Solution Manual for Modern Physics, 4th Edition by Krane | Complete Solutions for All 15 Chapters

All 15 Chapters Covered
M M M




SOLUTION MANUAL
M

, Table of Contents
M M



ChapterM1… ............................................................................ 1

ChapterM2… .......................................................................... 14

ChapterM3… .......................................................................... 47

ChapterM4… .......................................................................... 72

ChapterM5… .......................................................................... 96

ChapterM6… ........................................................................ 128

ChapterM7… ........................................................................ 151

ChapterM8… ........................................................................ 169

ChapterM9… ........................................................................ 183

ChapterM10… ...................................................................... 203

ChapterM11… ...................................................................... 226

ChapterM12… ...................................................................... 249

ChapterM13… ...................................................................... 269

ChapterM14… ...................................................................... 288

ChapterM15… ...................................................................... 305

SampleMFormulaMSheetMforMExams………………………….




viii

, Chapter 1 M



ThisMchapterMpresentsMaMreviewMofMsomeMtopicsMfromMclassicalMphysics.M IMhave
MoftenMheardMfromMinstructorsMusingMtheMbookMthatM“myMstudentsMhaveMalreadyMstudied

MaM yearMofMintroductoryMclassicalMphysics,MsoMtheyMdon’tMneedMtheMreview.”M ThisMrevi

ewMchapterMgivesMtheMopportunityMtoMpresentMaMnumberMofMconceptsMthatMIMhaveMfoun
dMtoMcauseMdifficultyMforMstudentsMandMtoMcollectMthoseMconceptsMwhereMtheyMareMavail
ableMforMeasyMreference.M For
example,MallMstudentsMshouldMknowMthatMkineticMenergyM2 isM M1M mv2M,MbutMfewMareMreadily
familiarMwithMkineticMenergyMasM p2M/M2mM,MwhichMisMusedMmoreMoftenMinMtheMtext.M The
expressionMconnectingMpotentialMenergyMdifferenceMwithMpotentialMdifferenceMforManMele
ctricMchargeMq,M UM MqVM,MzipsMbyMinMtheMblinkMofManMeyeMinMtheMintroductoryMcou
rseMandMis
rarelyMusedMthere,MwhileMitMisMofMfundamentalMimportanceMtoMmanyMexperimentalMset-
upsMinMmodernMphysicsMandMisMusedMimplicitlyMinMalmostMeveryMchapter.M ManyMintrod
uctoryMcoursesMdoMnotMcoverMthermodynamicsMorMstatisticalMmechanics,MsoMitMisMuseful
MtoM“review”MthemMinMthisMintroductoryMchapter.

IMhaveMobservedMstudentsMinMmyMmodernMcourseMoccasionallyMstrugglingMwithM
problemsMinvolvingMlinearMmomentumMconservation,ManotherMofMthoseMclassicalMconce
ptsMthatMresidesMinMtheMintroductoryMcourse.MAlthoughMweMphysicistsMregardMmomentu
mMconservationMasMaMfundamentalMlawMonMtheMsameMplaneMasMenergyMconservation,Mth
eMlatterMisMfrequentlyMinvokedMthroughoutMtheMintroductoryMcourseMwhileMformerMappea
rsMandMvirtuallyMdisappearsMafterMaMbriefManalysisMofM2-
bodyMcollisions.MMoreover,MsomeMintroductoryMtextsMpresentMtheMequationsMforMtheMfin
alMvelocitiesMinMaMone-
dimensionalMelasticMcollision,MleavingMtheMstudentMwithMlittleMtoMdoMexceptMplusMnumb
ersMintoMtheMequations.M ThatMis,MstudentsMinMtheMintroductoryMcourseMareMrarelyMcalled
MuponMtoMbeginMmomentum

conservationMproblemsMwithM pinitialM M pfinalM.M ThisMputsMthemMatMaMdisadvantageMinMthe
applicationMofMmomentumMconservationMtoMproblemsMinMmodernMphysics,MwhereMman
yMdifferentMformsMofMmomentumMmayMneedMtoMbeMtreatedMinMaMsingleMsituationM(forMe
xample,MclassicalMparticles,MrelativisticMparticles,MandMphotons).M ChapterM1MthereforeM
containsMaMbriefMreviewMofMmomentumMconservation,MincludingMworkedMsampleMprobl
emsMandMend-of-MchapterMexercises.
PlacingMclassicalMstatisticalMmechanicsMinMChapterM1M(asMcomparedMtoMitsMlocati
onMinMChapterM10MinMtheM2ndMedition)MoffersMaMnumberMofMadvantages.M ItMpermitsMtheM
useful
expressionM KavM 2MM3M kTM toMbeMusedMthroughoutMtheMtextMwithoutMadditionalMexplanation.MThe
failureMofMclassicalMstatisticalMmechanicsMtoMaccountMforMtheMheatMcapacitiesMofMdiatom
icMgasesM(hydrogenMinMparticular)MlaysMtheMgroundworkMforMquantumMphysics.M ItMisMes
peciallyMhelpfulMtoMintroduceMtheMMaxwell-
BoltzmannMdistributionMfunctionMearlyMinMtheMtext,MthusMpermittingMapplicationsMsuchM
asMtheMpopulationMofMmolecularMrotationalMstatesMinMChapterM9MandMclarifyingMreferenc
esMtoM“populationMinversion”MinMtheMdiscussionMofMtheMlaserMinMChapterM8.M Distributio
nMfunctionsMinMgeneralMareMnewMtopicsMforMmostMstudents.M TheyMmayMlookMlikeMordina
ryMmathematicalMfunctions,MbutMtheyMareMhandledMandMinterpretedMquiteMdifferently.M A

1

, bsentMthisMintroductionMtoMaMclassicalMdistributionMfunctionMinMChapterM1,MtheMstudents
’MfirstMexposureMtoMaMdistributionMfunctionMwillMbeM||2,MwhichMlayersManMadditionalMle
velMofMconfusionMonMtopMofMtheMmathematicalMcomplications.M ItMisMbetterMtoMhaveMaMc
hanceMtoMcoverMsomeMofMtheMmathematicalMdetailsMatManMearlierMstageMwithMaMdistributi
onMfunctionMthatMisMeasierMtoMinterpret.




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