The Foundations of
Modern Physics
Note: Most of the exercises in this chapter are to give you practice reasoning usingmacroscopic evidence
and observations to reason about microscopic processes.
37.2 The Emission and Absorption of Light
L
The figure shows the spectrum of a gas discharge tube.
400
nn
5(X)
'"+
nrl
600
nnt
What color would the discharge appear to your eye? Explain.
Ci";;
b";;;;
*or+
+r^.
*'tr+J
*rovol*3lhs
700 nnr
fotl in
+{.e
tl3o - 5lo nm fon3e.
2.
Light is emitted from a discharge tube only if current flows through the gas. The light immediately
if the current is interrupted for any reason, What conclusions can you draw about the
mechanism by which the light is emitted?
ceases
t*bs is
d.^u *o alettrBns
"horoo {ravcting \he lo'^5+h ot
emitteJ f*o* . +l^" cothole..
.
"l^a
fube-, thorn .arq .!^o\^t colltsionl
+t^" +*bo. V.r*h ; i; i*-+t,*
qunl .tho
b"t*** r.\re o\eclej',t (.*+["d" - f i./ po*"Ji clos)'\\^{
llln" c*rce^t i,n +he dis
;oi"J"r" u:+ il
e${t \i5ht
;"; i;,^+ .*.,t '
"t\*.*ro"s
{\e',
A and B are made of the same material and have equal diameters. The spectrum of thermal
radiation from sphere A peaks at a wavelength one{hird that at which B peaks. What is the ratio PolPu
of the power radiated by A to that radiated by B?
3. Spheres
d
I]l
c
o
\gcok "(
^o
O
N
o
P
+ so Tn = 3Ts or +
".Tr so Pn = (3)' Ps or
37-1
37-2
cHAprER
37
.
The Foundations of Modern Physics
37.3 Gathode Rays and X Rays
37.4 The Discovery of the Electron
4. Over 100 years ago it was observed
that a nearby source ofx rays or radioactivity causes a charged
electroscope to discharge. Replacing the air around the electroscope by a monatomic gas such as
heliurn does not change the outcome. However, no discharge occurs if the electroscope is in avacuum.
a. Do the x rays or radioactivity affect the electroscope itself, or do they affect the environment around
the electroscope? Use the observations to explain your reasoning.
Jh"y *.^st - +ho grnviror^w\cn+ afo\v\d th" n\n {*ottot. becqus'("ffeLt
in o, vo,c\^\A\^n
* i5 {!" cnvtron'no'nt (oir mo\a'co\"s or lqs) lhni
hos buo,u, ro*on,,l.
b. What is the mechanism by which the discharge occurs?
ioniai^q d:";:; . *"!".t\T,,,I;t|i]t"?n]il"t:l'
ch^no.A {raqvrov'ts ',it^tttn "ito io\^s'
\"
x rors-q,re
6;
';^ao*i'uo.
c. What can you infer from these observations about the properties of atoms? Possibilities you might
want to consider are the size of atoms, the mass of atoms, the divisibility of atoms, the structure of
atoms, and perhaps other properties.
Si"r<,o mo$ato*ic arases ( si"$c ^{o*) coutf . be igrniz.{ .rn
"
*lni. Ncv, *her\ +hn of ovq i s not inAivisib\e avrd mw* U
**a.';;' d
5.
s*or\ior fro.3*o'nts lh".t ho"*a- charSe'
A magnetic field exists in the space between two parallel electrodes.
a. Sketch the trajectory ofthe electron ifthe electrodes are uncharged.
b. Use plus and minus symbols to show how the electrodes should
charged to achieve zero deflection ofthe electron.
be
n
l*l '
. fi.tJ is oot of poqo :l '
lh:
113^o{i
bt {d elctro'ni qre- nolot'v"ty :ffi5d' [l '
ll..
}ho-
I
A Fastclectron
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i
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'
ft
' l-
' i'\ '
l-
I
I
l-l
u:::\I
6. Thomson observed deflection of the cathode-ray particles due to magnetic and electric fields, but
thlre
was no observed deflection due to gravity. Why not?
Jo. *o qro.t,ily rs !cn/ ^*.h svnnlle. tl.o^ *hu
The. fo*o
-"-4
**qr,J*i. f.'n.os bul^*s" of {hc v..) sn*ll
el..t
d *ho c^{holo -"roy po.ti.l"s.
i.
mqsJ
The Foundations of Modern Physics
7.
'
cHAPTER
37 37'3
Cathode rays cause a green spot to appear on the glass at the front of a Crookes tube. A magnetic field
deflects the spot sideways, but the spot remains the same size.lt does not smear or spread out. This is
an interesting observati on.
Front view
Siclc vtew
Spot without fleld
Spot with ficld
a. Assuming that cathode rays are negatively charged particles, what can you conclude about the
charge-to-mass ratios of different cathode-ray particles?
