Project Physics: Resource Book Discoveries in Physics

,m The Project Physics Course

A

Supplemental Unit

Resource Book

Discoveries

in

Physics

B

Resource Book

Supplemental Unit B

Discoveries

in

Physics

by David

L.

Anderson

Oberlin College

Published by

A Component of the Project Physics Course

(YflX) '^^'-"^' R'NEHART AND WINSTON, [nt) New York, Toronto

Inc.

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,

Programmed

16mm films and laboratory Development of the course has from the help of many colleagues listed

Transparencies,

equipment. profited

Tests,

Instruction Booklets, Film Loops,

in the text units.

Copyright

(r)

1973, Project Physics

All Rights Reserved

ISBN 0-03-089481-6 987654321 005

34567

Project Physics

is

a registered trademark

Table of Contents

NOTES ON THE TEXT CHAPTER

1

Notes on Chapter

CHAPTER

1

Page

1

The

12.

offering of a prize by the Uni-

was a fairly common means to work on a problem.

versity of Gottingen

The

Laws" and the "Orbit Parameters," and

film loop "Kepler's

transparencies T-17, T-18, "Motion

Under a Central Force" may be

men

of attracting able

Now

such prizes are

rarely,

ever, offered;

if

they are not needed.

useful for a review of planetary motion.

Page

a systematic count of the stars visible telescope. Also, he that

moved

Page

alert to

prediction of the planet's position, both in

his

and Leverrier had

unusual objects

later for

computed by

difficulties getting

another reason, used the

positions observed for Uranus. Often careful

map

of that

had an advantage over the British observers. The systematic approach used by the British observers would have been, indeed had

was

already been, successful; but

records can be searched for results unantici-

to

region,

Lexell as the basis for

searching old records that did contain earlier

Adams

anyone

search near their predicted positions. Galle, having at hand the unpublished star

Notice also that Johann Bode, whose

7.

Despite the prize for a mathematical

12.

in

into his field of view.

name appears orbit

was

Page

was engaged

Notice that Herschel

6.

costly

in

terms of time for observing and reducing the records.

pated by the recorder.

Page

Bode's law for the spacing of the

14.

Page 8. A variety of possible explanations were postulated to account for the scandalous

Kepler,

deviations of Uranus' position from those pre-

Despite the "forced

dicted by Bouvard. Discussion of these possibilities,

and others that students may propose, screening of ideas

illustrate the initial qualitative

and proposals within

scientific work.

Only after

was

the possibility of an outer perturbing planet fairly well difficult

accepted would anyone undertake the

task of trying to predict

its

planetary orbits deserves a note here. Like

pattern

Bode sought a fits fairly

pattern

fit"

well.

for

among

the orbits.

Mercury, Bode's

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.

position.

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

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.

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-

relative positions

ment

trary.

21, sufficient details are given

here so

The

conditions of the masses: their

initial

However,

they can proceed on this more complex analysis.

yield quantities

The approach uses the idea

student, the

toward a center of force

of

vector addition the continued a straight line

is

repeated blows

at regular intervals. inertial

combined with the

accelerations to yield a

new

motion

their velocities, are arbi-

which must which can be graphed by a

initial

conditions are rather

critical.

By

Many

in

threw the small planet out of the planetary

effects of the

velocity vector

and

for this experiment,

trial

conditions resulted

In

orbits

which

system.

and

displacement for the next iteration interval. If two large masses are simultaneously attracting

The scale is

of the

diagram

is

important.

too small, the vector additions are very

If it

diffi-

Notes on Experiment

make accurately. If it is too large, the unwieldy. Since the large planet becomes graph cult to

is

for

convenience put

AU

orbit at 4

a circular

initially into

from the sun,

it

moves

at

a uniform

rate in the circular orbit unperturbed by the

The data

small planet.

for the

two

initial

orbits

are:

Planet

Orbital radius, R, in

Period, T,

(365

in

Large

Small

4.0

3.1

doing the experiment as outlined

may make

they

the text,

in

a second analysis with different

Twenty

starting conditions.

recommended because

iteration steps are

that carries the small

planet through sizable orbital changes to a

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 point

aphelion. Note that the angles to these positions

AU

are to be laid

days

XR 3/2)

1990.0

2920.0

off

clockwise from the sun-small

planet line through the starting position, S

1.

