This occurs 
for the orbits of the asteroids and short-period 
comets which come near Jupiter every few 
cycles. 

5. The small planet will come fairly close 
to the large planet after only 6 years. This is an 
example of the "chase problem" discussed in 
Unit 2 of the text. There the frequency, f, of 
close approaches, is given by /^l = ^s — ^l- '"^ 
terms of the periods, T, this is 1 /Tsl = 1 /7"s — 
1/7l, which upon substituting the periods be- 
comes 1 /7sL = 1 /3.35 - 1 /8, or 0.1 73. Hence 
Tsl is about 5.8 years until another close ap- 
proach. Small perturbations will continually 
modify the orbit of the small planet slightly. 

6. After point S 3, the small planet would 
slow down and fall behind the predicted posi- 
tions. Compare the perturbed and the un- 
perturbed positions on the plot. 



Notes on Chapter 2 



7. On the plot between S 1 and S 4 the 
small planet is being accelerated, just as 
Uranus was by Neptune before 1822. Between 
points S 4 and S 15 the small planet is retarded 
in its motion and is pulled outward toward the 
large planet. Its orbit is drastically changed. 
After point S 15 the effect of the large planet 
diminishes rapidly as the small planet moves 
along its new orbit, 

CHAPTER 2 

Page 33. Technological developments allowing 
much lower pressures in evacuated tubes per- 
mitted new experiments on the current-carrying 
characteristics of gases at low pressures. The 
gas discharge tubes (Plucker tubes) used in 
the lab as the source of gaseous spectra have 
relatively high pressure. The discovery of the 
strange greenish glow in discharge tubes was 
followed by a wide variety of experimentation. 
This is typical — mapping the territory of the 
phenomenon, finding the conditions which were 
stable, and those which influenced the newly 
found phenomenon. 

Page 34. Even as new experimental results 
were being found, possible explanations were 
proposed. In this case only two possibilities 
were proposed; either the rays were electro- 
magnetic, or they were corpuscular. 

Page 36. Now Schuster proposes a modifica- 
tion of Crooke's particle proposal, perhaps the 
particles are charged fragments of molecules. 
The role of analogy is worth noting. His analysis 
for the derivation of q/m is simple and both 
B and R can be measured rather accurately. His 
estimation of v at least bracketed the range for 
q/m. Transparency T-32 "Magnetic Fields and 
Moving Charges" could be used here for review. 

Page 38. The work of Hertz illustrates how, as 
with Schuster and later Thomson, a basic as- 
sumption shapes the nature of the experimental 
questions. As is observed later, the mounting of 
the collecting can outside rather than inside the 
evacuated tube was an unfortunate choice by 
Hertz. Notice also the technical difficulties of 



Hertz: electric field too weak, and the high 
conductivity of the residual gas. 

Perhaps here is a useful place to emphasize 
the point that any experimental set-up will 
always give some results, even if it is "no 
reaction." Many assumptions go into the design 
of an experiment and the selection of the instru- 
ments to be used from those available. The 
interpretation of the experiment depends upon 
what the inquirer expected. In many instances 
later results reveal that because unexpected 
factors were operating, the experimenter came 
to unjustified conclusions. 

Page 41. Refer to Experiment 43, "The Photo- 
electric Effect." (Experiment V-1 in the revised 
Student Handbook.) 

Page 41. Three possible explanations existed 
for the value of 1840 for q/m. Perhaps students 
would wish to examine the three and propose 
their reasons for agreeing with Thomson that 
the size, and probably the mass, of the cathode 
ray particle was very small, although it carried 
the same charge as a hydrogen ion. 

Page 41. The discoveries of photoelectricity 
and X rays, occurred during studies of cathode 
rays. The discovery of radioactivity by Becquerel 
occurred during a study of x rays. Thus the 
investigations of cathode rays led to several 
new lines of evidence about atomic behavior 
and structure. Neither the scientific nor the 
applied consequences of the cathode ray studies 
could have been anticipated. 

Page 42. This special page provides more 
details about the procedure used by Thomson 
in 1897 to extend Schuster's analysis. The 
magnetic and electrical forces are applied 
simultaneously and balanced to produce a 
straight beam from which v could be derived. 

Page 43. Reference could be made to Experi- 
ments 41 "The Charge-to-Mass Ratio for an 
Electron," and to Experiment 42 "Measurement 
of Elementary Charge." (Experiments V-3 and 
V-4 in the revised Student Handbook.) 



Notes on Chapter 3 



Reference to Experiment 44 "Spec- 
troscopy" (Experiment V-6 in the revised 
Student Handbook) would remind students of 
their experiences with line spectra. 

Film loop "Rutherford Scattering" is re- 
lated to the development of the ideas. 

