Chapter 38 Workbook Solutions

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Wauantization
38.1 The Photoelectric Effect
38.2 Einstein's Explanation
1. a. A negatively charged electroscope can be discharged by shining
an ultraviolet light on it. How does this happen?
The , Hcoviolzt l,*;t .o",,,,rt, .of b*r,J\ns tf
UVright
""i..r +"+,'-wha; obso.bol bv {{na, q\e,"+.o",s
o* t[.o o\oitoqcooc . eiva orrrora,qh ensv"qY {o {l^c
e.\e-.tro*s *o a.\\ow '{fru asc*pe -ot +he ili"{"ons fro- *hq
S'.^r{o.ce of t\.o o-\e.\roscope.i o$*or "rhich *hoY qre repdleJ
&r^rc1 bI tlre rc,v''nciv,in5 no5*{ivo .h*r1e.
b. You might think that an ultraviolet light shining on an initially uncharged electroscope would cause
the electroscope to become positively charged as photoelectrons are emitted. ln fact, ultraviolet light
hu_r,lo notiggatle effect on an u1-charged e-leclroscope. Why not?
As *ho o\o.{r"r* \.^u. lt^" o\**roscote, t"\
l?"o,*, goti{i.nel1
ch*"o.J e\e.*roscope \ro}.,l".A o.'^d o',ra- gu\lcd bo'.'k bY ,
u\""ti"s\qti. o$ltolliov\s.*^\o.s 'lho o**"" a\ncrgrl is Lno*Sh
+. L*po * o ^"& S'^dh"r o\Nc\Y'
2. In the photoelectric effect experiment, a current is measured
while light is shining on the cathode. But this does not
appear to be a complete circuit, so how can there be a
TiH::: o^ +\" so,-rqco of -discroto- *ha., Current
melcr
*+i^1i."'nbi,-orb n^o*qf i,n
L.^*A[o b-^,,.',4\a.s. b*^'"d\a.s. " S*^.,- fgou^ *hc *ho ]i"U+ li:' 1i1ht shi'.inq shinin5 on '
t\a. c*thode-, This a.tnc^v rs a'rnotr t o*5\" *o o,ltoni" *hc
*o lo escorsc. sscorpa. S",..,.,. fcon +L' +h" J,,l*f...o J,^rf^.o o{ *hq.
tthode.,o"A
+; i[ l*"i;'.+ +h" ;**;--r"+" c\s ]he' flou'r
i,'. *hq, circ.nil.
ol*{r rt t
t"..r"\
"f "hqrSc
38-1

38-2 cHAPTER l$ . Quantization
3. Draw the trajectories of several typical photoelectrons when (a) LV =Vunode - Zcathode ) 0,
(b) -4top

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Quantization . cHAPTER 38 38-3
c. The current is zero for LV (E o). (K*o,*)
; r = Eeto.- (:J,
qnl (K-o,*)\= €qls.- (EJa.So (K*^*),((K*^x)r and
Vr