*"; ;;;i,';
*he
{ht sorno si"'co q'l\ cct\,'od': til-lilt*;:ii
?t
sqv\e. qrnnorr,nt h +1"," s^t^^s vn^9neti<
i"il"*,d
;i +ho siec of $." spo$ ra$o\i!\s {h. sqvne '
b. What can you conclude about the spe9d1 of different cathode-ray particles?
H',*Ir *ho Samc, doflertio^, choqqe - lo-vnqss rqlio,
nrolnc*,c fiold, *l,to sgo.di v*,^sl"alt b. +1^e so\u,rc,
ov\J
v= tg
t'B
In the absence offields, the green dot caused by the
cathode rays appears in the center ofthe front face ofthe
tube, as was shown in the figure of Exercise 7. Prior to
Thomson, it was discovered that an electrode in the center
ofthe front face collects a current ofnegative charge.
a. Can you conclude from this observation that cathode rays are negatively charged parlicies? Or is the
evidence insufficient to draw this conclusion? Explain,
11.*o otr"*"{i oo,s seeva\. io indi.o.te . +ho.+ ccthodr"--rcis
p,r:ji
*:$
ffi" ;d$i;\;i;a,
*: ' "T '{L+
^::* -=S'
Lvtqq-tncc- rO ovtra= w'\\'rsJr ts Yt vv^bqiil
l.:.,4"i.""t}iil"
UnT
:".#
-*plo.i^ +his' curcc$.
aoi^.ideut"\
":[?;![i::^
-t":ilL]4S q.:eP"r1]e
,evsv
Df
o
"o
t!
o
o.
O
N
o
I
foio*s tho so,nte Pa+f. Qs tl^e' ."{hode
ff
fcYs.
b. Why did Thomson carry out the experiment in which he placed the collecting electrode off to the
side of the tube? What was the significance of this experiment?
Tho^so^ p\qlrl *hc.- +.^be in.c,. . *i1"ofi: ft"\d., +ht J"q.tftd
}o *ha
lvB side.
rl(,\(,. A
rha etgcl{-o(,||{{o +t^.
rcrls To
off To
e\o.teoJd qTT
thc c^thod.{hc
catho({- I'oq\
corco"$ ,n1c\s Ae*c.*cl i^Jic.rti,n1, +\.d , \n" cothoJ. rc\ys
Qre, i^JeeA
"h""1dJ P""+i 'los '
^e9**iuc\*1
37-4
9.
cueplen 37
.
The Foundations of Modern Physics
Thomson found that (Qlm)cutnoa"ruy, = 1000(qlm)u-ion. (The charge-to-mass ratio of the hydrogen ion
H* was known from electrolysis.) This suggests either:
i'
4cathode
ii'
iii,
,uy, = 10004H-ion,
fficathode*r, =
#'H-ion,
or
Some combination of these,
In 1897, when Thomson made his measurements, whole atoms were thought to be the smallest unit of
matter and Millikan had not yet established that there is a fundamental unit of charge. So why did
Thomson reject option i? Cite specific experimental evidence.
Prcvi ou.slv
. axDoriv^cv*s hol Shorln {rl.rq-t C^thode r^yf
psnctro.+r'+hi*
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C4n
o{or,,s cqv\v\ol,
"n+"t foi\s b*+ +hct
Mc*tt..,l,o. rq.,s
<< M *-,o'''
10. Thomson used cathodes of aluminum, iron, platinum, and other metals. He found the same value
(qlm)cathoderay5 for each. What conclusion can you draw from this observation?
of
Nha*eva,r *ho .h".1"1 por+i ctes *grsr *h..1 \^lorc id.*i"*\
foc o.ll lhoso diffst;"+ alsnqe,'"+s .
o
!gl=
o
o
d
o
The Foundations of Modern Phvsics
'
cHAPTER
37 37'5
37.5 The Fundamental Unit of Charge
11'Thefigureshowsapositivelychargedoildrophe1datrestbetweentwo
electrodes.
@
a.Drawafree-bodydiagramforb'Iftheelectricfieldistumedoff'.@
the drop begins to fall very slowly
the oil drop while it is at rest.
Lr---:-]---_
at constant speed. Draw a freebody diagram ofthe drop as it
falls. Label all forces.
Label all forces.
I
tr
' orcl
$.
J
L
12. Millikan observed both positive and negative oil drops.
a. Wliy didn't all the oil drops have the same sign?
*Lc d"op\cts \Nsfe cholg{ \ loininl alecfi'ons ""1
"f chcclcd by losivl,3 eledronS.
Sowre \^le,fq
So*,r"
b. Did the fact that he observed both positive and negative drops affect his conclusion that he had
measured the "fundamental unit" of charge? Why or why not?
No. Bc.ouse
'urhcther posilive or ncative,, o,ll vlsrc in{egcr
ntrultiples of o.
rntinivruv"r
13.. Charge measurements on six
€g
lll
o
o
o.
O
d
o
oil drops give the following values, all in some unknown units of charge.
Drop
q
Drop
q
I
+7.0
+24.5
4
-28.0
5
+14.0
6
-r0.5
2
c
chcrg.