CHAPTER 3 

Teaching Aids likely to be useful with this 
chapter are: 

Transparencies T-42 Radioactive Disintegration 

Series 
T-43 Radioactivity Decay Curves 
T-44 Radioactivity Displacement 

Rules 
T-46 Chart of Nuclides 
T-47 Nuclear Equations 

Film loop "Collisions with an Unknown Object" 
and reference to Experiment 46 "Range of 
a, 13, and 7 Particles," and Experiment 47 (C) 
"Measurement of a Half-Life." (Experiments 
VI-2 and VI-3 in the revised Student Handbook). 

The film "People and Particles" is es- 
pecially appropriate to show in conjunction 
with Chapters 3 and 4 of this Supplementary 
Unit. 

The film "The World of Enrico Fermi" is 
also appropriate for showing with Chapter 4. 

Page 47. As the text makes clear, the dis- 
covery of nuclear fission could have been made 
at any time between 1934 and 1939, but it was 
not. The experimental evidence was inconclu- 
sive, but the possibility of an atom breaking 
into two medium sized parts was almost 
unimaginable. 

Page 48. The behavior of atoms which cap- 
tured a neutron of low energy (a slow neutron) 
seemed to be well known. One beta particle 
emission resulted in a stable daughter nucleus. 

Page 50. Again, the experiments of Irene 
Joliet-Curie and Paul Savitch, of Hahn and 
Strassmann, of Braun, Preiswerk and Scherrer, 
and of Droste illustrate the difficulties of ex- 



perimental work and the influences of assump- 
tions upon the equipmental design. 

Page 54. In line with the comment above, note 
the caution in the statement by Hahn and 
Strassmann: "A series of strange coincidences 
may, perhaps, have led to these results." 

Page 54. Meitner and Frisch benefited from 
some theoretical suggestions by Bohr about 
atomic nuclei being like liquid drops, an 
unusual but highly important analogy. The 
suggestion by Hahn and Strassmann that 
uranium hit by neutrons might actually split 
into two major parts with the release of great 
energy, plus the calculations by Meitner and 
Frisch were enough to open a whole new line 
of interpretations and experimentation. What 
had been confusing could now be interpreted. 
This illustrates well the generative power of a 
new idea. 

Page 57. The self-imposed decision to stop 
publishing papers about nuclear fission was 
remarkable. As early as 1940, nuclear scientists 
realized the enormous military potential of a 
fission weapon. They wished to contribute no 
information to the enemy who probably would 
attempt to develop such a weapon. Stopping 
publication was a dramatic example of the 
social concern of these scientists. 



CHAPTER 4 

Page 63. This chapter stresses the faith 
physicists have put in the general conservation 
laws. To save them, a new particle was 
"invented." 

Page 65. The peculiar continuous energy 
spectra of beta rays having all energies up to 
some maximum appeared to violate the con- 
servation laws for energy and momentum. 

Page 67. Pauli proposed a new particle with 
certain properties, a "might be like this." Fermi 
used the new quantum mechanics to develop a 
theory about the particle and to explain the 
beta ray spectrum and the missing momentum. 



Answers to End-of-Chapter Questions 



Thus an idea proposed by one man was 
elaborated by another. 

Page 68. While an experiment to detect 
neutrinos had been proposed, its application 
had to wait until 1956 when newly developed 
nuclear reactors would produce a sufficient 
supply of beta decays. Very sensitive scintilla- 
tion counters and complex computer circuitry 
were also essential in detecting reactions and 
ruling out events having other causes. Problem 
4.11 illustrates the mathematics of the analysis. 
You may wish to discuss with the students the 
diversity of complex apparatus and the theoreti- 
cal assumptions which lay between the sup- 
posed production of neutrons by neutrinos 
Eq. 4.3, on page 69, and the conclusion that 
the predicted events had actually occurred. 

Page 72. Problem 4.10 illustrates the calcula- 
tion of recoil energy, which is rarely above 
100 eV. The sketch in the margin of the text, 
page 72, illustrates the vector analysis for 
momentum conservation when the nucleus 
recoils upon emission of a beta ray and perhaps 
also a neutrino. 

Page 73. The experiment by Davis is one of 
the relatively few examples of a significant 



conclusion from a negative observation. His 
experimental design and operative care were 
so great that the absence of evidence for argon 
37 was accepted as evidence for the existence 
of antineutrinos. 

Page 75. The equations for the Danby and 
Lederman experiment are: 



or 



(a) v^ + P^e-, 



(b) vfi + P 



if i- = I'fi 



(4.7) 



(4.8) 



Since no electrons were produced, but about 
50 muons were recorded, the reaction of 
equation (b) seems to be occurring, while that 
of equation (a) is not. 

