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PrefaceThis book is intended as a modern physics text for science majors and engineering students who have already completed an introductory calculus-basedphysics course. The contents of this text may be subdivided into two broad categories: an introduction to the theories of relativity, quantum and statisticalphysics (Chapters 1 through 10) and applications of elementary quantum theory to molecular, solid-state, nuclear, and particle physics (Chapters 11through 16).OBJECTIVESOur basic objectives in this book are threefold:1. To provide simple, clear, and mathematically uncomplicated explanations of physical concepts and theories of modern physics.2. To clarify and show support for these theories through a broad range ofcurrent applications and examples. In this regard, we have attempted toanswer questions such as: What holds molecules together? How do electrons tunnel through barriers? How do electrons move through solids?How can currents persist indefinitely in superconductors?3. To enliven and humanize the text with brief sketches of the historical development of 20th century physics, including anecdotes and quotationsfrom the key figures as well as interesting photographs of noted scientistsand original apparatus.COVERAGETopics. The material covered in this book is concerned with fundamentaltopics in modern physics with extensive applications in science and engineering. Chapters 1 and 2 present an introduction to the special theory of relativity. Chapter 2 also contains an introduction to general relativity. Chapters 3through 5 present an historical and conceptual introduction to early developments in quantum theory, including a discussion of key experiments that showthe quantum aspects of nature. Chapters 6 through 9 are an introduction tothe real “nuts and bolts” of quantum mechanics, covering the Schrödingerequation, tunneling phenomena, the hydrogen atom, and multielectronivCopyright 2005 Thomson Learning, Inc. All Rights Reserved.

PREFACEatoms, while Chapter 10 contains an introduction to statistical physics. The remainder of the book consists mainly of applications of the theory set forth inearlier chapters to more specialized areas of modern physics. In particular,Chapter 11 discusses the physics of molecules, while Chapter 12 is an introduction to the physics of solids and electronic devices. Chapters 13 and 14 covernuclear physics, methods of obtaining energy from nuclear reactions,and medical and other applications of nuclear processes. Chapter 15 treatselementary particle physics, and Chapter 16 (available online at http://info.brookscole.com/mp3e) covers cosmology.CHANGES TO THE THIRD EDITIONThe third edition contains two major changes from the second edition: First,this edition has been extensively rewritten in order to clarify difficult concepts,aid understanding, and bring the text up to date with rapidly developing technical applications of quantum physics. Artwork and the order of presentationof certain topics have been revised to help in this process. (Many new photosof physicists have been added to the text, and a new collection of color photographs of modern physics phenomena is also available on the Book Companion Web Site.) Typically, each chapter contains new worked examples andfive new end-of-chapter questions and problems. Finally, the Suggestions for Further Reading have been revised as needed.Second, this edition refers the reader to a new, online (platform independent) simulation package, QMTools, developed by one of the authors, CurtMoyer. We think these simulations clarify, enliven, and complement the analytical solutions presented in the text. Icons in the text highlight the problemsdesigned for use with this software, which provides modeling tools to help students visualize abstract concepts. All instructions about the general use of thesoftware as well as specific instructions for each problem are contained on theBook Companion Web Site, thereby minimizing interruptions to the logicalflow of the text. The Book Companion Web Site at http://info.brookscole.mp3e also contains appendices and much supplemental information on current physics research and applications, allowing interested readers to digdeeper into many topics.Specific changes by chapter in this third edition are as follows: Chapter 1 in the previous editions, “Relativity,” has been extensively revisedand divided into two chapters. The new Chapter 1, entitled “Relativity I,”contains the history of relativity, new derivations of the Lorentz coordinateand velocity transformations, and a new section on spacetime and causality. Chapter 2, entitled “Relativity II,” covers relativistic dynamics and energyand includes new material on general relativity, gravitational radiation,and the applications GPS (Global Positioning System) and LIGO (theLaser Interferometer Gravitational-wave Observatory). Chapter 3 has been streamlined with a more concise treatment of theRayleigh-Jeans and Planck blackbody laws. Material necessary for a complete derivation of these results has been placed on our Book CompanionWeb Site. Chapter 5 contains a new section on the invention and principles of operation of transmission and scanning electron microscopes.Copyright 2005 Thomson Learning, Inc. All Rights Reserved.v

