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M O D E R N P H Y S I C S M O D E R N P H Y S I C S Third edition K e n n e t h S. K r a n e DEPARTMENT OF PHYSICS OREGON STATE UNIVERSITY JOHNWILEY&SONS,INC VPANDEXECUTIVEPUBLISHER KayePace EXECUTIVEEDITOR StuartJohnson MARKETINGMANAGER ChristineKushner DESIGNDIRECTOR JeofVita DESIGNER KristineCarney PRODUCTIONMANAGER JanisSoo ASSISTANTPRODUCTIONEDITOR ElaineS.Chew PHOTODEPARTMENTMANAGER HilaryNewman PHOTOEDITOR SheenaGoldstein COVERDESIGNER SengPingNgieng COVERIMAGE CERN/SCIENCEPHOTOLIBRARY/PhotoResearchers,Inc. ThisbookwassetinTimesbyLaserwordsPrivateLimitedandprintedandboundbyR.R.DonnelleyandSonsCompany,Von Hoffman.ThecoverwasprintedbyR.R.DonnelleyandSonsCompany,VonHoffman. Thisbookisprintedonacidfreepaper. 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Evaluationcopiesareprovidedtoqualifiedacademicsandprofessionalsforreviewpurposesonly,foruseintheircoursesduringthe nextacademicyear.Thesecopiesarelicensedandmaynotbesoldortransferredtoathirdparty.Uponcompletionofthereview period,pleasereturntheevaluationcopytoWiley.Returninstructionsandafreeofchargereturnmailinglabelareavailableat www.wiley.com/go/returnlabel.Ifyouhavechosentoadoptthistextbookforuseinyourcourse,pleaseacceptthisbookasyour complimentarydeskcopy.OutsideoftheUnitedStates,pleasecontactyourlocalsalesrepresentative. LibraryofCongressCataloging-in-PublicationData Krane,KennethS. Modernphysics/KennethS.Krane.--3rded. p.cm. Includesbibliographicalreferencesandindex. ISBN978-1-118-06114-5(hardback) 1.Physics.I.Title. QC21.2.K72012 539--dc23 2011039948 PrintedintheUnitedStatesofAmerica 10987654321 PREFACE This textbook is meant to serve a first course in modern physics, including relativity,quantummechanics,andtheirapplications.Suchacourseoftenfollows the standard introductory course in calculus-based classical physics. The course addresses two different audiences: (1) Physics majors, who will later take a morerigorouscourseinquantummechanics,findanintroductorymoderncourse helpful in providing background for the rigors of their imminent coursework in classical mechanics, thermodynamics, and electromagnetism. (2) Nonmajors, who may take no additional physics class, find an increasing need for concepts frommodernphysicsintheirdisciplines—aclassicalintroductorycourseisnot sufficient background for chemists, computer scientists, nuclear and electrical engineers,ormolecularbiologists. Necessaryprerequisitesforundertakingthetextincludeanystandardcalculus- basedcoursecoveringmechanics,electromagnetism,thermalphysics,andoptics. Calculusisusedextensively,butnopreviousknowledgeofdifferentialequations, complex variables, or partial derivatives is assumed (although some familiarity withthesetopicswouldbehelpful). Chapters1–8constitutethecoreofthetext.Theycoverspecialrelativityand quantum theory through atomic structure. At that point the reader may continue with Chapters 9–11 (molecules, quantum statistics, and solids) or branch to Chapters 12–14 (nuclei and particles). The final chapter covers cosmology and canbeconsideredthecapstoneofmodernphysicsasitbringstogethertopicsfrom relativity(specialandgeneral)aswellasfromnearlyallofthepreviousmaterial coveredinthetext. The unifying theme of the text is the empirical basis of modern physics. Experimentaltestsofderivedpropertiesarediscussedthroughout.Theseinclude thelatesttestsofspecialandgeneralrelativityaswellasstudiesofwave-particle duality for photons and material particles. Applications of basic phenomena are extensivelypresented,anddatafromtheliteratureareusednotonlytoillustrate those phenomena but to offer insight into how “real” physics is done. Students usingthetexthavetheopportunitytostudyhowlaboratoryresultsandtheanalysis based on quantum theory go hand-in-hand to illuminate such diverse topics as Bose-Einsteincondensation,heatcapacitiesofsolids,paramagnetism,thecosmic microwave background radiation, X-ray spectra, dilute mixtures of 3He in 4He, andmolecularspectroscopyoftheinterstellarmedium. Thisthirdeditionoffersmanychangesfromthepreviousedition.Mostofthe chapters have undergone considerable or complete rewriting. New topics have beenintroducedandothershavebeenrearranged.Moreexperimentalresultsare