Solution Manual for Modern Physics, 4th Edition by Krane (All 15 Chapters Covered)

All 15 Chapters Covered
r r r




SOLUTION MANUAL
r

, Table of Contents
r r




Chapterr1… ............................................................................. 1

Chapterr2… ........................................................................... 14

Chapterr3… ........................................................................... 47

Chapterr4… ........................................................................... 72

Chapterr5… ........................................................................... 96

Chapterr6… ......................................................................... 128

Chapterr7… ......................................................................... 151

Chapterr8… ......................................................................... 169

Chapterr9… ......................................................................... 183

Chapterr10…........................................................................ 203

Chapterr11…........................................................................ 226

Chapterr12…........................................................................ 249

Chapterr13…........................................................................ 269

Chapterr14…........................................................................ 288

Chapterr15…........................................................................ 305

SamplerFormularSheetrforrExams………………………….




viii

, Chapter 1 r




Thisrchapterrpresentsrarreviewrofrsomertopicsrfromrclassicalrphysics.r Irhaveroftenrhea
rdrfromrinstructorsrusingrtherbookrthatr“myrstudentsrhaveralreadyrstudiedraryearrofrintroducto
ryrclassicalrphysics,rsortheyrdon’trneedrtherreview.”r Thisrreviewrchapterrgivesrtheropportunit
yrtorpresentrarnumberrofrconceptsrthatrIrhaverfoundrtorcauserdifficultyrforrstudentsrandrtorcoll
ectrthoserconceptsrwherertheyrareravailablerforreasyrreference.r For
2
example,rallrstudentsrshouldrknowrthatrkineticrenergyrisr r1r mv
2
r,rbutrfewrarerreadily


familiarrwithrkineticrenergyrasr p2r/r2mr,rwhichrisrusedrmoreroftenrinrthertext.r The
expressionrconnectingrpotentialrenergyrdifferencerwithrpotentialrdifferencerforranrelectricrch
argerq,r Ur rqVr,rzipsrbyrinrtherblinkrofranreyerinrtherintroductoryrcourserandris
rarelyrusedrthere,rwhileritrisrofrfundamentalrimportancertormanyrexperimentalrset-
upsrinrmodernrphysicsrandrisrusedrimplicitlyrinralmostreveryrchapter.r Manyrintroductoryrcou
rsesrdornotrcoverrthermodynamicsrorrstatisticalrmechanics,rsoritrisrusefulrtor“review”rthemrinr
thisrintroductoryrchapter.
Irhaverobservedrstudentsrinrmyrmodernrcourseroccasionallyrstrugglingrwithrproblem
srinvolvingrlinearrmomentumrconservation,ranotherrofrthoserclassicalrconceptsrthatrresidesri
nrtherintroductoryrcourse.rAlthoughrwerphysicistsrregardrmomentumrconservationrasrarfund
amentalrlawronrthersamerplanerasrenergyrconservation,rtherlatterrisrfrequentlyrinvokedrthroug
houtrtherintroductoryrcourserwhilerformerrappearsrandrvirtuallyrdisappearsrafterrarbriefranaly
sisrofr2-
bodyrcollisions.rMoreover,rsomerintroductoryrtextsrpresentrtherequationsrforrtherfinalrvelocit
iesrinrarone-
dimensionalrelasticrcollision,rleavingrtherstudentrwithrlittlertordorexceptrplusrnumbersrintorth
erequations.r Thatris,rstudentsrinrtherintroductoryrcourserarerrarelyrcalledruponrtorbeginrmome
ntum
conservationrproblemsrwithr pinitialr r pfinalr .r Thisrputsrthemratrardisadvantagerinrthe
applicationrofrmomentumrconservationrtorproblemsrinrmodernrphysics,rwherermanyrdiffere
ntrformsrofrmomentumrmayrneedrtorbertreatedrinrarsinglersituationr(forrexample,rclassicalrpa
rticles,rrelativisticrparticles,randrphotons).r Chapterr1rthereforercontainsrarbriefrreviewrofrmo
mentumrconservation,rincludingrworkedrsamplerproblemsrandrend-of-rchapterrexercises.
PlacingrclassicalrstatisticalrmechanicsrinrChapterr1r(asrcomparedrtoritsrlocationrinrCh
apterr10rinrther2ndredition)roffersrarnumberrofradvantages.r Itrpermitsrtheruseful
expressionr Kavr rr32r kTr torberusedrthroughoutrthertextrwithoutradditionalrexplanation.rThe
failurerofrclassicalrstatisticalrmechanicsrtoraccountrforrtherheatrcapacitiesrofrdiatomicrgasesr(
hydrogenrinrparticular)rlaysrthergroundworkrforrquantumrphysics.r Itrisrespeciallyrhelpfulrtori
ntroducertherMaxwell-
Boltzmannrdistributionrfunctionrearlyrinrthertext,rthusrpermittingrapplicationsrsuchrasrtherpo
pulationrofrmolecularrrotationalrstatesrinrChapterr9randrclarifyingrreferencesrtor“populationri
nversion”rinrtherdiscussionrofrtherlaserrinrChapterr8.r Distributionrfunctionsrinrgeneralrarerne
wrtopicsrforrmostrstudents.r Theyrmayrlookrlikerordinaryrmathematicalrfunctions,rbutrtheyrar
erhandledrandrinterpretedrquiterdifferently.r Absentrthisrintroductionrtorarclassicalrdistributio
nrfunctionrinrChapterr1,rtherstudents’rfirstrexposurertorardistributionrfunctionrwillrber||2,rwhi
chrlayersranradditionalrlevelrofrconfusionronrtoprofrthermathematicalrcomplications.r Itrisrbett
errtorhaverarchancertorcoverrsomerofrthermathematicalrdetailsratranrearlierrstagerwithrardistribu
tionrfunctionrthatrisreasierrtorinterpret.

