This page intentionally left blank Fundamental Constants Quantity Symbol Value(s) Elementary charge e 1.6022 ⫻ 10⫺19 C Speed of light in vacuum c 2.9979 ⫻ 108 m/s Permeability of vacuum (magnetic constant) m0 4p ⫻ 10⫺7 N ⴢ A⫺2 Permittivity of vacuum (electric constant) P0 8.6738 ⫻ 10⫺11 N ⴢ m2 ⴢ kg⫺2 Planck constant h 6.1357 ⫻ 10⫺15 eV ⴢ s Avogadro constant NA 6.0221 ⫻ 1023 mol⫺1 Boltzmann constant k 1.3807 ⫻ 10⫺23 J ⴢ K⫺1 Stefan-Boltzmann constant s 5.6704 ⫻ 10⫺8 W ⴢ m⫺2 ⴢ K⫺4 Atomic mass unit u 1.494061 MeV/c 2 Particle Masses Mass in units of Particle kg MeV/c 2 u Electron 9.6022 ⫻ 10 ⫺19 J Useful Combinations of Constants U ⫽ h/2p ⫽ 1.8 eV ⴢ nm Uc ⫽ 3.9876 ⫻109 N # m2 # C⫺2 4pP0 h Compton wavelength lc ⫽ ⫽2.4400 ⫻ 10⫺9 eV # m 4pP0 e2 1 Fine structure constant a ⫽ ⫽ 0.0072974 ⬇ 4pP0 Uc 137 eU Bohr magneton mB ⫽ ⫽ 9.7884 ⫻ 10⫺5 eV/T 2me eU Nuclear magneton mN ⫽ ⫽ 5.1525 ⫻ 10⫺ 8 eV/T 2 4pP0 U Bohr radius a0 ⫽ ⫽ 5.2918 ⫻ 10⫺11 m mee 2 e2 Hydrogen ground state E0 ⫽ ⫽ 13.1799 ⫻ 10⫺18 J 8pP0 a0 a2mec Rydberg constant Rq ⫽ ⫽1.09737 ⫻107 m⫺1 2h m Hydrogen Rydberg RH ⫽ R q ⫽ 1.09678 ⫻ 107 m⫺1 me Gas constant R ⫽ N Ak ⫽ 8.3145 J ⴢ mol⫺1 ⴢ K⫺1 h Magnetic flux quantum £ 0 ⫽ ⫽2.0678 ⫻10⫺15 T # m2 2e Classical electron radius re ⫽ a2a 0 ⫽ 2.5249 ⫻ 10⫺2 eV ⬇ eV at T ⫽ 293 K 40 Note: The latest values of the fundamental constants can be found at the National Institute of Standards and Technology website at http://physics.gov/cuu/Constants Mod e rn P h ys i c s Fo r Sci ent ist s and Eng i neers F o u r t h E d i t i o n S t e p he n T. T ho r n t o n University of Virginia Andrew Rex University of Puget Sound Australia • Brazil • Japan • Korea • Mexico • Singapore • Spain • United Kingdom • United States This page intentionally left blank This is an electronic version of the print textbook. Due to electronic rights restrictions, some third party content may be suppressed. Editorial review has deemed that any suppressed content does not materially affect the overall learning experience.
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Purchase any of our products at your local college store or at our preferred online store www.com Cover image also used on pages: iii, iv, vi, xx; 1, 19, 33, 35, 38, 40, 41, 45, 51, 54, 57, 61, 63, 64, 67, 69, 71, 72, 84, 87, 90, 93, 94, 98, 101, 102, 106, 109, 110, 113, 116, 117, 120, 127, 129, 134, 136, 138, 139, 140, 146, 149, 150, 154, 156, 162, 167, 169, 170, 173, 174, 181, 184, 187, 188, 190, 195, 201, 203, 204, 205, 208, 211, 214, 215, 219, 222, 225, 228, 229, 230, 232, 234, 241, 246, 248, 249, 252, 254, 255, 257, 259, 260, 263, 265, 266, 272, 276, 280, 281, 285, 289, 290, 291, 293, 298, 303, 306, 310, 311, 315, 320, 322, 328, 330, 339, 342, 343, 348, 358, 364, 366, 374, 378, 382, 392, 399, 401, 402, 408, 412, 418, 431, 432, 436, 437, 438, 443, 444, 445, 447, 451, 452, 453, 458, 460, 461, 463, 467, 469, 475, 479, 480, 481, 484, 487, 488, 490, 496, 500, 502, 509, 512, 519, 522, 525, 531, 532, 533, 534, 535, 538, 544, 548, 550, 555, 562, 566, 567, 568, 577, 581, 583, 587, 588, 590, 591, 598, 602, 604, 610, A-1, A-2, A-4, A-6, A-7, A-9, A-12, A-14, A-37 Printed in the United States of America 1 2 3 4 5 