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Solution Manual for Modern Physics, 4th Edition by Krane

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This comprehensive solution manual provides detailed, step-by-step solutions to all the problems in Kenneth S. Krane's "Modern Physics," 4th Edition. Covering all 15 chapters, from special relativity and quantum mechanics to atomic, nuclear, and particle physics, this guide is an essential resource for verifying your work and deepening your understanding of complex concepts. Each solution is clearly explained, making it an invaluable tool for students in university-level physics courses to prepare for exams and master the material.

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All 15Chapters Covered
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SOLUTION MANUAL
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, Table of Contents
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Chapterj1….............................................................................. 1

Chapterj2…............................................................................ 14

Chapterj3…............................................................................ 47

Chapterj4…............................................................................ 72

Chapterj5…............................................................................ 96

Chapterj6….......................................................................... 128

Chapterj7….......................................................................... 151

Chapterj8….......................................................................... 169

Chapterj9….......................................................................... 183

Chapterj10…........................................................................ 203

Chapterj11…........................................................................ 226

Chapterj12…........................................................................ 249

Chapterj13…........................................................................ 269

Chapterj14…........................................................................ 288

Chapterj15…........................................................................ 305

SamplejFormulajSheetjforjExams………………………….




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Thisjchapterjpresentsjajreviewjofjsomejtopicsjfromjclassicaljphysics.j Ijhavejoftenjhear
djfromjinstructorsjusingjthejbookjthatj“myjstudentsjhavejalreadyjstudiedjajyearjofjintroductor
yjclassicaljphysics,jsojtheyjdon’tjneedjthejreview.”j Thisjreviewjchapterjgivesjthejopportunityj
tojpresentjajnumberjofjconceptsjthatjIjhavejfoundjtojcausejdifficultyjforjstudentsjandjtojcollectj
thosejconceptsjwherejtheyjarejavailablejforjeasyjreference.j For
example,jalljstudentsjshouldjknowjthatjkineticjenergyjisj j1j mv2 2j,jbutjfewjarejreadily
familiarjwithjkineticjenergyjasj p2j/j2mj,jwhichjisjusedjmorejoftenjinjthejtext.j The
expressionjconnectingjpotentialjenergyjdifferencejwithjpotentialjdifferencejforjanjelectricjcha
rgejq,j Uj jqVj,jzipsjbyjinjthejblinkjofjanjeyejinjthejintroductoryjcoursejandjis
rarelyjusedjthere,jwhilejitjisjofjfundamentaljimportancejtojmanyjexperimentaljset-
upsjinjmodernjphysicsjandjisjusedjimplicitlyjinjalmostjeveryjchapter.j Manyjintroductoryjcour
sesjdojnotjcoverjthermodynamicsjorjstatisticaljmechanics,jsojitjisjusefuljtoj“review”jthemjinjth
isjintroductoryjchapter.
Ijhavejobservedjstudentsjinjmyjmodernjcoursejoccasionallyjstrugglingjwithjproblemsj
involvingjlinearjmomentumjconservation,janotherjofjthosejclassicaljconceptsjthatjresidesjinjt
hejintroductoryjcourse.jAlthoughjwejphysicistsjregardjmomentumjconservationjasjajfundam
entaljlawjonjthejsamejplanejasjenergyjconservation,jthejlatterjisjfrequentlyjinvokedjthroughou
tjthejintroductoryjcoursejwhilejformerjappearsjandjvirtuallyjdisappearsjafterjajbriefjanalysisjof
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bodyjcollisions.jMoreover,jsomejintroductoryjtextsjpresentjthejequationsjforjthejfinaljvelociti
esjinjajone-
dimensionaljelasticjcollision,jleavingjthejstudentjwithjlittlejtojdojexceptjplusjnumbersjintojthej
equations.j Thatjis,jstudentsjinjthejintroductoryjcoursejarejrarelyjcalledjuponjtojbeginjmoment
um
conservationjproblemsjwithj pinitialj j pfinalj.j Thisjputsjthemjatjajdisadvantagejinjthe
applicationjofjmomentumjconservationjtojproblemsjinjmodernjphysics,jwherejmanyjdiffere
ntjformsjofjmomentumjmayjneedjtojbejtreatedjinjajsinglejsituationj(forjexample,jclassicaljpart
icles,jrelativisticjparticles,jandjphotons).j Chapterj1jthereforejcontainsjajbriefjreviewjofjmom
entumjconservation,jincludingjworkedjsamplejproblemsjandjend-of-jchapterjexercises.
PlacingjclassicaljstatisticaljmechanicsjinjChapterj1j(asjcomparedjtojitsjlocationjinjCha
pterj10jinjthej2ndjedition)joffersjajnumberjofjadvantages.j Itjpermitsjthejuseful
expressionj Kavj jj3j2kTj tojbejusedjthroughoutjthejtextjwithoutjadditionaljexplanation.jThe
failurejofjclassicaljstatisticaljmechanicsjtojaccountjforjthejheatjcapacitiesjofjdiatomicjgasesj(h
ydrogenjinjparticular)jlaysjthejgroundworkjforjquantumjphysics.j Itjisjespeciallyjhelpfuljtojint
roducejthejMaxwell-
Boltzmannjdistributionjfunctionjearlyjinjthejtext,jthusjpermittingjapplicationsjsuchjasjthejpop
ulationjofjmolecularjrotationaljstatesjinjChapterj9jandjclarifyingjreferencesjtoj“populationjin
version”jinjthejdiscussionjofjthejlaserjinjChapterj8.j Distributionjfunctionsjinjgeneraljarejnewjt
opicsjforjmostjstudents.j Theyjmayjlookjlikejordinaryjmathematicaljfunctions,jbutjtheyjarejha
ndledjandjinterpretedjquitejdifferently.j Absentjthisjintroductionjtojajclassicaljdistributionjfun
ctionjinjChapterj1,jthejstudents’jfirstjexposurejtojajdistributionjfunctionjwilljbej||2,jwhichjlay
ersjanjadditionaljleveljofjconfusionjonjtopjofjthejmathematicaljcomplications.j Itjisjbetterjtojha
vejajchancejtojcoverjsomejofjthejmathematicaljdetailsjatjanjearlierjstagejwithjajdistributionjfun
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1

