All 15Chapters Covered
j j j
SOLUTION MANUAL
j
, Table of Contents
j j
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………………………….
viii
, Chapter 1 j
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 jqVj,jzipsjbyjinjthejblinkjofjanjeyejinjthejintroductoryjcoursejandjis
rarelyjusedjthere,jwhilejitjisjofjfundamentaljimportancejtojmanyjexperimentaljset-
upsjinjmodernjphysicsjandjisjusedjimplicitlyjinjalmostjeveryjchapter.j Manyjintroductoryjcour
sesjdojnotjcoverjthermodynamicsjorjstatisticaljmechanics,jsojitjisjusefuljtoj“review”jthemjinjth
isjintroductoryjchapter.
Ijhavejobservedjstudentsjinjmyjmodernjcoursejoccasionallyjstrugglingjwithjproblemsj
involvingjlinearjmomentumjconservation,janotherjofjthosejclassicaljconceptsjthatjresidesjinjt
hejintroductoryjcourse.jAlthoughjwejphysicistsjregardjmomentumjconservationjasjajfundam
entaljlawjonjthejsamejplanejasjenergyjconservation,jthejlatterjisjfrequentlyjinvokedjthroughou
tjthejintroductoryjcoursejwhilejformerjappearsjandjvirtuallyjdisappearsjafterjajbriefjanalysisjof
j2-
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
ctionjthatjisjeasierjtojinterpret.
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
j j j
SOLUTION MANUAL
j
, Table of Contents
j j
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………………………….
viii
, Chapter 1 j
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 jqVj,jzipsjbyjinjthejblinkjofjanjeyejinjthejintroductoryjcoursejandjis
rarelyjusedjthere,jwhilejitjisjofjfundamentaljimportancejtojmanyjexperimentaljset-
upsjinjmodernjphysicsjandjisjusedjimplicitlyjinjalmostjeveryjchapter.j Manyjintroductoryjcour
sesjdojnotjcoverjthermodynamicsjorjstatisticaljmechanics,jsojitjisjusefuljtoj“review”jthemjinjth
isjintroductoryjchapter.
Ijhavejobservedjstudentsjinjmyjmodernjcoursejoccasionallyjstrugglingjwithjproblemsj
involvingjlinearjmomentumjconservation,janotherjofjthosejclassicaljconceptsjthatjresidesjinjt
hejintroductoryjcourse.jAlthoughjwejphysicistsjregardjmomentumjconservationjasjajfundam
entaljlawjonjthejsamejplanejasjenergyjconservation,jthejlatterjisjfrequentlyjinvokedjthroughou
tjthejintroductoryjcoursejwhilejformerjappearsjandjvirtuallyjdisappearsjafterjajbriefjanalysisjof
j2-
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
ctionjthatjisjeasierjtojinterpret.
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