viiiPREFACEessay topics covered are recent developments in general relativity, the scanning tunneling microscope, superconducting devices, the history of the laser,laser cooling of atoms, solar cells, and how the top quark was detected. Theguest essays are either included in the text or referenced as being on our Website at appropriate points in the text.Mathematical Level. Students using this text should have completed a comprehensive one-year calculus course, as calculus is used throughout the text.However, we have made an attempt to keep physical ideas foremost so as not toobscure our presentations with overly elegant mathematics. Most steps are shownwhen basic equations are developed, but exceptionally long and detailed proofswhich interrupt the flow of physical arguments have been placed in appendices.Appendices and Endpapers. The appendices in this text serve several purposes. Lengthy derivations of important results needed in physical discussionshave been placed on our Web site to avoid interrupting the main flow of arguments. Other appendices needed for quick reference are located at the end ofthe book. These contain physical constants, a table of atomic masses, and a listof Nobel prize winners. The endpapers inside the front cover of the book contain important physical constants and standard abbreviations of units used inthe book, and conversion factors for quick reference, while a periodic table isincluded in the rear cover endpapers.Ancillaries. The ancillaries available with this text include a Student Solutions Manual, which has solutions to all odd-numbered problems in the book,an Instructor’s Solutions Manual, consisting of solutions to all problems in thetext, and a Multimedia Manager, a CD-ROM lecture tool that contains digitalversions of all art and selected photographs in the text.TEACHING OPTIONSAs noted earlier, the text may be subdivided into two basic parts: Chapters 1through 10, which contain an introduction to relativity, quantum physics, andstatistical physics, and Chapters 11 through 16, which treat applications tomolecules, the solid state, nuclear physics, elementary particles, and cosmology. It is suggested that the first part of the book be covered sequentially. However, the relativity chapters may actually be covered at any time because E 2 p 2c 2 m2c4 is the only formula from these chapters which is essential for subsequent chapters. Chapters 11 through 16 are independent of one anotherand can be covered in any order with one exception: Chapter 14, “NuclearPhysics Applications,” should follow Chapter 13, “Nuclear Structure.”A traditional sophomore or junior level modern physics course for science,mathematics, and engineering students should cover most of Chapters 1through 10 and several of the remaining chapters, depending on the studentmajor. For example, an audience consisting mainly of electrical engineering students might cover most of Chapters 1 through 10 with particular emphasis ontunneling and tunneling devices in Chapter 7, the Fermi-Dirac distribution inChapter 10, semiconductors in Chapter 12, and radiation detectors in Chapter14. Chemistry and chemical engineering majors could cover most of Chapters 1through 10 with special emphasis on atoms in Chapter 9, classical and quantumCopyright 2005 Thomson Learning, Inc. All Rights Reserved.

PREFACEstatistics in Chapter 10, and molecular bonding and spectroscopy in Chapter 11.Mathematics and physics majors should pay special attention to the unique development of operator methods and the concept of sharp and fuzzy observablesintroduced in Chapter 6. The deep connection of sharp observables with classically conserved quantities and the powerful role of sharp observables in shapingthe form of system wavefunctions is developed more fully in Chapter 8.Our experience has shown that there is more material contained in thisbook than can be covered in a standard one semester three-credit-hourcourse. For this reason, one has to “pick-and-choose” from topics in the second part of the book as noted earlier. However, the text can also be used in atwo-semester sequence with some supplemental material, such as one of manymonographs on relativity, and/or selected readings in the areas of solid state,nuclear, and elementary particle physics. Some selected readings are suggested at the end of each chapter.ACKNOWLEDGMENTSWe wish to thank the users and reviewers of the first and second editions whogenerously shared with us their comments and criticisms. In preparing thisthird edition we owe a special debt of gratitude to the following reviewers:Melissa Franklin, Harvard UniversityEdward F. Gibson, California State University, SacramentoGrant Hart, Brigham Young UniversityJames Hetrick, University of the PacificAndres H. La Rosa, Portland State UniversityPui-tak (Peter) Leung, Portland State UniversityPeter Moeck, Portland State UniversityTimothy S. Sullivan, Kenyon CollegeWilliam R. Wharton, Wheaton CollegeWe thank the professional staff at Brooks-Cole Publishing for their fine workduring the development and production of this text, especially Jay Campbell,Chris Hall, Teri Hyde, Seth Dobrin, Sam Subity, Kelley McAllister, StaceyPurviance, Susan Dust Pashos, and Dena Digilio-Betz. We thank Suzon O.Kister for her helpful reference work, and all the authors of our guest essays:Steven Chu, Melissa Franklin, Roger A. Freedman, Clark A. Hamilton, Paul K.Hansma, David Kestenbaum, Sam Marshall, John Meakin, and Clifford M. Will.Finally, we thank all of our families for their patience and continual support.Raymond A. SerwayLeesburg, VA 20176Clement J. MosesDurham, NC 27713Curt A. MoyerWilmington, NC 28403December 2003Copyright 2005 Thomson Learning, Inc. All Rights Reserved.ix