60/T. fractional period

per iteration interval

Our

0.0301

0.0205

Degrees per 60 days

X 60/T) Speed in AU/60 days

1.29 inches

3.28

cm

Average distance

1.

0.586

0.516

Scaled speed/60 days

1.47

3.72

as 2.25 AU.

planet of 1/100 of the sun's mass, the relation between the two accelerating effects at the same

The new period

2.

The

3.

e

=

distance are 1:10;

c/a

^'"""^^

=

100'

WhenFp = F„10flp = Values

for these

fl,.

is

a temporary orbit for the small

large planet will continue to attract

intermittently

example

graphs are given

R

in

inches and

ws F curves

in

Graph paper subdivided in 1/20 inch or 1/10 cm units is easy to use and leads to higher accuracy.

change

its orbit.

The small planet

will

come

fairly

close

small planet are important to emphasize the effects of the perturbations

an

"chase problem" discussed in Unit 2 of the text. There the frequency, f, of close approaches, is given by /^l = ^s — ^l- '"^ of the

/Tsl = 1 /7"s — 1/7l, which upon substituting the periods becomes 1 /7sL = 1 /3.35 - 1 /8, or 0.1 73. Hence

terms of the periods,

Tsl

Predicted unperturbed positions for the

is

about 5.8 years

T, this is

until

1

another close ap-

proach. Small perturbations

will

continually

modify the orbit of the small planet

slightly.

caused by the large

planet. Selection of the starting places, as

Figure 4 of the text

is

important.

However, some brave students may wish

choose other

The

5.

either set of units.

in

about 0.45;

is

1/2.25.

to the large planet after only 6 years. This is

centimeters for graphing the

indicated

-).

cycles.

M.

ft:

orbit)

for the orbits of the asteroids

S

100

new

3.35 years (2.25^

is

eccentricity

of the

This occurs and short-period comets which come near Jupiter every few it

M.

M,'

and

=

This

4.

planet. /?2

of the small planet

from sun (the semi-major axis

The graphs for the values of the displacement as a function of R should be drawn with some care. By assuming a mass for the large

F.

gave the following answers to the

10.84

7.40

(360

planet

plot

questions at the end of the experiment:

starting places; or,

if

to

they enjoy

6.

After point

slow down and tions.

Compare

fall

S

3,

the small planet would

behind the predicted posi-

the perturbed and the un-

perturbed positions on the

plot.

Notes on Chapter 2

On

7.

the plot between S

small planet

is

1

and S 4 the

Hertz: electric field too weak,

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. After point

orbit

Its

S 15 the

drastically changed.

is

its

new

effect of the large planet

reaction." of

orbit,

2

Page

Technological developments allowing

much lower pressures in evacuated tubes permitted 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.

strange greenish glow

The discovery

in

—

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 In this

case only two

possibilities

were proposed; either the rays were electromagnetic, or they were corpuscular.

Page

36.

tion of

Now

The

Schuster proposes a modifica-

Crooke's particle proposal, perhaps the

particles are role of

charged fragments

analogy

is

even

results,

if it

Many assumptions go

is

will

"no

into the

design

to

instru-

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

Refer to Experiment 43, "The Photo-

41.

electric Effect."

(Experiment V-1

in

the revised

Student Handbook.)

Page

of molecules.

worth noting. His analysis

q/m is simple and both B and R can be measured rather accurately.

Three possible explanations existed q/m. Perhaps students

41.

for the value of 1840 for

would wish their

to

examine the three and propose

reasons for agreeing with Thomson that

the size, and probably the mass, of the cathode

was very small, although same charge as a hydrogen ion.

ray particle

the

proposed.

a useful place to emphasize

of the

discharge tubes was

followed by a wide variety of experimentation. This

is

an experiment and the selection of the

ments

CHAPTER 33.

Perhaps here

the point that any experimental set-up

always give some

diminishes rapidly as the small planet moves

along

and the high

conductivity of the residual gas.

it

carried

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.

for the derivation of

His

Page

42.

This special page provides more

estimation of v at least bracketed the range for

details about the

q/m. Transparency T-32 "Magnetic Fields and Moving Charges" could be used here for review.

in

procedure used by Thomson

1897 to extend Schuster's analysis. The

magnetic and electrical forces are applied simultaneously and balanced to produce a

Page

38.