38-4 cuaprcn 38 . Quantization
9. Consider the following characteristics of the photoelectric effect:
i. The generation of photoelectrons.
@ ffl. existence of a threshold frequency.
iii. The photoelectric cLlrrent increases with increasing light intensity.
iv. The photoelectric current is independent of LV for AZ > 0.
v. The photoelectric current decreases slowly as AZ becomes more negative.
@rn.
Qlfne
stopping potential is independent of the light intensity.
photoelectron current appears instantly when the light is tumed on.
Which of these cannot be explained by classical physics?
Nothing ivr d^ssi "ot p\ si.s "^l ox plain
(^s oiposed To haU,+ \ntc,',si\) ,ss' *he
*hc sioppinS potoi"lio.\ i'nlogonA""if of
10. The figure shows a current-versus-potential
difference graph for a photoelectric effect
experiment. On the figure, draw and label graphs for
the following three situations:
i. The light intensity is increased.
ii. The light frequency is increased.
iii. The cathode work function is increased.
In each case. no other oarameters of the exoeriment
qre ohqnocA' i) n{qrx cr^rrQ.nt inirco.se'
1 t. The figure shows u .rrr.ni-tut#3ur-il;;.?ti"s ' i
graph for a photoelectric effect experiment. On the
figure, draw and label graphs for the following
three situations:
i. The light intensity is increased.
ii. The anode-cathode potential difference is
increased.
iii. The cathode work function is increased.
In each case, no other parameters of the experiment
are chaneed.
-'- -"-"e-- L.) A s^orq i-.tensQ. li"ht
ii.) Sovno fo, L.^+ Ii.,""
iii ')9 o \ncf co'Se's '
a, *htrshotd fioq*",n.y
" i^sto"r* t' c1^"corr{ of
lilht inntensi\.
co,rASe-S Ct \o.rger C\^ffc,nt.
i v,\Cr e-Ases
ii, ;
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12. The figure shows a stopping potential-versusfrequency
graph for a photoelectric effect experiment.
On the figure, draw and label graphs for the following
two situations:
i. The light intensity is increased,
ii. The cathode work function is increased.
In each case, no other parameters of the experiment
are changed.
13. In a photoelectric effect experiment, the frequency of the light is increased. As a result:
i. There are more photoelectrons. iii. Both i and ii,
Cn.
photoelectrons are faster.
Explain your choice.
E u\n. = hf witl olso
cl,\So irncfeo,.SLS.
iv. Neither i nor ii.
Quantization . cHAPTER 38 38-5
increa,sc o'!e so K^o*= Es1o.- E o
14. ln a photoelectric effect experiment, the intensity of the light is increased. As a result:
Qfn.r.
are more photoelectrons. iii. Both i and ii.
ii. The photoelectrons are faster. iv, Neither i nor ii.
il il:::'n ,^i"^.e ti q\r* d"riuors a, larler nr,rmbcr e{ r,#
euqrnta lo *hc- Si"fo.o ejoclinq q - \orgcr n\ wtbcf oT
;i J. e\ cctr o v,s q.v\ t {horc by co,*,.sin3 q \ 6f* cr.trrenf .
15. A gold cathode (work function = 5.1 eV) is illuminated with light of wavelength 250 nm. It is found
that the photoelectron current is zero when LV = 0 V. Would the current change if:
a. The intensity is doubled?
No. $= "/t = 3xlos'./s,/"so:,lg-i* : l. !.* lgts H e
$o= +. fr$qq = l.!.3* to,S He f .fo
b. The anode-cathode potential difference is increased to LV = 5,5 V?
No. {' fo
c. The cathode is changed to aluminum (work function = 4.3 eV)?
Je-s. + = e/x = 3xlo8'/t/rSo xl0-{",1 =
'r .3 e\
{J\" I o''sNs :1.0'l x\015
l, ).x lols He
ll+