Page 78. The acceptance of neutrinos which 
have such very small capture cross-sections has 
led to changes in the mechanism considered 
possible within stars. Thus the theory to ac- 
count for supernovae has been reexamined. 
Probably the detection of neutrinos from rela- 
tively nearby supernova, such as that which 
formed the Crab nebula in Taurus in 1054 AD, 
is a task unlikely to be undertaken because of 
the size and cost of the equipment. 



ANSWERS TO END-OF-CHAPTER QUESTIONS 



CHAPTER 1 

1.1 The discovery of Uranus was an ac- 
cident in the sense that Herschel, when he 
found it, was not looking for a new planet. 

Accidental aspect of the discovery of 
Neptune: The elements of Neptune's orbit, as 
calculated by Adams and by Leverrier, were in 
error, but happened to predict the position of 
the planet precisely enough for it to be found. 
The errors in the elements were shown by later 
calculations when more complete data were 
available for the positions of Neptune. 



Accidental aspects of the discovery of 
Pluto: 

(a) Faintness of Pluto's image on the 1919 
plates, so that it was overlooked at that time. 

(b) The perturbations of Uranus which 
were thought to have been caused by Pluto 
may not, in fact, have really been due to Pluto 
(which turned out to have a very small mass). 
Nevertheless, they led to "predictions" which 
led Tombaugh to find Pluto. 



6 



Answers to End-of-Chapter Questions 



1 .2 In what way or ways was the time 
ripe for the work of Adams and of Leverrier? 
(a) Uranus had been observed long enough for 
the residuals of its motion, particularly since its 
conjunction with Neptune in 1820, to be large 
enough to be a major problem, (b) Since the 
publication of Newton's Principia in 1685, many 
mathematicians, astronomers, and physicists 
had worked out highly ingenious techniques for 
deriving orbits and computing the perturbing 
effects acting between planets. Thus, the 
analytical tools were available. 



Relative Max. forces on Uranus by Neptune = 

18 



11.02 



= .149 



1.64 



95 

Saturn— —= 1.05 

9.52 

, Neptune 0.149 „ „„^ 
Force on Uranus by . .. — = -n:r-r = 0.091 



Jupiter 1.64 
Neptune 0.149 



Saturn 



1.05 



= 0.142 



1.3 The maximum force exerted on 
Uranus by Neptune is 14% of that exerted by 
Saturn, and 9% of that exerted by Jupiter. 
(It is approximately 15 times that [at the least] 
exerted by Piuto on Uranus. One says "at the 
least" because the mass of Pluto is not well 
known, but is certainly no more than that of 
the Earth.) 







Avg. 


Least 






Solar 


Dist. 






Dist. 


Uranus 


Jupiter mass 


318 earth's 


5.2 AU 


13.9 


Saturn mass 


95 earth's 


9.6 


9.5 


Uranus mass 


15 earth's 


19.1 





Neptune mass 


18 earth's 


30.1 


11.0 



1 .4 The gaps in the periods of asteroids 
occur at certain fractions of the period of 
Jupiter, at what are called resonant periods. 
Evidently the repetition of similar perturbations 
at frequent conjunctions changes the asteroid 
orbits to ones which are non-resonant which 
the asteroids then follow for longer intervals. 

1.5 See Table at the bottom of the page. 

1 .6 Angular Diameter of Neptune 

= (28 X 103)/29.1 AU) (93 X 10« mi/AU) = 
1.04 X 10- rad (206,265 "/rad) = 
2.1 seconds of arc 

1.7 Student's discussion including per- 
haps clear statement of premises which seem 
possible, knowledge of available data, concern 
for predicting new observations, background of 
the writer, etc. 



1.5 



(1) 


(2) 


(3) 


(4) 


(5) 


(6) 


(7)* 




Relative 


Dist. from 


(Diam.)- 




(Area) 


Relative 


Planet 


diameter 


sun, A.U. 


rel. area 


(Dist.)- 


(Dist.)2 


Brightness 


Mars 


0.52 


1.52 


0.27 


2.30 


0.117 


0.475 


Jupiter 


10.97 


5.2 


120. 


27.0 


4.45 


0.238 


Saturn 


9.03 


9.6 


82. 


92.0 


0.89 


0.012,1 


Uranus 


3.72 


19.6 


13.8 


384 


0.36 


0.000,104 


Neptune 


3.38 


30.1 


11.4 


910 


0.0125 


0.000,014,7 


Pluto 


0.45? 


39.5 


0.21 


1600 


0.00013 


0.000,000,086 



* On the assumption that all planets reflect the same fraction of incident light. 