The work

of Hertz illustrates how, as

with Schuster and later

Thomson, a basic

sumption shapes the nature of the experimental questions.

As

is

observed

later,

straight

beam from which

v could

be derived.

as-

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

43. Reference could be made to Experiments 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.)

Page

Notes on Chapter 3 perimental work and the influences of assump-

Reference to Experiment 44 "Spectroscopy" (Experiment V-6

the revised

in

tions

upon the equipmental design.

Page

54.

Student Handbook) would remind students of experiences with

their

line spectra.

In line

the caution

Film loop "Rutherford Scattering"

development

lated to the

CHAPTER

is re-

of the ideas.

likely to

with the

be useful with

this

comment above, Hahn and

Strassmann: "A series of strange coincidences to

these results."

Page

54.

some

theoretical suggestions by

Meitner and Frisch benefited from

atomic nuclei being

like liquid

Bohr about

drops, an

chapter are:

unusual but highly important analogy. The

Transparencies T-42 Radioactive Disintegration

suggestion by Hahn and Strassmann that

T-43 Radioactivity Decay Curves T-44 Radioactivity Displacement

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

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).

"People and Particles"

pecially appropriate to

into

Frisch were

Rules

film

hit by neutrons might actually split two major parts with the release of great energy, plus the calculations by Meitner and

uranium

Series

The

note

the statement by

may, perhaps, have led

3

Teaching Aids

in

show

in

new Page

idea.

57.

The self-imposed decision

enormous

es-

conjunction

with Chapters 3 and 4 of this Supplementary

was

remarkable. As early as 1940, nuclear scientists realized the

is

to stop

publishing papers about nuclear fission

fission

military potential of a

weapon. They wished

information to the

to contribute

no

enemy who probably would

attempt to develop such a weapon. Stopping

Unit.

was a dramatic example

publication

The

"The World

of Enrico Fermi"

is

also appropriate for showing with Chapter

4.

Page

film

As the

47.

text

makes

clear, the dis-

any time between 1934 and 1939, but

not.

was

The experimental evidence was inconclu-

sive, but the possibility of

into

it

CHAPTER

4

Page

This chapter stresses the faith

made

covery of nuclear fission could have been at

of the

social concern of these scientists.

an atom breaking

two medium sized parts was almost

63.

physicists have put laws.

in

the general conservation

To save them, a new

particle

was

"invented."

unimaginable.

Page Page

The behavior

48.

of

atoms which cap-

tured a neutron of low energy (a slow neutron)

seemed

to

be well known. One beta particle in a stable daughter nucleus.

65.

The peculiar continuous energy

spectra of beta rays having

some maximum appeared servation laws for

all

energies up to

to violate

the con-

energy and momentum.

emission resulted

Strassmann, of Braun, Preiswerk and Scherrer,

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

and

beta ray spectrum and the missing

Page

Page

50.

Again, the experiments of Irene

Joliet-Curie

and Paul Savitch,

of

Hahn and

of Droste illustrate the difficulties of ex-

67.

Pauli

momentum.

Answers

to

End-of-Chapter Questions

Thus an idea proposed by one man was

conclusion from a negative observation. His

elaborated by another.

experimental design and operative care were

so great that the absence of evidence for argon

Page

37 was accepted as evidence for the existence

While an experiment to detect

68.

neutrinos had been proposed,

had to wait

until

its

application

of antineutrinos.

1956 when newly developed

nuclear reactors would produce a sufficient

supply of beta decays. Very sensitive

scintilla-

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

and complex computer circuitry were also essential in detecting reactions and ruling out events having other causes. Problem

tion counters

4.11 illustrates the

mathematics

(a)

assumptions which

and perhaps

of a beta ray

also a neutrino.

Page

The experiment by Davis

73.

is

one

vfi

+P

(b)

(4.7)

(4.8)

seems

of equation (a)

conservation when the nucleus

upon emission

(b)

equation

Problem 4.10 illustrates the calculation of recoil energy, which is rarely above 100 eV. The sketch in the margin of the text, page 72, illustrates the vector analysis for recoils

I'fi

50 muons were recorded, the reaction of

72.

momentum

=

Since no electrons were produced, but about

posed production of neutrons by neutrinos Eq. 4.3, on page 69, and the conclusion that the predicted events had actually occurred.