presentedandrecentdiscoveriesarehighlighted,suchastheWMAPmicrowave background data and Bose-Einstein condensation. End-of-chapter problem sets now include problems organized according to chapter section, which offer the studentanopportunitytogainfamiliaritywithaparticulartopic,aswellasgeneral problems,whichoftenrequirethestudenttoapplyabroaderarrayofconceptsor techniques. The number of worked examples in the chapters and the number of end-of-chapter questions and problems have each increased by about 15% from thepreviousedition.Therangeofabilitiesrequiredtosolvetheproblemshasbeen vi Preface broadened,sothatthiseditionincludesbothmorestraightforwardproblemsthat buildconfidenceaswellasmoredifficultproblemsthatwillchallengestudents. Each chapter now includes a brief summary of the important points. Some of the end-of-chapter problems are available for assignment using the WebAssign program(www.webassign.net). Anewdevelopmentinphysicsteachingsincetheappearanceofthe2ndedition ofthistexthasbeentheavailabilityofalargeandrobustbodyofliteraturefrom physics education research (PER). My own teaching style has been profoundly influenced by PER findings, and in preparing this new edition I have tried to incorporate PER results wherever possible. One of the major themes that has emerged from PER in the past decade or two is that students can often learn successful algorithms for solving problems while lacking a fundamental understanding of the underlying concepts. Many approaches to addressing this problem are based on pre-class conceptual exercises and in-class individual or groupactivitiesthathelpstudentstoreasonthroughdiverseproblemsthatcan’tbe resolvedbypluggingnumbersintoanequation.Itisabsolutelyessentialtodevote class time to these exercises and to follow through with exam questions that requiresimilaranalysisandarticulationoftheconceptualreasoning.Moredetails regarding the application of PER to the teaching of modern physics, including references to articles from the PER literature, are included in the Instructor’s Manual for this text, which can be found at www.wiley.com/college/krane. The Instructor’s Manual also includes examples of conceptual questions for in-class discussionorexamsthathavebeendevelopedandclasstestedthroughthesupport of a Course, Curriculum and Laboratory Improvement grant from the National ScienceFoundation. Specificchangestothechaptersincludethefollowing: Chapter1:ThesectionsonUnitsandDimensionsandonSignificantFigures have been removed. In their place, a more detailed review of applications of classical energy and momentum conservation is offered. The need for special relativity is briefly established with a discussion of the failures of theclassicalconceptsofspaceandtime,andtheneedforquantumtheoryis previewedinthefailureofMaxwell-Boltzmannparticlestatisticstoaccount fortheheatcapacitiesofdiatomicgases. Chapter2:Spacetimediagramshavebeenintroducedtohelpillustraterelation- ships in the twin paradox. The application of the relativistic conservation laws to decay and collisions processes is now given a separate section to help students learn to apply those laws. The section on tests of special relativityhasbeenupdatedtoincluderecentresults. Chapter 3: The section on thermal radiation has been rewritten, and more detailed derivations of the Rayleigh-Jeans and Planck formulas are now given. Chapter 4: New experimental results for particle diffraction and interference arediscussed.Thesectionsontheclassicaluncertaintyrelationshipsandon wavepacketconstructionandmotionhavebeenrewritten. Chapter 5: To help students understand the processes involved in applying boundaryconditionstosolutionsoftheSchro¨dingerequation,anewsection onwaveboundaryconditionshasbeenadded.Anewintroductorysection on particle confinement introduces energy quantization and helps to build theconnectionbetweenthewavefunctionandtheuncertaintyrelationships. Timedependenceofthewavefunctionisintroducedmoreexplicitlyatan Preface vii earlier stage in the formulism. Graphic illustrations for step and barrier problems now show the real and imaginary parts of the wave function as wellasitssquaredmagnitude. Chapter 6: The derivation of the Thomson model scattering angle has been modified, and the section on deficiencies