Answers to End-of-Chapter Questions 
CHAPTER 2 

2.1 Evidence that cathode rays are not 
electromagnetic waves: 

(a) They are deflected by magnetic fields. 
Electromagnetic waves are not. For example, 
a flashlight beam is not deflected when it is 
sent between the poles of a strong magnet. 
Radio and light waves are not deflected by the 
earth's magnetic field, which, though weak, 
extends very far into space. Gamma rays are 
not bent by strong magnetic fields, while alpha 
and beta rays are. 

(b) They convey electric charge, as shown 
by the experiments of Perrin and Thomson. 
Electromagnetic waves do not convey charge. 

(c) Cathode rays are deflected by strong 
electric fields, as shown by Thomson's experi- 
ments and, of course, by many modern cathode 
ray oscilloscopes. Electromagnetic waves are 
not deflected by electric fields. 

2.2 At the time of J. J. Thomson's ex- 
periments there was little direct information 
about the actual size of the electron's charge 
compared to that of the hydrogen ion. The 
cathode ray experiments suggested that the 
ratio of the charge to the mass of the cathode 
ray particles was about 1800 times the cor- 
responding ratio for hydrogen ions. One 
needed evidence for the comparative masses 
of electrons and ions in order to make use of 
the ratio measurements. Thomson suggested 
that Lenard's experiments indicated that the 
size (and presumably the mass) of cathode ray 
particles (i.e., electrons) was much smaller 
than that of atoms. Further, the Zeeman effect 
indicated that electrons are contained within 
atoms, and therefore, must be smaller than 
atoms (or ions). As the view developed that 
ionization was the result of adding or sub- 
tracting electrons from neutral atoms, then of 
course the equivalence of the charges followed 
automatically. 

2.3 The time was ripe for the discovery 
of the electron in the 1890's because 



(a) The technology needed was available: 

(1) Good vacuum pumps. 

(2) Well-developed glassblowing tech- 
niques, including methods for making 
metal-to-glass seals for electrodes. 
(This was not mentioned as such in 
the text, but was implied for the work 
of Perrin, Thomson, etc.) 

(3) Circuits for the production of high 
voltages and instruments for the 
measurement of very weak currents 
were available. 

(4) Spectroscopic techniques of good 
resolving power (for Zeeman effect 
measurements). 

(b) Many scientists at the time were in- 
terested in the problems raised by investiga- 
tions in the conductivity of gases under low 
pressure, and of the optical spectra produced 
by such gases. 

(c) The controversy over the nature of 
cathode rays stimulated interest in the field. 

2.4 (a) Where the effects of the electric 
and magnetic fields cancel, we have 



qE = qvB, or v = — , and 

B 

^ V V 

Since E = -;, 1^ = 7^-7; 
d Bd 



so v = 



200 volts 



1.0 X 10-3 



N 



amp-m 
2.0 X 10" m/sec 
Nm coul 



X 0.01 m 



/volt • amp _ coul sec _ m \ 
V N ~ N ~ sec/ 

(b) When the magnetic field acts alone, a 
circular orbit results, and 

mv- q V 



m 



2.0 X 10" 



m 
sec 



1.0 X 10-'' 



N 



ampm 
= 1.8 X IQi^ coul/kg 



X 0.114 m 



8 



Answers to End-of-Chapter Questions 



/am 



p-m 



coul 
sec 



m 



sec 



kgm 
sec- 



sec 



coul 



* The MKSA unit for B is N/amp. m and is now called the tesia 
(after the electrical engineer Nikola TesIa). 

2.5 (a) Since V - A(PE)/g by definition, 
then qV = A{PE). Since the electrons start from 
rest, then A(PE) will equal their gain in kinetic 
energy, or qV = V2mv-. The value of v is then 



- C^Y^ 



"n^y 



Since V = 5000 volts, or 5000 joules/ 
coulomb, V = (2 X 1.76 X 10" x 5.0 x lO^)'/^ = 
4.2 X 10' m/sec. 

(b) E = V/d = 3x10^ volts/meter = 
3 X 10* newtons/coulomb. 

(c) F = 3 X 10* newtons/coulomb x 
1.6 X 10-1" coulomb = 4.8 x lO-^' newtons. 

(d) a = 4.8 X 10-1-^ n/9.1 x lO-^^ kg = 
5.28 X 1015 m/s-'. 

(e) t = 5x 10-2 m/4.2 x 10' m/sec = 

1.2 x 10-9 sec. 

(f) The final velocity in the vertical 
component, v,, is given by v,. = V; +at-\- gt. But 
i^i is zero since the electron enters horizontally. 
From (d) we have a = 5.3 x lO^' m/sec= and 
from (e) we have t = ^.2x 10-^ sec. The value 
of a + g is the same as that of a, for g of 9.8 
m/sec- is negligible compared to a of 

5.3 X 1015 m/sec-. 

Therefore, v, = 5.3 x lO^^ m/sec^ x 1.2 x 10-^ 
sec, or V,. = 6.4 x 10" m/sec. 