38-6 cH,qprpn 38 . Quantization
38.3 Photons
16. When we say that a photon is a "quantum of light," what does that mean? What is quantized?
18. Thefrequencyofabeamoflightisincreasedbutthelight'sintensityisunchanged.Asaresult:
i. The photons travel faster.
iii. There are fewer photons per second.
19.
Lig\n* cow\es ir. packets .of ensrg\. Jha f**do*o^tn\ , u*i\
# \i3ht a.\ e,r.\ it o, pLoton. The'L^og1 rs qucvrtiztd.
17. Theintensityofabeamoflightisincreasedbutthelight'sfrequencyisunchanged.Asaresult:
i. The photons travel faster, iii. The photons are larger.
ii, Each photon has more energy. (iilrn.r. are more photons per second.
Which of these (perhaps more than one) are true? Explain.
A r^Aore- \,',tcnsc \,qht Ae,\iu-o-rs $torg h3!,t luato {o. -tha
s*.t^." ;',*f.' *oi.*
"^A " l\^otoo[.{'. or,,', . pL" se.o*d in
{h" ot,ro*oe\c}ri. t\ccc, sioni\or\11 o
"ff"d.t .3ceotc"
,^t",,lSi\1 s,reorns Yr\sfo- pho\o*i Pst Second '
Gacn
photon has more energy.
Which of these (perhaps more than one) are true? Explain.
E= hf
Photons are sometimes represented by pictures like this. Just what
is this a picture of? Explain what this "graph" shows.
-This is a Nq{c, poclret.This is qr
et"itr *i1ne*i c, v.rqvQ-
" 1l,+h ^, wavc\cn5th
qnd fr"q, *iL"y b*+ '{l'J {l.dt is o.[s o,\s o t s o,.i*ho't
o v"t(-w\n
dis.r4{g' q.',,J 'lo.o\izQ.A \iV.. o, go."*i.lc.
20. Light of wavelength ),=lpm is emitted from point A,
A plroton is detected 5 pm away at point B. On the
figure, draw the trajectory that a photon follows between
points A and B.
iv. There are more photons per second.
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38.4 Matter Waves and Energy Quantization
Quantization . cHAPTER 38 38-7
21. Electron I is accelerated from rest through a potential difference of 100 V. Electron 2 is accelerated
from rest through a potential difference of 200 V. Afterward, which electron has the larger de Broglie
wavelength? Explain.
E\ertror, \. K.=loOeV Kt=
r= h
AmV
).00 e.V v
-Tl^erdo.e Vlt \, qvd So +1"'^+
.\ aK
-.1?
1, r 1r.
22. An electron and a proton are each accelerated from rest through a potential difference of 100 V.
Afterward, which particle has the larger de Broglie wavelength? Explain.
Nit\^ \=h/*., qnA v=]+ rh;^ \=+ =
So *tr,e svna,llc,r v\^ss tor"orpo.rl, *o tha. \or3cr
Nc,,*ror. t.** \. The h',qhec ,1
*o o hiqhor sgcJ o.
'5 ^tl
Ae.t. l"^oo"ot ^r" r^ro*\J to'*'Po"J
smo,l\Q,r *o.no\o.3+h .
h
.ltK^
23. Neutron beam t has a temperature of 500 K. Neutron beam 2 has a temperature of 5 K. Which
neutrons have the larger de Broglie wavelength? Explain.
24. A neutron is shot straight up with an initialspeed of 100 m/s. As it rises, does its de Broglie
wavelength increase, decrease, or not change? Explain.
Tncreases. fs i+ rise,J'* it--a q^d moment*nn d..tu r".
\hh
\-T=h-v
25. Double-slit interference of electrons occurs because:
i. The electrons passing through the two slits repel each other.
ii. Electrons collide with each other behind the slits.
iii. Electrons collide with the edges of the slits.
@acn
electron goes through both slits.
v. Tlre energy of the electrons is quantized.
vi. Only certain wavelengths of the electrons fit through the slits.
\^ro{q\an3+h.
Which of these (perhaps more than one) are correct? Explain.
\Al+V, q wcok e\a.c+ri c [covn . No cqrt send o nc ele."+ro',
o*+ a |,me- *[.ro*q\ *\^o qioar o.*l s+ilt otse,rve,
q\n 1r^*ur{e1-cncQ.'ir' *V,c ^t*s
roso\ti".3 po.**or". df e.l.itrutrs.

38-8 cH,qpren 38 . Quantization
26. Can an electron with a de Broglie wavelength of 2 pm pass through a slit that is lpm wide?
Y* , b.^t \\ s Ai"o.\ o,^. o{{qr^ po.ssin5 }h.o^3\" is
rAncef to.in .
27 . The figure shows the standing de Broglie wave of a particle
in a box.
u
a. What is the quantum number? I
b. Can you determine from this picture whether the "classical" particle is moving to the right or to the
left? If so. which is it? If not, why not?
No,*hi. is
^
*J*"" wq{a- i^ thofo.^ of o st wo,vQ
^Ain1.
nto.,lq- \^p of \"^n"ti*'5 w^ves movins ',,n bo*h dirgz+ions.
28. A particle in a box of length Zu has Et =2 eY. The same particle in a box of length Z6 has Ez = 50 eV.
What is the ratio LalLb2
E*= Y.]lf , E,= \ahe :
8;fr / T* *
ru\;
Ix/uu" _ so - Lo \