Page

i-

if

or

between the sup-

lay

+ P^e-,

of the analysis.

You may wish to discuss with the students the diversity of complex apparatus and the theoretical

v^

is

to

be occurring, while that

not.

The acceptance of neutrinos which 78. have such very small capture cross-sections has led to changes in the mechanism considered possible within stars. Thus the theory to account for supernovae has been reexamined. Page

Probably the detection of neutrinos from relatively nearby supernova, such as that which

formed the Crab nebula in Taurus in 1054 AD, is a task unlikely to be undertaken because of

of

the size and cost of the equipment.

the relatively few examples of a significant

ANSWERS TO END-OF-CHAPTER QUESTIONS CHAPTER

The discovery

1.1

cident

found

in it,

1

of

Uranus was an acwhen he

the sense that Herschel,

was not looking

for a

new

Accidental aspects of the discovery of Pluto:

planet. (a)

Neptune: The elements of Neptune's calculated by error, but

Adams and

happened

orbit,

Faintness of Pluto's image on the 1919

plates, so that

Accidental aspect of the discovery of

it

was overlooked

at that time.

as

by Leverrier, were

(b)

in

to predict the position of

The perturbations

were thought

may

to

of

Uranus which

have been caused by Pluto have really been due to Pluto

enough for it to be found. The errors in the elements were shown by later calculations when more complete data were

(which turned out to have a very small mass).

available for the positions of Neptune.

led

the planet precisely

6

not, in fact,

Nevertheless, they led to "predictions" which

Tombaugh

to find Pluto.

Answers

what way or ways was the time Adams and of Leverrier? Uranus had been observed long enough for 1 .2

In

to

End-of-Chapter Questions

Relative Max. forces on Uranus by Neptune

18

ripe for the work of (a)

the residuals of

its

motion, particularly since

conjunction with Neptune

in

=

its

1.64

enough to be a major problem, (b) Since the in

1685,

.149

11.02

1820, to be large

publication of Newton's Principia

=

95

—= 1.05

many

Saturn—

9.52

mathematicians, astronomers, and physicists had worked out highly ingenious techniques for deriving orbits and computing the perturbing effects acting

between planets. Thus, the were available.

analytical tools

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

exerted by Piuto

[at the least]

on Uranus. One says

"at the

because the mass known, but is certainly no more than that of

least"

the Earth.)

of Pluto

is

not well

,

Force on Uranus by

—=

Neptune .

..

Jupiter

0.149 -n:r-r

=

„ „„^ 0.091

1.64

Neptune

0.149

Saturn

1.05

= 0.142

Answers

End-of-Chapter Questions

to

CHAPTER

2

The technology needed was (1) Good vacuum pumps.

(a)

Evidence that cathode rays are not

2.1

Well-developed glassblowing tech-

(2)

electromagnetic waves:

available:

methods

niques, including

making

for

metal-to-glass seals for electrodes.

They are deflected by magnetic fields. Electromagnetic waves are not. For example, a flashlight

beam

is

not deflected

when

it

the text, but of

is

sent between the poles of a strong magnet.

Radio and

light

far into space.

Gamma

voltages and instruments for the

measurement of very weak currents were available. (4) Spectroscopic techniques of good

rays are

not bent by strong magnetic fields, while alpha

and beta rays

Circuits for the production of high

(3)

waves are not deflected by the

earth's magnetic field, which, though weak,

extends very

was not mentioned as such in was implied for the work Perrin, Thomson, etc.)

(This

(a)

power

resolving

are.

(for

Zeeman

effect

measurements). (b)

They convey

electric charge, as

shown

by the experiments of Perrin and Thomson. Electromagnetic waves do not convey charge.

Many

(b)

terested

in

At the time of

2.2

periments there was

J. J.

little

pressure, and of the optical spectra produced

by such gases. (c)

Thomson's ex-

direct information

2.4

hydrogen

to that of the

ion.

Where

(a)

and magnetic

about the actual size of the electron's charge

compared

The controversy over the nature

cathode rays stimulated interest

not deflected by electric fields.

qE =

so v

ratio for

the ratio measurements.