, SuggestionsjforjAdditionaljReading

Somejdescriptive,jhistorical,jphilosophical,jandjnonmathematicaljtextsjwhichjgivejgoodjback
groundjmaterialjandjarejgreatjfunjtojread:
A.jBaker,jModernjPhysicsjandjAnti-Physicsj(Addison-Wesley,j1970).
F.jCapra,jThejTaojofjPhysicsj(ShambhalajPublications,j1975).
K.jFord,jQuantumjPhysicsjforjEveryonej(HarvardjUniversityjPress,j2005).
G.jGamow,jThirtyjYearsjthatjShookjPhysicsj(Doubleday,j1966).
R.jMarch,jPhysicsjforjPoetsj(McGraw-Hill,j1978).
E.jSegre,jFromjX-RaysjtojQuarks:jModernjPhysicistsjandjtheirjDiscoveriesj(Freeman,j1980).
G.jL.jTrigg,jLandmarkjExperimentsjinjTwentiethjCenturyjPhysicsj(Crane,jRussak,j1975).
F.jA.jWolf,jTakingjthejQuantumjLeapj(Harperj&jRow,j1989).
G.jZukav,jThejDancingjWujLijMasters,jAnjOverviewjofjthejNewjPhysicsj(Morrow,j1979).

Gamow,jSegre,jandjTriggjcontributedjdirectlyjtojthejdevelopmentjofjmodernjphysicsjandjthei
rjbooksjarejwrittenjfromjajperspectivejthatjonlyjthosejwhojwerejpartjofjthatjdevelopmentjcanjo
ffer.jThejbooksjbyjCapra,jWolf,jandjZukavjofferjcontroversialjinterpretationsjofjquantumjme
chanicsjasjconnectedjtojeasternjmysticism,jspiritualism,jorjconsciousness.


MaterialsjforjActivejEngagementjinjthejClassroom

A.j ReadingjQuizzes

1. InjanjidealjgasjatjtemperaturejT,jthejaveragejspeedjofjthejmolecules:
(1) increasesjasjthejsquarejofjthejtemperature.
(2) increasesjlinearlyjwithjthejtemperature.
(3) increasesjasjthejsquarejrootjofjthejtemperature.
(4) isjindependentjofjthejtemperature.

2. Thejheatjcapacityjofjmolecularjhydrogenjgasjcanjtakejvaluesjofj3R/2,j5R/2,jandj7R/2jatjdif
ferentjtemperatures.j Whichjvaluejisjcorrectjatjlowjtemperatures?
(1)j3R/2 (2)j5R/2 (3)j7R/2

Answers 1.j3 2.j1


B.j ConceptualjandjDiscussionjQuestions

1. Equaljnumbersjofjmoleculesjofjhydrogenjgasj(molecularjmassj=j2ju)jandjheliumjgasj(mol
ecularjmassj=j4ju)jarejinjequilibriumjinjajcontainer.
(a) Whatjisjthejratiojofjthejaveragejkineticjenergyjofjajhydrogenjmoleculejtojthejaver
agejkineticjenergyjofjajheliumjmolecule?
KjH /jK He  (1)j4 (2)j2 (3) 2 (4)j1 (5)j1/ 2 (6)j1/2 (7)j1/4




2

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