,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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