38.5 Bohr's Model of Atomic Quantization
38.6 The Bohr Hydrogen Atom
38.7 The Hydrogen Spectrum
Quantization . cHAPTER 38 38-9
30. J. J. Thomson studied the ionization of atoms in collisions with electrons. He accelerated electrons
through a potential difference, shot them into a gas of atoms, then used a mass spectrometer to detect
any ions produced in the collisions. By using different gases, he found that he could produce singly
ionized atoms of allthe elements that he tried. When he used higher accelerating voltages, he was able
to produce doubly ionized atorns of all elements except hydrogen.
a. Why did Thornson have to use higher accelerating voltages to detect doubly ionized atoms than to
detect singly ionized atoms?
To ..,o*" a sinq\y ioniznd dto,^.n, otto gleJco"' **t b" aor'.ouuJ
4.o,- the 61*oua. A'do*b!1 ionizoA oto- fcq.rirqg Jhc re,v,novq.l of
*vro. c\e.g*cons ylhich **kls rnoec. onergY qnd'thorttoce highar
$,Cce\ege.{i r,q vo\to,qtS.
b. What conclusion-or conclusions about hydrogen atoms can you draw from these observations? Be
specific as to how your conclusions are related to the observations.
H"lroo.or. e,r.,.st not hqv" two e-\sctrons tho.t can bc nc,vro{el
to lrcjct.- o, do.^b\y ionizeA a*ov"r. ll1Aeolc^ hos o".\1 oylo
g\q,*r o'n .
3 1. If an electron is in a stationary state of an atom, is the electron at rest? If not, what does the term
mean?
No , th. e\q-ctron ,"tron is \^ot o* rc-s+. T+ is in o\n o\lot^tol orbi+'
ott"*"a , or 1. *t"li.f 'or bi{s are, co"lloA stotton4rY
\c. o",\*,
stalcs. '
32. The diagram shows the energy level diagram of element X.
a. Wliat is the ionization energy of element X?
lE,l = '1 uv
E = o eV
-leV-ll=3 i I 240 nnr
-2cV - n=2
g b. An atom in the ground state absorbs a photon, then emits a photon with a wavelength of 1240 nm.
What conclusion can you draw about the energy of the photon that was absorbed?
5
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ErU,oto'.,= 3c\
@ c. An atom in the ground state has a collision with an electron, then emits a photon with a wavelength
of 1240 nm. What conclusion can you draw about the initial kinetic energy of the electron?
Eur."= 3 oV
--4 eV

38-1 0 cHAPTER 38 . Quantization
33. The figure shows a hydrogen atom, with an electron orbiting a proton.
a. What force or forces act on the electron?
Thc pro*o,^ exor+s a Co.^lo*b e\ec+r'r<
focce on tlne. olert'on-
b. On the figure, draw the electron's velocity, acceleration, and the
force vectors.
34. Bohr did not inclr-rde the gravitational force in his analysis of the
hydrogen atom. Is this one of the reasons that his modelof the hydrogen atom had only limited
success? Explain.
No, thu grovilati onq\ fun..
e\er*r i c fo rce .
35. a. The stationary state of hydrogen shown on the left has quantum number n =
b. On the right, draw the stationary state of the r -
36. The n = 3 state of hydrogen has E3 = -l .51 eV.
a. Why is the energy negative?
1 state.
Jwo Fcw pqc*is\e,s $a. dis*o.ncc
;;; "ri+h
Zgro. " i'"+L^ii^i' po*cnti .*"q$Y- q$y. Th.., electcon
'I1nc, ele.tcon
iu,["'i; +h; -irril*. atom qnA
*oqethcc in tha
leJs *hon O e-V.
b. What is the physical significance of the specific number 1.51 eV?
\,s i s *he \ir,J,irl,o q-nef qy of o.n c\ec+co''
s{a*iono,ry s***e. 'ruit ir +ho hrrrovrnt of
ho.vQ, *o 'oAd *o &ee *ha. e\ec*ro". to*
ls h^\,\ch, rn\ch s^nltor {Lo.'n tho.
q
tetw"on *h"t"t r'= oa hqvq,
or,d Dcoton afo
S o ^"St horr. o.rn
b J.^"d
Ql^efsY
i'' *ho n =3
a\e,r3Y $e *oold
*ho o4orn.
d
I
=
E
o
o
o.
d
o