1

, SuggestionsrforrAdditionalrReading

Somerdescriptive,rhistorical,rphilosophical,randrnonmathematicalrtextsrwhichrgivergoodrbac
kgroundrmaterialrandrarergreatrfunrtorread:
A.rBaker,rModernrPhysicsrandrAnti-Physicsr(Addison-Wesley,r1970).
F.rCapra,rTherTaorofrPhysicsr(ShambhalarPublications,r1975).
K.rFord,rQuantumrPhysicsrforrEveryoner(HarvardrUniversityrPress,r2005).
G.rGamow,rThirtyrYearsrthatrShookrPhysicsr(Doubleday,r1966).
R.rMarch,rPhysicsrforrPoetsr(McGraw-Hill,r1978).
E.rSegre,rFromrX-RaysrtorQuarks:rModernrPhysicistsrandrtheirrDiscoveriesr(Freeman,r1980).
G.rL.rTrigg,rLandmarkrExperimentsrinrTwentiethrCenturyrPhysicsr(Crane,rRussak,r1975).
F.rA.rWolf,rTakingrtherQuantumrLeapr(Harperr&rRow,r1989).
G.rZukav,rTherDancingrWurLirMasters,rAnrOverviewrofrtherNewrPhysicsr(Morrow,r1979).

Gamow,rSegre,randrTriggrcontributedrdirectlyrtortherdevelopmentrofrmodernrphysicsrandrthe
irrbooksrarerwrittenrfromrarperspectiverthatronlyrthoserwhorwererpartrofrthatrdevelopmentrcan
roffer.rTherbooksrbyrCapra,rWolf,randrZukavrofferrcontroversialrinterpretationsrofrquantumr

mechanicsrasrconnectedrtoreasternrmysticism,rspiritualism,rorrconsciousness.


MaterialsrforrActiverEngagementrinrtherClassroom

A.r ReadingrQuizzes

1. InranridealrgasratrtemperaturerT,rtheraveragerspeedrofrthermolecules:
(1) increasesrasrthersquarerofrthertemperature.
(2) increasesrlinearlyrwithrthertemperature.
(3) increasesrasrthersquarerrootrofrthertemperature.
(4) isrindependentrofrthertemperature.

2. Therheatrcapacityrofrmolecularrhydrogenrgasrcanrtakervaluesrofr3R/2,r5R/2,randr7R/2ratrd
ifferentrtemperatures.r Whichrvaluerisrcorrectratrlowrtemperatures?
(1)r3R/2 (2)r5R/2 (3)r7R/2

Answers 1.r3 2.r1


B.r ConceptualrandrDiscussionrQuestions

1. Equalrnumbersrofrmoleculesrofrhydrogenrgasr(molecularrmassr=r2ru)randrheliumrgasr(mo
lecularrmassr=r4ru)rarerinrequilibriumrinrarcontainer.
(a) Whatrisrtherratiorofrtheraveragerkineticrenergyrofrarhydrogenrmoleculertortherave
ragerkineticrenergyrofrarheliumrmolecule?
KrH /rK He  (1)r4 (2)r2 (3) 2 (4)r1 (5)r1/ 2 (6)r1/2 (7)r1/4




2