Contents Overview1 Relativity I12 Relativity II413 The Quantum Theory of Light654 The Particle Nature of Matter1065 Matter Waves1516 Quantum Mechanics in One Dimension1917 Tunneling Phenomena 2318 Quantum Mechanics in Three Dimensions9 Atomic Structure29510 Statistical Physics33411 Molecular Structure12 The Solid State26037240413 Nuclear Structure46314 Nuclear Physics Applications15 Elementary Particles50354716 Cosmology (Web Only)Appendix ABest Known Values for Physical ConstantsAppendix BTable of Selected Atomic MassesAppendix CNobel PrizesA.7Answers to Odd-Numbered ProblemsIndexI.1xCopyright 2005 Thomson Learning, Inc. All Rights Reserved.A.12A.2A.1

Contents11.11.2RELATIVITY I3 THE QUANTUM THEORYOF LIGHT 65Special Relativity 2The Principle of RelativityThe Speed of Light1.3133.16The Michelson – Morley Experiment73.2Details of the Michelson – MorleyExperiment 81.41.5Enter Planck 72The Quantum of EnergyPostulates of Special Relativity 10Consequences of Special Relativity 13Simultaneity and the Relativity of TimeTime Dilation 15Length Contraction 18The Twins Paradox (Optional) 21The Relativistic Doppler Shift 221.6The Lorentz IVITY II 41Relativistic Momentum andthe Relativistic Formof Newton’s Laws 41Relativistic Energy 44Mass as a Measure of Energy 48Conservation of RelativisticMomentum and Energy 52General Relativity 5377Light Quantization and the PhotoelectricEffect 80The Compton Effect and X-Rays 86X-Rays 86The Compton Effect893.6Particle – Wave Complementarity 943.7Does Gravity Affect Light? (Optional) 95Summary 98Web Appendix Calculation of the Number of Modesof Waves in a CavityPlanck’s Calculation of the AverageEnergy of an Oscillator4 THE PARTICLE NATUREOF MATTER 1064.14.2Gravitational Radiation, or a Good WaveIs Hard to Find 56Summary 59Web Essay The Renaissance of General RelativityClifford M. Will74The Rayleigh–Jeans Law and Planck’sLaw (Optional) 77Rayleigh–Jeans LawPlanck’s Law 79Lorentz Velocity Transformation 291.7 Spacetime and CausalitySummary 35Hertz’s Experiments—Light as anElectromagnetic Wave 66Blackbody Radiation 68The Atomic Nature of Matter 106The Composition of Atoms 108Millikan’s Value of the Elementary Charge 113Rutherford’s Model of the Atom 1194.3The Bohr Atom125Spectral Series 126Bohr’s Quantum Model of the Atom130xiCopyright 2005 Thomson Learning, Inc. All Rights Reserved.