(g) The displacement in the vertical direc- 
tion, dy, is given by d,. = Va aj-. Values for a and 
for t were found in (d) and in (e). Therefore, 

dy = V2 5.3 X 1015 m/sec- x (1.2 x 10-" 
sec)-, or dj. = 3.75 x 10-^ m, or 0.375 cm 

(h) The electron will have its original 
horizontal velocity component because there 
will have been no force acting on it in the hori- 
zontal direction. The ratio of its vertical velocity. 



as it leaves the deflecting plates, to its horizontal 
velocity will be i^,/i^h = 6.4x 10'74/2x 10^ = 0.15. 
The vertical deflection when it hits the screen 
will then be (0.15) (30 cm) = 4.5 cm 

(i) If magnetic force (Bqv) is to equal electric 
force (Eq), then Bqv = Eq, giving B = E/v = 
3 X 10V4.2 X 10" = 7.1 X 10-*webers/m2 

2.6 (a) Paper is typically 0.15 millimeter 
thick — about 50 times thicker than Lenard's foils. 
(Student might like to measure, for comparison, 
the thickness of household aluminum foil.) 

(b) The volume of a gram-atom of aluminum 
would be about 10 cm^. It would contain 

6 X 10-^ atoms. Each atom would therefore 
occupy about 1.7 x 10--^ cm'. One edge of a cube 
with that volume would be the cube root of the 
volume, or 2.6 x 10-"^ cm 

(c) Number of layers = (thickness of foil)/ 
(thickness of a single layer) = 12,000. 

2.7 The probability for surviving through 
150 mean-free-paths would be (Va)^^^ = 1.4 x 
10-*5, (log p = 150 log {V2) = 150 (-0.30) = -45). 

2.8 A meter reading of 0.50 milliamp is 
equivalent to 0.50 x 10-' coul. of charge passing 
in 1 second. 

(a) Since the average current for 40 pulses 
per second is 0.50 x 10-' coul., the charge per 
pulse is 1 /40 of that amount, or 1 .25 x 10-= coul. 

(b) Since the charge on one electron is 
1.6 X 10-1" coul., the number of electrons per 
pulse is 



1.25 X 10 -coul 
1.6 X 10-i"coul/electron 



, or 7.8 X 1013 electrons. 



(c) The energy per second equals the 
power. Since the current is 0.50 milliamp and 
the potential difference is 20,000 volts, the 
power is 

0.50 X 10-' amps x 2.0 x 10* volts, 
which is 1.0 X 101 or 10 watts. 

This amount of power will heat a small light bulb, 
so the foil is likely to be heated considerably. 



9 



Answers to End-of-Chapter Questions 

2.9 Most important was the development 
of the mercury high-vacuum pump. The experi- 
mentation could not have been carried out 
without: development of glass-working tech- 
niques, high voltage generators, creation and 
control of magnetic and electric field, and the 
electrometer. 



2.10 

(a) Waves 



1 . Produced greenish glow in tube at end 
opposite cathode (negative plate) 
Produced chemical reactions like 
ultraviolet light 

Produced by any metal serving as the 
cathode 

2. Behaved like light (light is polarized in 
a magnetic field) 

3. Molecular mean free path in tube only 
about 0.6 cm 

4. No Doppler shift of spectral lines, 
therefore not a moving source 

5. Hertz: Current separated from glow of 

beam 

No deflection in electric field 

Beam penetrated thin foils 

No charge on collector outside 

tube 



(b) Particles 

1. Beam bent by a magnetic field 

2. Crookes: Beam heats foils and moves 
vanes 

3. Schuster assumed particles with mass, 
then from q/m = v/BR estimated q/m 
as less than 10'° coul/kg 

4. Perrin and Thomson: Charge on 
collector inside tube 

Negative charge was deflected 
magnetically into collector 

Beam deflected by electric field 

Remeasured q/m for beam and 
results consistent with those from 
photoelectric experiments and also 
for beta particles in radioactive 
experiments 
Zeeman splitting required same value 

of q/m 



2.11 



Evidence 



Schuster: Beam bends in magnetic field as 
though it had a negative charge, q 



Perrin and Thomson: Beam deflected in 
electric field 



From electrolysis value of q/m known 
for hydrogen ion 

Thomson: Molecular mean free path in 
tube about one cm 



Arguments and Conclusions 

If beam consists of negatively charged particles, 

they must have some mass m 

Then q/m = v/BR (measured 6 and R and 

estimated v) 