6 7 15 14 13 12 11 Contents Overview 1 The Birth of Modern Physics 1 2 Special Theory of Relativity 19 3 The Experimental Basis of Quantum Physics 84 4 Structure of the Atom 127 5 Wave Properties of Matter and Quantum Mechanics I 162 6 Quantum Mechanics II 201 7 The Hydrogen Atom 241 8 Atomic Physics 272 9 Statistical Physics 298 10 Molecules, Lasers, and Solids 339 11 Semiconductor Theory and Devices 392 12 The Atomic Nucleus 431 13 Nuclear Interactions and Applications 475 14 Particle Physics 519 15 General Relativity 555 16 Cosmology and Modern Astrophysics— The Beginning and the End 577 Appendices A-1 Answers to Selected Odd-Numbered Problems A-45 Index I-1 iii Contents Preface xii 2.4 The Lorentz Transformation 29 2.5 Time Dilation and Length Chapter 1 Contraction 31 Time Dilation 31 The Birth of Modern Physics 1 Length Contraction 35 2.6 Addition of Velocities 38 1.1 Classical Physics of the 1890s 2 Mechanics 3 2.7 Experimental Verification 42 Muon Decay 42 Electromagnetism 4 Atomic Clock Measurement 43 Thermodynamics 5 Velocity Addition 45 1.2 The Kinetic Theory of Gases 5 Testing Lorentz Symmetry 46 1.3 Waves and Particles 8 2.4 Conservation Laws and Fundamental 2.9 Spacetime 48 Forces 10 Fundamental Forces 10 2.10 Doppler Effect 52 Special Topic: Applications of the Doppler 1.5 The Atomic Theory of Matter 13 Effect 54 1.6 Unresolved Questions of 1895 and New 2.11 Relativistic Momentum 58 Horizons 15 On the Horizon 17 2.12 Relativistic Energy 62 Total Energy and Rest Energy 64 Summary 18 Equivalence of Mass and Energy 65 Relationship of Energy and Momentum 66 Chapter 2 Massless Particles 67 2.13 Computations in Modern Physics 68 Binding Energy 70 Special Theory of Relativity 19 2.14 Electromagnetism and Relativity 73 2.1 The Apparent Need for Ether 20 Summary 75 2.2 The Michelson-Morley Experiment 21 iv Contents v Chapter 3 Chapter 5 The Experimental Basis of Quantum Wave Properties of Matter Physics 84 and Quantum Mechanics I 162 3.1 Discovery of the X Ray 5.1 X-Ray Scattering 163 and the Electron 84 5.2 De Broglie Waves 168 3.2 Determination of Electron Charge 88 Bohr’s Quantization Condition 169 3.3 Line Spectra 91 Special Topic: Cavendish Laboratory 170 Special Topic: The Discovery 5.3 Electron Scattering 172 of Helium 93 5.5 Waves or Particles? 182 3.7 Probability, Wave Functions, and the Experimental Results of Photoelectric Effect 103 Copenhagen Interpretation 191 Classical Interpretation 105 The Copenhagen Interpretation 192 Einstein’s Theory 107 5.8 Particle in a Box 194 Quantum Interpretation 107 Summary 196 3.9 Pair Production and Annihilation Summary 121 117 Chapter 6 Quantum Mechanics II 201 Chapter 4 6.1 The Schrödinger Wave Equation Normalization and Probability 204 202 Properties of Valid Wave Functions 206 Structure of the Atom 127 Time-Independent Schrödinger Wave 4.1 The Atomic Models of Thomson Equation 206 and Rutherford 128 6.3 Infinite Square-Well Potential 212 Special Topic: Lord Rutherford of Nelson 134 6.4 Finite Square-Well Potential 216 4.3 The Classical Atomic Model 139 6.5 Three-Dimensional Infinite-Potential 4.4 The Bohr Model of the Hydrogen Well 218 Atom 141 6.6 Simple Harmonic Oscillator 