xiiCONTENTS4.4Bohr’s Correspondence Principle,or Why Is Angular MomentumQuantized? 1394.5Direct Confirmation of Atomic EnergyLevels: The Franck – Hertz ExperimentSummary 1435 MATTER WAVES5.1The Pilot Waves of De Broglie5.55.65.7Field Emission 239 Decay 242Ammonia Inversion 245Decay of Black Holes 247Summary 248Essay The Scanning Tunneling MicroscopeRoger A. Freedman and Paul K. Hansma 2531521538 QUANTUM MECHANICS INTHREE DIMENSIONS 260159Wave Groups and DispersionMatter Wave Packets5.4141164169Fourier Integrals (Optional)170Constructing Moving Wave Packets1738.18.2The Heisenberg Uncertainty Principle173A Different View of the Uncertainty Principle175If Electrons Are Waves, What’sWaving? 178The Wave–Particle Duality 179The Description of ElectronDiffraction in Terms of 179A Thought Experiment: MeasuringThrough Which Slit the Electron Passes5.8A Final NoteSummary 1868.38.46.48.51848.6AntihydrogenSummary 289The Born Interpretation 191Wavefunction for a Free ParticleWavefunctions in the Presenceof Forces 197The Particle in a Box 200194205The Finite Square Well (Optional)The Quantum Oscillator 212Expectation Values 217Observables and Operators 221209Quantum Uncertainty and the Eigenvalue Property(Optional) 222SummaryAtomic Hydrogen and Hydrogen-likeIons 277The Ground State of Hydrogen-like Atoms 282Excited States of Hydrogen-like Atoms 284186Charge-Coupled Devices (CCDs)6.56.66.76.8Particle in a Three-Dimensional Box 260Central Forces and AngularMomentum 266Space Quantization 271Quantization of Angular Momentum andEnergy (Optional) 273Lz Is Sharp: The Magnetic Quantum Number 275兩L兩 Is Sharp: The Orbital Quantum Number 276E Is Sharp: The Radial Wave Equation 2766 QUANTUM MECHANICS INONE DIMENSION 1916.16.26.3The Square Barrier 231Barrier Penetration: SomeApplications 238The Davisson–Germer Experiment 154The Electron Microscope5.37.17.2151De Broglie’s Explanation ofQuantization in the Bohr Model5.27 TUNNELING PHENOMENA 231224Copyright 2005 Thomson Learning, Inc. All Rights Reserved.99.1287ATOMIC STRUCTURE295Orbital Magnetism and theNormal Zeeman Effect 2969.2The Spinning Electron 3029.3The Spin – Orbit Interaction andOther Magnetic Effects 3099.4Exchange Symmetry and theExclusion Principle 3129.5Electron Interactions and ScreeningEffects (Optional) 3169.6The Periodic Table 3199.7X-Ray Spectra and Moseley’s Law 325Summary 328

CONTENTS1010.1STATISTICAL PHYSICS334The Maxwell – Boltzmann Distribution33512 THE SOLID STATE12.1The Maxwell Speed Distribution forGas Molecules in Thermal Equilibrium atTemperature T 341The Equipartition of Energy 34310.210.310.4Under What Physical Conditions AreMaxwell – Boltzmann StatisticsApplicable? 344Quantum Statistics 34612.212.3Applications of Bose – EinsteinStatistics 35112.412.5420377Molecular Rotation 378Molecular Vibration 381Molecular Spectra 385Electron Sharing and theCovalent Bond 390The Hydrogen Molecular Ion 390The Hydrogen Molecule 39611.5Bonding in Complex Molecules(Optional) 397Summary 399Web Appendix Overlap Integrals of AtomicWavefunctionsCopyright 2005 Thomson Learning, Inc. All Rights Reserved.425Semiconductor Devices433SuperconductivityLasers 447443Absorption, Spontaneous Emission,and Stimulated Emission 447Population Inversion and Laser ActionSemiconductor Lasers 451Bonding Mechanisms: A Survey 373Ionic Bonds 374Covalent Bonds 374van der Waals Bonds 375The Hydrogen Bond 377Band Theory of SolidsThe p -n Junction 433Light-Emitting and -AbsorbingDiodes — LEDs and Solar Cells 436The Junction Transistor 437The Field-Effect Transistor (FET) 439The Integrated Circuit 44112.612.711 MOLECULARSTRUCTURE 37211.311.4Quantum Theory of MetalsIsolated-Atom Approach to Band Theory 425Conduction in Metals, Insulators, andSemiconductors 426Energy Bands from Electron Wave Reflections 429352Molecular Rotation and VibrationClassical Free Electron Modelof Metals 413Replacement of vrms with vF 421Wiedemann – Franz Law Revisited 422Quantum Mean Free Path of Electrons 423An Application of Fermi – Dirac Statistics:The Free-Electron Gas Theoryof Metals 356Summary 360Essay Laser Manipulation of AtomsSteven Chu 36611.2405Ohm’s Law 414Classical Free Electron Theoryof Heat Conduction 41810.511.1404Ionic Solids 405Covalent Solids 408Metallic Solids 409Molecular Crystals 409Amorphous Solids 410Wavefunctions and the Bose – EinsteinCondensation and Pauli ExclusionPrinciple 346Bose – Einstein and Fermi – DiracDistributions 347Blackbody Radiation 351Einstein’s Theory of Specific HeatBonding in Solidsxiii449Summary 454Web Essay The Invention of the LaserS. A. MarshallWeb Essay Photovoltaic ConversionJohn D. MeakinWeb Chapter Superconductivity1313.1NUCLEAR STRUCTURESome Properties of Nuclei464Charge and Mass 465Size and Structure of Nuclei 466Nuclear Stability 468Nuclear Spin and Magnetic Moment 469Nuclear Magnetic Resonance and MagneticResonance Imaging 470463