of the Bohr model has been rewritten. Chapter 7: To ease the entry into the 3-dimensional Schro¨dinger analysis of the hydrogen atom in spherical coordinates, a new section on the one- dimensionalhydrogenatomhasbeenadded.Angularmomentumconcepts relatingtothehydrogenatomarenowintroducedbeforethefullsolutions tothewaveequation. Chapter8:Muchofthematerialhasbeenreorganizedforclarityandeaseof presentation.Thescreeningdiscussionhasbeenmademoreexplicit. Chapter9:Moreemphasishasbeengiventotheuseofbondingandantibonding orbitalstopredicttherelativestabilityofmolecules.Sectionsonmolecular vibrationsandrotationshavebeenrewritten. Chapter 10: This chapter has been extensively rewritten. A new section on thedensityofstatesfunctionallowsstatisticaldistributionsforphotonsor particles to be discussed more rigorously. New applications of quantum statisticsincludeBose-Einsteincondensation,whitedwarfstars,anddilute mixturesof3Hein4He. Chapter11:Thechapterhasbeenrewrittentobroadentheapplicationsofthe quantumtheoryofsolidstoincludenotonlyelectricalconductivitybutalso theheatcapacityofsolidsandparamagnetism. Chapter12:Toemphasizetheunityofvarioustopicswithinmodernphysics, this chapter now includes proton and neutron separation energies, a new sectiononquantumstatesinnuclei,andnuclearvibrationalandrotational states,allofwhichhaveanaloguesinatomicormolecularstructure. Chapter13:Thediscussionofthephysicsoffissionhasbeenexpandedwhile that of the properties of nuclear reactors has been reduced somewhat. Becausemuchcurrentresearchinnuclearphysicsisrelatedtoastrophysics, thischapternowfeaturesasectiononnucleosynthesis. Chapter 14: New material on quarkonium and neutrino oscillations has been added. Chapter 15: Chapters 15 and 16 of the 2nd edition have been collapsed into a single chapter on cosmology. New results from COBE and WMAP are included,alongwithdiscussionsofthehorizonandflatnessproblems(and theirinflationarysolution). Manyreviewersandclass-testersofthemanuscriptofthiseditionhaveoffered suggestions to improve both the physics and its presentation. I am particularly gratefulto: DavidBannon,OregonStateUniversity GeraldCrawford,FortLewisCollege LutherFrommhold,UniversityofTexas-Austin GaryGoldstein,TuftsUniversity LeonGunther,TuftsUniversity GaryIhas,UniversityofFlorida viii Preface PaulLee,CaliforniaStateUniversity,Northridge JeffLoats,MetropolitanStateCollegeofDenver JayNewman,UnionCollege StephenPate,NewMexicoStateUniversity DavidRoundy,OregonStateUniversity RichSchelp,ErskineCollege WeidianShen,EasternMichiganUniversity HongtaoShi,SonomaStateUniversity JanetTate,OregonStateUniversity JeffreyL.Wragg,CollegeofCharleston WeldonWilson,UniversityofCentralOklahoma I am also grateful for the many anonymous comments from students who used themanuscriptatthetestsites.Iamindebtedtoallthosereviewersandusersfor theircontributionstotheproject. Fundingforthedevelopmentandtestingofthesupplementalexercisesinthe Instructor’s Manual was provided through a grant from the National Science Foundation. I am pleased to acknowledge their support. Two graduate students at Oregon State University helped to test and implement the curricular reforms: K. C. Walsh and Pornrat Wattasinawich. I appreciate their assistance in this project. The staff at John Wiley & Sons have been especially helpful throughout the project. I am particularly grateful to: Executive Editor Stuart Johnson for his patienceandsupportinbringingtheneweditionintoreality;AssistantProduction Editor Elaine Chew for handling a myriad of complicated composition and illustration details with efficiency and good humor; and Photo Editor Sheena Goldstein for helping me navigate the treacherous waters of new copyright and permissionrestrictions. Inmyresearchandotherprofessionalactivities,Ioccasionallymeetphysicists whousedearliereditionsofthistextwhentheywerestudents.Somereportthat theirfirstexposuretomodernphysicskindledthesparkthatledthemtocareers in physics. For many students, this course offers their first insights into what physicists really do and what is exciting, perplexing, and challenging about our profession. I hope students who use this new edition will continue to find those inspirations. Corvallis,Oregon KennethS.Krane August2011 [email protected]