Obtained maximum and minimum values for 

q/m 

Established both electric and magnetic field of 

known strength 

From F^, = F,„,,. derived v 

Solved q/m = v/BR 

Found q/m = 1/1840 of charge to mass ratio of 

hydrogen ion 

Particle must be very small 



10 



Answers to End-ot-(Jhapter Questions 



2.11 (continued) Evidence 

Edison: Hot filaments release charged 
particles 

Hertz: Charged particles from illuminated 
metals (photoelectric effect) 

Zeeman: Spectral lines split when source 
is in magnetic field 

Millikan: Oil drop experiment 



Arguments and Conclusions 

All the charged particles in these experiments 
were equivalent ("electrons") 



Theory requires Thomson's value of q/m 
Electrons are components of all atoms 

Derived smallest charge on oil droplets, value 
of q, thus of m 



CHAPTER 3 



3.1 Experiments of critical importance in 
the discovery of fission: 

(a) The discovery of the neutron (Bothe, 
Becker, Chadwick). 

(b) The experiments of Fermi and his 
collaborators using neutrons to make radioac- 
tive isotopes, leading to the discovery of "trans- 
uranic elements." 

(c) The work of Hahn, Meitner, and others 
extending the experiments of Fermi's group, 
leading to the discovery of many "transuranic 
isotopes," and the problems of "triple 
isomerism" and "inheritability of isomerism." 

(d) Curie and Savitch's discovery of the 
3.5 hour activity of "actinium," which led to 
the work of Hahn and Strassmann. 

(e) Intensified work by Hahn and Strass- 
mann on the chemistry of the 3.5 hour activity 
and related isotopes, culminated in the chemi- 
cal labeling of some of the activities produced 
by neutron bombardment of uranium as 
lanthanum and barium. This led to the tenta- 
tive suggestion that fission was occurring. 

(f) Frisch and Meitner's hypothesis that 
uranium was, in fact, undergoing nuclear fis- 
sion, and to Frisch's (and others') experiments 



showing that fission products emerged with the 
appropriate amount of kinetic energy. 

(Note: there were, of course, other im- 
portant experiments which served to provide 
clues — sometimes misleading clues — and 
hence motivation for further research, but 
which were not themselves in the direct line as 
shown above.) 

3.2 Glossary created by student. 

3.3 There is no obvious set of "right 
answers" to this question. Students will no 
doubt wish to consider such questions as 
whether a 1930 discovery of nuclear fission 
would have influenced the work and the demise 
of the League of Nations; whether Britain and 
France and the United States would have 
awakened to the Nazi menace sooner; whether 
there might have been noticeable economic 
effects of a possible development of nuclear 
energy for peaceful purposes on the course of 
the Depression; and the like. If, on the other 
hand, the discovery had not been made until 
1950, there are interesting questions as to how 
and when the war against Japan would have 
ended; how postwar American politics would 
have developed without (a) the false security 
provided from 1945 through 1947 by the con- 
cept of "The Atomic Secret," or (b) without the 
jolting fright provided by the first Russian 
atomic explosion in 1947. 



11 



Answers to End-of-Chapter Questions 



3.4 One distinction wliich may be helpful 
is that between scientific discoveries, on the 
one hand, and their technological applications, 
on the other. While discoveries such as that of 
nuclear fission are, of course, strongly depend- 
ent on the state of technological developments, 
the actual discoveries themselves in many 
cases could not have been anticipated or made 
to occur earlier by deliberate choice by society. 
The concept of nuclear fission was simply too 
bizarre to be entertained seriously until the 
chemical evidence for barium and lanthanum 

in the products was overwhelming. An excep- 
tionally brilliant physicist might have conceived 
the idea earlier, but he could not have been 
told to do so. A government might have de- 
cided to marshal a big research effort, which 
would have accelerated the discovery, but 
there was no apparent reason for a government 
to spend money, and scientists' time, on the 
problem of the transuranic elements in the 
mid-1 930's. Once a discovery is made, a gov- 
ernment or corporation may decide to invest 
large resources on its application to practical 
problems. And a government or corporation 
may set up laboratories and support scientists, 
in the hope that new discoveries will occur, 
which may then be applied to technological 
problems. One may even make shrewd guesses 
as to some (but not all) of the areas in which 
exciting discoveries may emerge. Discoveries 
in the non-predictable areas sometimes have 
the most far-reaching consequences. 

3.5 Neptune was clearly looked for and 
then found. Nuclear fission, on the other hand, 
was not expected. The electron is not so easily 
categorized: the discovery of cathode rays was 
a surprise, but the experiments which showed 
their properties were certainly planned. 