^ = E

electrons)

Zeeman

atoms, and therefore, must be smaller than

1.0

X

10-3

2.0

X

10"

V

amp _ ~ N

(b)

When

V

Bd

N

The time was

and q

8

1.0

X

1.8

X

10-''

ripe for the discovery

because

m

_ m \ ~ sec/

sec

N

2.0

m

of the electron in the 1890's

0.01

coul

coul

mv-

charges followed

automatically.

2.3

X

m/sec

tracting electrons from neutral atoms, then of of the

and

the magnetic field acts alone, a

circular orbit results,

As the view developed that was the result of adding or sub-

course the equivalence

,

= 7^-7;

1^

amp-m

•

(or ions).

ionization

B

effect

indicated that electrons are contained within

atoms

V d

-;,

Nm /volt

was much smaller

than that of atoms. Further, the

=—

200 volts

=

Thomson suggested

size (and presumably the mass) of cathode ray (i.e.,

v

or

that Lenard's experiments indicated that the

particles

of

field.

the cor-

hydrogen ions. One needed evidence for the comparative masses of electrons and ions in order to make use of responding

qvB,

Since

the

we have

The

cathode ray experiments suggested that the charge to the mass of the cathode

was about 1800 times

in

the effects of the electric

fields cancel,

ratio of the

ray particles

in-

gases under low

tions in the conductivity of (c) Cathode rays are deflected by strong electric fields, as shown by Thomson's experiments and, of course, by many modern cathode ray oscilloscopes. Electromagnetic waves are

were

scientists at the time

the problems raised by investiga-

=

IQi^

X

V

m

10"

sec

N

ampm

X

coul/kg

0.114

m

Answers coul

/am p-m

sec

sec

kgm

as

m

The sec

sec*

The

MKSA

unit for

B

will

N/amp. m and

is

now

is

vertical deflection

2.5

rest,

then A(PE)

qV

energy, or

-

Since V

(a)

= A{PE).

qV

(i)

A(PE)/g by

definition,

equal their gain

in

V2mv-. The value of v

If

is

then

3

X

(b)

E = V/d = 3x10^ newtons/coulomb.

X

Bqv

a

X

5.28

1.2

x

t

3 X 10* newtons/coulomb x coulomb = 4.8 x lO-^' newtons.

= 4.8 X = 5x

The

component, is

10-1-^

x

n/9.1

lO-^^ kg

(c)

=

X

is

10-2

m/4.2 x

given by

v,, is

The

10'

=

m/sec

v,.

=

V;

+at-\-

gt.

But

negligible

compared

in 1

=

of layers

sec, or

x

(a)

pulse

V,.

=

10-^

X

10-' coul. of

x

is

0.50

(g)

for

t

given by

were found dy

=

V2 5.3

sec)-, or

dj.

d,.

=

X

Va aj-.

and

in (d)

1015

the vertical direc-

Values for a and

in (e).

m/sec- x

= 3.75 x

Therefore, (1.2

x

10-"

10-^ m, or 0.375

cm

=

1.4

x

=

-45). is

charge passing

10-' coul., the

x

/40 of that amount, or

charge per

.25

x

10-= coul.

is

number of electrons per

is

1.25 X 10 -coul or X 10-i"coul/electron (c)

the potential difference

power

7.8

X

1013 electrons.

The energy per second equals the

power. Since the current

is

is

0.50 milliamp and

20,000 volts, the

is

0.50

The electron will have its original horizontal velocity component because there

1

Since the charge on one electron

,

in

(Va)^^^

150 (-0.30)

reading of 0.50 milliamp

10-1" coul., the

pulse

1.6

foil)/

12,000.

Since the average current for 40 pulses

is 1

(b)

m/sec^ x 1.2 x 6.4 x 10" m/sec.

The displacement

tion, dy, is

(thickness of

=

second.

to a of

lO^^

=

150 log {V2)

A meter

per second

1.6

5.3

foil.)

cm

10-"^

equivalent to 0.50

the vertical

foils.

measure, for comparison,

probability for surviving through

=

10-*5, (log p

1015 m/sec-.