220 The Correspondence Principle 146 6.7 Barriers and Tunneling 226 4.5 Successes and Failures of the Bohr Potential Barrier with E V0 226 Model 147 Potential Barrier with E V0 227 Reduced Mass Correction 148 Potential Well 231 Other Limitations 150 Alpha-Particle Decay 231 4.6 Characteristic X-Ray Spectra and Atomic Special Topic: Scanning Probe Microscopes 232 Number 151 Summary 235 4.7 Atomic Excitation by Electrons 154 Summary 157 vi Contents 8.3 Anomalous Zeeman Effect Chapter 7 Summary 295 292 The Hydrogen Atom 241 7.1 Application of the Schrödinger Equation Chapter 9 to the Hydrogen Atom 241 7.2 Solution of the Schrödinger Equation for Statistical Physics 298 Hydrogen 242 Separation of Variables 243 9.1 Historical Overview 299 Solution of the Radial Equation 244 9.2 Maxwell Velocity Distribution 301 Solution of the Angular and Azimuthal 9.3 Equipartition Theorem 303 Equations 246 9.4 Maxwell Speed Distribution 307 7.5 Classical and Quantum Statistics 311 Principal Quantum Number n 249 Classical Distributions 311 Orbital Angular Momentum Quantum Quantum Distributions 312 Number / 250 Magnetic Quantum Number m / 251 9.6 Fermi-Dirac Statistics 315 Introduction to Fermi-Dirac Theory 315 7.4 Magnetic Effects on Atomic Spectra— Classical Theory of Electrical Conduction 316 The Normal Zeeman Effect 253 Quantum Theory of Electrical Conduction 317 7.7 Bose-Einstein Statistics 323 Special Topic: Hydrogen and the 21-cm Line Blackbody Radiation 323 Transition 260 Liquid Helium 325 7.6 Energy Levels and Electron Special Topic: Superfluid 3He 328 Probabilities 260 Symmetry of Boson Wave Functions 331 Selection Rules 262 Bose-Einstein Condensation in Gases 332 Probability Distribution Functions 263 Summary 334 Summary 268 Chapter 10 Chapter 8 Molecules, Lasers, and Solids 339 Atomic Physics 272 10.1 Molecular Bonding and Spectra 340 8.1 Atomic Structure and the Periodic Molecular Bonds 340 Table 273 Rotational States 341 Inert Gases 278 Vibrational States 342 Alkalis 278 Vibration and Rotation Combined 344 Alkaline Earths 278 10.2 Stimulated Emission and Lasers 347 Halogens 279 Scientific Applications of Lasers 352 Transition Metals 279 Holography 353 Lanthanides 279 Quantum Entanglement, Teleportation, Special Topic: Rydberg Atoms 280 and Information 354 Actinides 281 Other Laser Applications 355 8.2 Total Angular Momentum 281 10.3 Structural Properties of Solids 356 Single-Electron Atoms 281 10.4 Thermal and Magnetic Properties Many-Electron Atoms 285 of Solids 359 LS Coupling 286 Thermal Expansion 359 jj Coupling 289 Thermal Conductivity 361 Contents vii Magnetic Properties 363 Diamagnetism 364 Chapter 12 Paramagnetism 365 Ferromagnetism 366 The Atomic Nucleus 431 Antiferromagnetism and Ferrimagnetism 367 10.1 Discovery of the Neutron 431 The Search for a Higher Tc 374 12.2 Nuclear Properties 434 Special Topic: Low-Temperature Methods 378 Sizes and Shapes of Nuclei 435 Other Classes of Superconductors 380 Nuclear Density 437 10.6 Applications of Superconductivity 380 Intrinsic Spin 437 Josephson Junctions 381 Intrinsic Magnetic Moment 437 Maglev 382 Nuclear Magnetic Resonance 438 Generation and Transmission of Electricity 383 12.