3.6 Energy released per atom = 208 MeV. 



U235 235.04393 




La 139 


138.9061 


n + 1.00867 




Mo 95 


94.9057 


236.05260 




2n 


2.0173 


-235.8291 




7e- 


— 


0.2235 


235.8291 


931 MeV X 


0.2235 = 


= 208 MeV. 





3.7 The energy would be about 150 MeV. 
This does not agree exactly with the answer to 
problem 6 because of the roughness of the 
approximations made in this problem, partic- 
ularly the assumption that R = 2 x 10-^* meters. 

The total kinetic energy after the fragments 
fly apart equals the work necessary to move 
them from a great distance to a separation of 
only 2 X 10-1^ m. Consequently, 



work = 



kQ,Q, 



9 X 109 



nm^ 
coup 



X 54 X 1.6 X 10-^9 coul X 38 X 1.6 X lO-^^ coul 



2 X 10-" m 

= 2.36 X 10-11 nm. Since 1 eV = 1.6 x lO-i" joul, 

.u X . . ■ w 2.36 X 10-11 nm ^ ^„ ^^„ „ 
the total energy m eV is zr^ — r^r^:^ r-rr = 1 .48 x 10^ eV 



1.6 X 10-19 nm/eV 



148 MeV. 



3.8 Students should be urged to solve the 
problem algebraically first, and then to substitute 
numerical values. If m^, v-^ and E^ are the mass, 
velocity, and kinetic energy of the first particle, 
and rrio, v^ and E., those of the second, then 
Ei/Eo = Vzm.v.'/Vzm.v.^-. Then EJE., = 
m^v^v^/m.M.Vo = vjv., = m^/m^ (since 

/r?iVi = rrioV^). Hence for Sr^^ (particle 1 ) and 
Xe"« (particle 2), E,/E. = 1 .45. Since 
El + Eo = E„ (the total energy), E., will be 
41 % of Eo and E^ will be 59% of E^. 

3.9 An alpha particle of initial energy 

4 MeV would produce about 130,000 ion pairs 
while coming to rest: 



4 X 10" eV 
30 eV 
ion pairs. 



= 1.3 X 10^' ion pairs, or 130,000 



A 100 MeV-fission fragment would produce 
about 3.3 million ion pairs: 



100 X 10" eV 
30 eV 



= 3.3 X 106 ion pairs 



If the negative ions in the latter case were 
collected, the pulse would contain about 
5.4 X 10 1' coulomb: 

3.3 X 10" X 1.6 X 10-19 c = 5.3 X IQi^ c 



12 



Answers to End-of-Chapter Questions 



If the pulse lasts 0.001 second, the current 
would be 5.4 x 10^" ampere: 



Average current = 5.3 x 10 
5.3 X 10" amp. 



710-^^ = 



While this is a very small current by ordinary 
standards (the current in a light bulb is of the 
order of one ampere), it can be amplified and 
detected fairly easily. 

3.10 (a) If small amounts of a barium salt 
to serve as a carrier are dissolved in solutions 
containing the neutron-bombarded uranium, and 
then precipitated out of solution by the addition 
of appropriate reagents, the precipitate is found 
to contain radioactive material. Before the 
concept of fission was taken seriously, this 
radioactive material was naturally thought to be 
an isotope of that element near uranium in the 
periodic table which had chemical properties 
like those of barium — i.e., radium. Radium itself 
could not be used as the carrier because it was 
radioactive, and its activity would mask the 
activity of the unknown material. 

(b) The prevailing opinion about twofold 
emission of alpha particles by neutron- 
bombarded uranium was that it was (1) unlikely, 
but (2) the only conceivable mechanism by 
which uranium could be converted to radium. 
At least two groups of physicists tried to detect 
the emission of alpha particles under these 
circumstances. 

(c) In 1938 nuclear isomerism had been 
known to exist for only a year. The apparent 
triple isomerism — and inheritable isomerism, at 
that — of the bombardment products seemed 
strange, but the experimental "facts" seemed 
to demand such explanations. 



CHAPTER 4 

4.1 One can think of radioactive decay as 
a process in which a nucleus changes from an 
unstable arrangement of its constituents to a 
more stable arrangement, either by emitting a 
particle or by emitting a gamma ray. If a given 
isotope, in the decay process, always emits 



alpha particles or gamma rays with a very 
specific amount of energy, the implication is 
strong that the "unstable arrangement" for all 
such atoms is somehow alike, at least as far 
as energy content is concerned — and likewise 
the "more stable arrangement" to which each 
one decays. A crude analogy might be as 
follows: if stones dropped from a bridge all hit 
the water with the same kinetic energy, one 
would be safe in assuming that they all came 
from the same level. If they hit the water with 
a continuous spectrum of energies, one would 
have to assume (a) that they were dropped from 
an infinite variety of levels, or (b) that they were 
slowed down, in the course of dropping, by 
some unknown mechanism. 