=

equal electric

B = E/v =

typically 0.15 millimeter

is

like to

Number

2.8

final velocity in

Therefore, v,

Paper

(a)

2.7

(d)

m/sec-

to

10-*webers/m2

150 mean-free-paths would be

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 5.3

= 7.1 X

(thickness of a single layer)

zero since the electron enters horizontally.

From

is

Eq, giving

— about 50 times thicker than Lenard's

volume, or 2.6 x

10-9 sec.

(f)

i^i

=

volts/meter

1015 m/s-'.

(e)

=

(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

=

F

10-1"

(d)

=

m/sec.

10*

(c)

1.6

cm

4.5

the thickness of household aluminum

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

2.6

thick

(Student might

C^Y^

-

X

= 0.15.

screen

hits the

magnetic force (Bqv)

3 X 10V4.2 X 10"

kinetic

"n^y 4.2

it

10^

Since the electrons start from

will

=

=

then be (0.15) (30 cm)

force (Eq), then

then

when

horizontal

its

= 6.4x 10'74/2x

i^,/i^h

called the tesia

engineer Nikola TesIa).

(after the electrical

leaves the deflecting plates, to

it

velocity will be

coul

End-of-Chapter Questions

to

X

10-'

amps x

2.0

x

10* volts,

(h)

will

have been no force acting on

zontal direction.

The

it

in

the hori-

ratio of its vertical velocity.

which

is

1.0

X

This amount of power

so the

foil is likely

to

101 or 10 watts. will

heat a small light bulb,

be heated considerably. 9

Answers

to

End-of-Chapter Questions

Most important was the development mercury high-vacuum pump. The experi-

2.9 of the

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

(b)

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

Particles 1.

field

Crookes: Beam heats vanes

3.

Schuster assumed particles with mass,

Produced by any metal serving as the cathode

Behaved

bent by a magnetic

2.

ultraviolet light

2.

Beam

foils

and moves

q/m = v/BR estimated as less than 10'° coul/kg then from

polarized

like light (light is

in

q/m

a magnetic field) 4. 3.

Molecular mean free path

about 0.6 4.

in

tube only

Perrin

cm

No Doppler

Negative charge was deflected magnetically into collector

shift of spectral lines,

Beam

therefore not a moving source 5.

Hertz: Current separated from

glow

photoelectric experiments and also

experiments

Zeeman of q/m

splitting required

same value

Arguments and Conclusions

Beam bends it

beam and

for beta particles in radioactive

Evidence

though

for

results consistent with those from

of

tube

Schuster:

deflected by electric field

Remeasured q/m

beam No deflection in electric field Beam penetrated thin foils No charge on collector outside

2.11

and Thomson: Charge on

collector inside tube

in magnetic field as had a negative charge, q

If

beam

consists of negatively charged particles,

they must have

some mass

Then q/m

= v/BR

estimated

v)

m

(measured 6 and R and

Obtained maximum and minimum values

for

q/m Perrin

and Thomson: Beam deflected

in

electric field

From for

electrolysis value of

Thomson: Molecular mean tube about one cm 10

q/m known

hydrogen ion

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 hydrogen

free path

in

Particle

ion

must be very small

to

mass

ratio of

Answers

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

Edison: Hot filaments release charged

All

particles

Hertz:

Charged

End-ot-(Jhapter Questions

Arguments and Conclusions

Evidence

2.11 (continued)

to

particles from illuminated

metals (photoelectric effect)

Zeeman: Spectral is in

magnetic

lines split

when source

field

Theory requires Thomson's value of q/m Electrons are components of all atoms Derived smallest charge on

Millikan: Oil drop experiment

of q, thus of

CHAPTER

critical

importance

in

The discovery

showing

of the neutron (Bothe,

emerged

with the

(Note: there were, of course, other im-

portant experiments which served to provide

Becker, Chadwick).

—

—

3.2

Glossary created by student.

sometimes misleading clues and hence motivation for further research, but which were not themselves in the direct line as shown above.) clues

The experiments

(b)

that fission products

appropriate amount of kinetic energy.

the discovery of fission:

(a)

droplets, value

3

Experiments of

3.1

oil

m

of

Fermi and his

collaborators using neutrons to tive isotopes, leading to the

make

radioac-

discovery of "trans-

uranic elements."

The work

(c)

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."