3
-7.0
tn these units, what is the fundamentalunit of charge? Explain.
Tho f"lqmstdl u,r,.i{ of chonge hc,ro is 3.5. Alt of
+h" Jcops qre. .h".g"d in in*e5er m.^ltiplc,s of 3,5.
37-6
cHAprER
37
.
The Foundations of Modern Physics
37.6 The Discovery of the Nucleus
37.7 lnto the Nucleus
14. A block of uranium emits alpha particles continuously. As Rutherford showed, each alpha particle
has a charge and a mass.
a. Does the continuous emission of these particles violate the law of conservation of mass?
why not?
No. Jho
o^o.^rnt
"f
rry\qss
If not,
of lhe n^iltei alph* portrctcs is equql
tofl*o*or^r*ofv\qsslost\'lhq'urqvrirrnT'
b. Does the continuous emission of these particles violate the law of conservation of charge? If not,
why not?
N
o. Jho
exccttrl
o*or^,nl
"\,^*\
of .J,.oro. on *ho er.rittcd clphq p^t{i.los
+" +h"
o*i*^* of char3e \ost'\
t[c.
iJ
uro'.i,^'nr.
15. A proton gains 50 eV of kinetic energy by moving through a potential difference. What is AZ?
A\
= 5Ov
16. An electron, a proton, and a helium nucleus (tte*) accelerate
through the 10 V potential difference between two capacitor plates.
For each, what is the particle's increase in kinetic energy AK in
electron volts?
Electron
Proton
He++
aK= lOn'V
lOeV
a,K=
LK= \0n\
d=*[L-=,lFl0v
The Foundations of Modem Physics
.
cHAprER
37 37-7
17. Rutherford studied alpha particles using the same crossed-field technique that Thomson had invented
to study cathode rays, Assuming that valpha = Vcathode ray (which turns out to be true), would the
deflection of an alpha parlicle by a magnetic field be larger than, smaller than, or the same as the
deflection of a cathode-ray particle by the same field? Explain.
-Tho.
qh {ho fo..o exef'tcJ o^ .{he olpha
S*^lter *Iron,
Dafiicl{- is \^,i.. is lo,rqe bc**so ",ihoi"}"ito {li't"
Jt^..g .e lho c"tho4.
-i\'t f;\y p"{'.\l i{ is SOoo {i",Q.s
hto{'q !"\6ssi;;
;i
..drJ "ill d"fl"*
lsss '
18. Once Thomson showed that atoms consist of very light negative electrons and a much more massive
positive charge, why didn't physicists immediately consider a solar-system model of electrons orbiting
a positive nucleus? Why would physicists in 1900 object to such a model?
S"i"^tists ql {q" liwre could wot ivncqivre thc
ayfyg$notr
-hJ"^.*ita,o
h oh J",nsrlu o{ {h. }in,v *r^.\.*, ftfr ;tro
Nhi+ uro..^tj' hote oro{orts {oqo{her i*n'o nucteus whe!^
lLcru
\^lo.s
o.
krnourn cepu\si\s'
fsrco
bot,^ren^ gcotons.
19. Suppose you throw a small, hard rubber ball through a tree. The tree has many outer leaves, so you
cannot see clearly into the tree. Most of the time your ball passes through the tree and comes out the
other side with little or no deflection. On occasion, the ball emerges at a very large angle to your
direction of throw. On rare occasions, it even comes straight back toward you. From these observations,
what can you conclude about the structure ofthe tree? Be specific as to how you arrive at these
conclusionsy' om the ob s erv ations.
a qlar^ci1g btow, #,o de1se,
lhe bqcKvlqrd q*$:
S oliA vr\qss iowreu[sre in *he" *rce.
rcprcsorn\s c\ Aico"t b\o* *o A do se solia vnass insids.
Jhc Very lorle o^s\u
iwnplies
37-8
cHepren 37
.
The Foundations of Modern Physics
20. Beryllium is the fourth element in the periodic table. Draw pictures similar to Figure 37.20 showing the
structure of neutral Be, of Be+, of Be++, and of the negative ion Be-.
f
b-
--E
ld\
\o-
_/
Be
I
I
,
\
@
Be-
Be+*
Be+
\
f@
t \q--g h
\
o
b
@
@
./-Or
/
21. The element hydrogen has three isotopes. The most common has I = 1 . A rare form of hydrogen
(called deuterium) has A = 2. An unstable, radioactive form of hydrogen (called tritium) has A = 3.
Draw pictures similar to Figure 37.23 showing the structure of these three isotopes. Show all the
electrons, protons, and neutrons ofeach.
2
b
\
@)
/
A=1
/
/
to
I
l
o
A=2
&
\
I
A=3
22. ldentify the element, the isotope, and the charge state. Give your answer in symbolic form, such as
4
H"* o, 8 Be-.
.-'--a
w
e---'
Li*
b.
-_--e,_, 'z
/3
pq
r
(n)
iWl
o@o
\/
"(D,'€t-----O
'tco
o
tI]
o
6
o
A
o
N
@