4.2 (a) The total energy released is 
identical irrespective of whether the alpha or 
the beta particle is emitted first. Evidently one 
specific energy state in the Po-218 is related to 
another specific energy state when the nucleus 
has become Bi-214. 

(b) In no cases of beta decay does the 
nucleus lose more energy than maximum 
observed in the beta-ray spectrum. 

4.3 (a) The shape of the continuous beta 
ray spectrum, and (b) the dependence on the 
half-life of an isotope upon the energy of the 
beta-rays. 

4.4 The neutrino is almost incapable of 
disturbing atoms or molecules through which it 
is traveling. Particles can be detected only by 
causing ionization or some other change in the 
detector. The neutrino is almost incapable of 
causing such disturbances because it has little 
or no mass, no electric charge, and little or no 
magnetic moment, etc. Reines and Cowan were 
able to detect the very rare interactions which 
occurred when they used a very intense source 
of neutrinos and very sensitive detectors with 
large numbers of "target" nuclei. 

4.5 Reines and Cowan succeeded in 
catching neutrinos, as it were. A crude analogy: 
one could show that energy disappeared into a 
radio transmitting station, and be fairly well 



13 



Answers to End-of-Chapter Questions 



convinced that Maxwell's theory of electricity 
and magnetism could account for that 
disappearance by postulating the radiating 
of energy in the form of electromagnetic waves. 
But one would still like to be able — as Hertz 
was able to do — to show that these waves could 
actually be received. 

4.6 (a) Neutrinos, produced in positron 
emission from nuclei, or in negative electron 
capture by nuclei, (b) Anti-neutrinos, produced 
in ordinary (e.g., negative) beta emission from 
nuclei, (c) the muon neutrino and (d) the muon 
anti-neutrino, produced together with muons in 
the decay of pi mesons. The necessity for 
"ordinary" neutrinos and anti-neutrinos to be 
different was shown by the Davis experiment. 
(Sec. 4.8) That "ordinary" neutrinos are 
different from those associated with muons has 
been shown by the experiments of Danby and 
Lederman, and by others. (Sec. 4.10) 

4.7 Neutrinos might account for stellar 
supernovae by providing an understandable 
mechanism for the sudden release of large 
amounts of energy from the interior regions of 
a star, permitting it to collapse and then 
explode. Additional evidence for or against 
such a theory is likely to come from further 
theoretical investigations (a) of conditions 
inside stars thought to be capable of becoming 
supernovae, and (b) of the cross-sections for 
the required processes, such as neutrino 
production by high energy gamma rays. It is 
not very likely that ten thousand ton detectors 
will be built and then maintained in readiness for 
a hundred years or so, for actual observations. 

4.8 7.83 + 3.26 = 11 .09 MeV., and 
5.61 +5.48= 11.09 MeV. 

4.9 (1/4) (3.26) + 7.83 = 8.64 MeV. 
5.61 + (1/4) (5.48) = 6.98 MeV. 



4.10 Pv = momentum of neutrino = P„ 
momentum of nucleus 

P^,= —, where E^ = energy of neutrino 
c = velocity of light 

but P,, = Pn = n^v, where m = mass of nucleus 
and V = recoil velocity 
of nucleus 

then, mv = — , and v = —^. 
c mc 

However, E^ = Vz mv-, where £„ = 

energy of nucleus 



or£n = 



2mc-' 

For m, mass of the nucleus, we can substitute 
m = Am^, where A is the atomic weight of the 
nucleus and m^ is the mass of one atomic 
weight unit. 



Then E„ = 



£•-. 



2x7 {m^c') 



-, but m^c- = 931 MeV, 



so 



E.,= }^-^T. =5.7X10-^ MeV 



14 X 931 



57 eV. 



4.1 1 In the text it was stated that 50 
interactions were observed during the passage 
of 10^^ neutrinos through the spark chamber, so 
(N,/Nv) = 50 X ^0''\ Substitution of the 
constants of the apparatus gives a cross 
section o- = 3.6 x 10 '^ cmVatom. (Note: A = 
27 grams/gram-atom, D = 2.7 grams/cm^, L = 
90 Inches = 229 cm, and A/, = 6 x 10-^ 
atoms/gram-atom.) 

The neon gas may be neglected because 
the number of neon nuclei in the beam is much 
smaller than the number of aluminum nuclei. 

4.12 The id, ego, and superego are 
qualitative concepts not having any physical 
attributes. However, the gene and atom and the 
neutrino do have physical attributes which 
allow their study through physical reactions. 



14 



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