Curie and Savitch's discovery of the

(d)

3.5 hour activity of "actinium,"

the work of

Intensified

(e)

mann on

which led

to

Hahn and Strassmann.

there might have been noticeable economic

work by Hahn and Strass-

the chemistry of the 3.5 hour activity

and related isotopes, culminated

in

the chemi-

some of the activities produced by neutron bombardment of uranium as

cal labeling of

lanthanum and barium. This led tive

to the tenta-

suggestion that fission was occurring.

(f)

Frisch and Meitner's hypothesis that

uranium was, sion,

and

in fact,

to Frisch's

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

undergoing nuclear

fis-

(and others') experiments

effects of a possible

development of nuclear

energy

purposes on the course

for peaceful

the Depression; and the

like.

If,

of

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 concept of "The Atomic Secret," or (b) without the jolting fright

provided by the

atomic explosion

in

first

Russian

1947.

11

Answers

to

End-of-Chapter Questions

One distinction wliich may be helpful 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 depend3.4

is

that

ent on the state of technological developments, the actual discoveries themselves

many

in

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 excephave conceived

tionally brilliant physicist might

the idea earlier, but he could not have been told to

do

so.

A government might have

cided to marshal a big research

effort,

de-

which

would have accelerated the discovery, but was no apparent reason for a government to spend money, and scientists' time, on the there

problem

of the transuranic

mid-1 930's.

Once

elements

a discovery

the

in

made, a gov-

is

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

exciting discoveries in

all)

of the areas in

may emerge.

which

Discoveries

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

was showed

categorized: the discovery of cathode rays a surprise, but the experiments which their properties

3.6

U235

were certainly planned.

Energy released per atom 235.04393

=

208 MeV.

Answers

If

the pulse lasts 0.001 second, the current

would be 5.4 x 10^" ampere:

5.3

Average current X 10" amp.

While

this is

=

=

a

in

bulb

light

is

of the

can be amplified and

it

follows:

stones dropped from a bridge

if

If

small amounts of a barium salt

to serve as a carrier are dissolved in solutions

from the same

have

then precipitated out of solution by the addition

an

of appropriate reagents, the precipitate to contain radioactive material.

found

is

those of barium

radioactive,

and

activity of the

to

assume

(a) that

hit

all

came

the water with

they were dropped from they were

the course of dropping, by

in

—

i.e.,

radium. Radium

its

activity

unknown

itself

it

was

would mask the

4.2

The

(a)

The

energy released

total

identical irrespective of

the beta particle

first.

Evidently one

the Po-218

in

is

whether the alpha or

emitted

is

specific energy state

is

related to

another specific energy state when the nucleus

has become Bi-214.

material. (b)

bombarded uranium was

In

no cases of beta decay does the

nucleus lose more energy than

prevailing opinion about twofold

observed

emission of alpha particles by neutron-

(2)

they

If

all hit

one

some unknown mechanism.

Before the

could not be used as the carrier because

but

assuming that they

level.

infinite variety of levels, or (b) that

slowed down,

was taken seriously, this material was naturally thought to be

radioactive

(b)

in

kinetic energy,

fission

an isotope of that element near uranium in the periodic table which had chemical properties like

all

a continuous spectrum of energies, one would

containing the neutron-bombarded uranium, and

concept of

same

the water with the

would be safe (a)

is

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

fairly easily.

3.10

rays with a very

—

standards (the current detected

710-^^

gamma

of energy, the implication

strong that the "unstable arrangement" for

a very small current by ordinary

order of one ampere),

amount

specific

x 10

5.3

alpha particles or

End-of-Chapter Questions

to

it was (1) unlikely, mechanism by

in

maximum

the beta-ray spectrum.

that

the only conceivable

4.3

The shape of the continuous beta and (b) the dependence on the an isotope upon the energy of the

(a)

ray spectrum,

which uranium could be converted to radium. At least two groups of physicists tried to detect

half-life of

the emission of alpha particles under these

beta-rays.

circumstances. 4.4 In

(c)

known triple

that

to exist for only a year.

isomerism

—

of the

strange, but to

The apparent

— and inheritable isomerism,

is

at

bombardment products seemed the experimental "facts" seemed

demand such

The neutrino

is

almost incapable of

disturbing atoms or molecules through which

1938 nuclear isomerism had been

traveling. Particles

causing ionization or detector.