xiv13.213.3CONTENTSBinding Energy and Nuclear ForcesNuclear Models 476Liquid-Drop Model 476Independent-Particle ModelCollective Model 47913.413.547215.4478Radioactivity 479Decay Processes 484Natural Radioactivity15.515.615.749249315.815.9Nuclear Reactions 503Reaction Cross Section 506Interactions Involving Neutrons 508Nuclear Fission 510Nuclear Reactors 513Neutron Leakage 515Regulating Neutron Energies 515Neutron Capture 515Control of Power Level 515Safety and Waste Disposal 51614.6Nuclear Fusion14.814.914.10Colored Quarks, or QuantumChromodynamics 577Experimental Evidence for Quarks 578Explanation of Nuclear Force in Termsof Quarks 579Electroweak Theory and theStandard Model 580Beyond the Standard Model 582Summary 583Essay How to Find a Top Quark 590Melissa Franklin and David Kestenbaum52652653753915 ELEMENTARY PARTICLES 547The Fundamental Forces in Nature 548Positrons and Other Antiparticles 550Copyright 2005 Thomson Learning, Inc. All Rights Reserved.56857116 COSMOLOGY (Web Only)526Tracing 536Neutron Activation AnalysisRadiation Therapy 538Food Preservation 53915.115.2The Eightfold WayQuarks 574Grand Unification Theory and SupersymmetryString Theory — A New Perspective 582Radiation Damage in Matter 530Radiation Detectors 532Uses of Radiation 536Summary15.1015.12Interaction of Particles with MatterHeavy Charged ParticlesElectrons 528Photons 528Strange Particles and Strangeness 561How Are Elementary Particles Producedand Particle Properties Measured? 563The Original Quark Model 574Charm and Other Developments 57515.11517Fusion Reactions 518Magnetic Field Confinement 521Inertial Confinement 523Fusion Reactor Design 524Advantages and Problems of Fusion14.7559Resonance Particles 564Energy Considerations in Particle Production49514 NUCLEAR PHYSICSAPPLICATIONS 50314.114.214.314.414.5Conservation LawsBaryon Number 560Lepton Number 560Four Radioactive Series 492Determining the Age of the EarthSummaryMesons and the Beginning ofParticle Physics 553Classification of Particles 556Hadrons 556Leptons 557The Solar Neutrino Mystery andNeutrino Oscillations 558Alpha Decay 484Beta Decay 487Carbon Dating 489Gamma Decay 49113.615.3APPENDIX A BEST KNOWN VALUESFOR PHYSICALCONSTANTS A.1APPENDIX B TABLE OF SELECTEDATOMIC MASSES A.2APPENDIX CNOBEL PRIZESANSWERS TO ODD-NUMBEREDPROBLEMS A.12INDEXI.1A.7582

1. A. Piccard2. E. Henriot3. P. Ehrenfest4. E. Herzen5. Th. de Donder6. E. Schroedinger7. E. Verschaffelt8. W. Pauli9. W. Heisenberg10. R.H. FowlerThe “architects” of modern physics. This unique photograph shows many eminentscientists who participated in the Fifth International Congress of Physics held in 1927by the Solvay Institute in Brussels. At this and similar conferences, held regularly from1911 on, scientists were able to discuss and share the many dramatic developmentsin atomic and nuclear physics. This elite company of scientists includes fifteen Nobelprize winners in physics and three in chemistry. (Photograph courtesy of AIP Niels BohrLibrary)Copyright 2005 Thomson Learning, Inc. All Rights Reserved.11. L. Brillouin12. P. Debye13. M. Knudsen14. W.L. Bragg15. H.A. Kramers16. P.A.M. Dirac17. A.H. Compton18. L.V. de Broglie19. M. Born20. N. Bohr21. I. Langmuir22. M. Planck23. M. Curie24. H.A. Lorentz25. A. Einstein26. P. Langevin27. C.E. Guye28. C.T.R. Wilson29. O.W. Richardson

1 RELATIVITY I 1 1.1 Special Relativity 2 1.2 The Principle of Relativity 3 The Speed of Light 6 1.3 The Michelson–Morley Experiment 7 Details of the Michelson–Morley Experiment 8 1.4 Postulates of Special Relativity 10 1.5 Consequences of Special Relativity 13 Simultaneity and the Relativity

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