tr
o
rI]
o
o
O
N
o
37. Why is there no stationary state of hydrogen with E = -9 eY ?
Quantization . cHAPTER 3s 38-1 1
T[,is is ^d o\^s af {he q, o.,,'tizel , allo*ro-b\e, ane-rg]y
lo.r"ls fo" {ha hydroqon ho*, E, : - 13. 6 O e\ *nd
Ex= - 3,tlo u\, o^A -1t'";" qrq "o s*tos i,r hl'lcqn
{h ..t ..ro qltowool.
38. Draw and label an energy level diagram for hydrogen. On it, show all the transitions by which an
electron in the n = 4 state could emit a photon.
n=3 - E3: -e.g{eV E*= O
n:l
.lffiE{.-O.85e.V
E,. -l.5lcV
Ea.' - 3,'{o eV
€,= - 13.60 eV
39. a. Which states of a hydrogen atom can be excited by collision with an electron with kinetic energy
K: 12.5 eV? Explain.
: -Ir.,o r,= | anl ^= 3 slo.*qs. -ll"c. ofo"t"orn cqvr |nqv\sS". up to l.l.ScV.
tothe- a*oua. Et tokq-s 10. ). oV to-i*ip i" ft^" *=ta s*^te *"'d
l\, oq Q-V to 1*vnp to {-he v\=3 st*te'
b. After the collision, the electron:
i. Bonnces off with K > 12.5 eY" @eoun".s
' ii. Bounces off with K = 12.5 eY. iv. Has been absorbed.
Explain your choice.
';;
off with K < 12'5 eY.
"' of -hh" e'\c'ctron^'s in'{i o.\ alrcc'gy I s *'o^''trrol *o +h'o'
" '
q{onn lo'oj'.iio-"1{'i-o :"'t:+; .+1+" -il+ 'i[' ql"'{ron s+ill
h.^s sovna. *^o*'.* of oncrg) lsf*.
c. After the collision, the atom emits a photon. List all the possible n I m transitions that might occur
as a result of this collision.
Tf *hc. o.tovn i s i^i*io,.lty e*.i*cJ {o n= A. i+ .o*nll *l.o-n
emit q p\o*o"t. in *h" fro,nsilio", l. + [ . If *hc- qfo-
is i^i*iol\y qxcitod *o,n=3 lho possible *ro,sitions o\re
3+}. -|hc.r,, I
).-l$r 3+1.

38-12 cHAPTER 38 . Quantization
40. The longest wavelength in the Balmer series is 656 nm.
a, What transition is this?
3-) )
b. If light of this wavelength shines on a container of hydrogen atoms, will the light be absorbed? Why
or why not?
No. Etse^*,o.\[1 a\\ of t1.," q*ovns in o.
hf{"o5o" .3"t r:t:Jt
thc e,f o.,.nj sta:tc n= [ . J\tcfc. ov. v\o e\eitronS ln tlo n
st..{s 'l;{ ;-(A-o,brocb'+L; o*.ig1 -o,*J
i*r To lho n=3
stdc,
41 . a. How many electrons, protons, and neutrons are in a hydrogen-like 12 C ion ?
(" pr o{ons, G nqv$ron s