some

The neutrino

is

other change

causing such disturbances because

magnetic moment,

etc.

in

the

almost incapable of

or no mass, no electric charge, and

explanations.

it

can be detected only by

Reines and

it

has

little

little

or no

Cowan were

able to detect the very rare interactions which

CHAPTER

4

occurred when they used a very intense source

and very sensitive detectors with numbers of "target" nuclei.

of neutrinos

One can

4.1

a process

in

think of radioactive

its

more stable arrangement, particle or by emitting a in

large

which a nucleus changes from an

unstable arrangement of

isotope,

decay as

constituents to a

either by emitting a

gamma

ray.

If

a given

the decay process, always emits

4.5

Reines and

Cowan succeeded in were. A crude analogy:

catching neutrinos, as

one could show

it

that energy disappeared into a

radio transmitting station, and be fairly well

13

Answers

End-of-Chapter Questions

to

4.10

momentum

disappearance by postulating the radiating energy in the form of electromagnetic waves. But one would still like to be able as Hertz

P^,=

of

= momentum

Pv

convinced that Maxwell's theory of electricity and magnetism could account for that

—,

do

to

—

show

to

waves could

that these

c but

=

P,,

=

Pn

= P„

= energy of neutrino = velocity of light

where E^

—

was able

of neutrino

nucleus

of

n^v,

actually be received.

where m and V

= mass of nucleus = recoil velocity

of nucleus 4.6

Neutrinos, produced

(a)

emission from nuclei, or ordinary

muon

the Davis experiment.

was shown by

from those associated with muons has

Neutrinos might account for stellar

of

—^.

mc

where £„

energy from the

a star, permitting

it

or£n

=

m=

Am^, where

weight

and then

is

come from

likely to

further

theoretical investigations (a) of conditions

inside stars thought to be capable of

supernovae, and

(b) of

becoming

the required processes, such as neutrino

gamma

rays.

the

mass

of

one atomic

=

£•-.

-, but m^c-

2x7 {m^c')

E.,= }^-^T. =5.7X10-^ 14

X

=

931 MeV,

MeV

931

57 eV. 4.1

In

the text

it

was

stated that 50

were observed during the passage neutrinos through the spark chamber, so

It

of 10^^

(N,/Nv)

= 50 X

^0''\ Substitution of the

constants of the apparatus gives a cross

the cross-sections for

production by high energy

is

substitute

the atomic weight of the

interactions

explode. Additional evidence for or against

such a theory

A is

we can

unit.

Then E„

so

nucleus

of

2mc-'

For m, mass of the nucleus,

interior regions of

to collapse

=

energy

supernovae by providing an understandable mechanism for the sudden release of large

amounts

=

Vz mv-,

nucleus and m^

been shown by the experiments of Danby and Lederman, and by others. (Sec. 4.10)

4.7

and v

pi

(Sec. 4.8) That "ordinary" neutrinos are different

,

=

However, E^

muon muons in

produced together with mesons. The necessity for "ordinary" neutrinos and anti-neutrinos to be different

—c

mv =

neutrino and (d) the

anti-neutrino,

the decay of

then,

produced

negative) beta emission from

(e.g.,

nuclei, (c) the

positron

in

negative electron

(b) Anti-neutrinos,

capture by nuclei, in

in

is

cmVatom. (Note: A = 27 grams/gram-atom, D = 2.7 grams/cm^, L = 90 Inches = 229 cm, and A/, = 6 x 10-^

section

o-

=

3.6

x 10

'^

atoms/gram-atom.)

not very likely that ten thousand ton detectors will

be

built

and then maintained

a hundred years

4.8 5.61

7.83

+5.48=

+

in

readiness for

or so, for actual observations.

3.26

=

11 .09 MeV.,

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

and 4.12

11.09 MeV.

qualitative attributes.

4.9 5.61

14

+

(1/4) (3.26)

(1/4) (5.48)

=

+

7.83

6.98

=

MeV.

8.64

MeV.

The

id,

ego, and superego are

concepts not having any physical However, the gene and atom and the

neutrino do have physical attributes which

allow their study through physical reactions.

HOLT, RINEHART

AND WINSTON, INC.