INTRODUCTION TO THE STRUCTURE OF MATTER A Course in Modern Physics John J. Brehm and William J. Mullin University of Massachusetts Amherst, Massachusetts Fachberelch 5?@8hnlsdie Hochschule Darmstadt! HochschulstraSa 2 301222 WILEY John Wiley & Sons New York Chichester Brisbane Toronto Singapore
CONTENTS CHAPTER ONE RELATIVITY 1-1 1-2 1-3 14 1-5 1-6 1-7 1-8 1-9 1-10 1-11 The Luminiferous Aether Principles of Relativity Time Dilation and Length Contraction Relative-Motion Symmetry The Lorentz Transformation Transformation of Velocity Space-Time Reiativistic Momentum and Energy Reiativistic Dynamics Collisions and Reactions Four-Vectors 2 6 11 20 25 32 38 44 SO 53 BO 66 CHARTER TWO PHOTONS 73 2-1 2-2 2-3 24 2-5 2-6 2-7 2-8 Blackbody Radiation Standing Electromagnetic Waves The Maxwell-Boltzmann Distribution The Quantum Hypothesis The Photoelectric Effect XRays The Compton Effect Y Rays and Electron-Positron Pairs 75 93 99 103 107 114 118 xiil
xlv Contents CHAPTER THREE INTRODUCTION TO THE ATOM 122 3-1 The Reality of Molecules and Atoms 122 3-2 The Electron. 126 3-3 The Nuclear Model of the Atom 131 34 Rutherford Scattering 134 3-5 The Quantum Picture of the Atom 744 3-6 The Bohr Model of the One-Electron Atom 149 3-7 Characteristic X Rays 161 3-8 Atomic Processes and the Excitation of Atoms 165 3-9 The Laser 170 3-10 The Quantum of Action 175 178 CHAPTER FOUR MATTER WAVES m 4-1 4-2 4-3 44 4-5 4-6 De Broglie's Hypothesis Electron Diffraction Particle-Wave Duality Determinism and Randomness The Uncertainty Principle Waves and Wave Packets 182 185 188 193 195 205 216 CHAPTER FIVE QUANTUM MECHANICS 219 5-1 5-2 5-3 54 5-5 5-6 5-7 5-8 5-9 5-10 5-11 The Schrddinger Equation Probability Interpretation Stationary States The One-Dimensional Box The Harmonic Oscillator Eigenfunctions and Eigenvalues Expectation Values Radiative Transitions Barrier Penetration Two-Particle Systems in One Dimension The Three-Dimensional Box 220 226 231 234 240 251 260 268 271 283 288 294 CHAPTER SIX QUANTIZATION OF ANGULAR MOMENTUM 300 6-1 Central Forces 301 6-2 The Schrddinger Equation in Spherical Coordinates 303
Contents xv 6-3 64 6-5 6-6 6-7 6-8 Rotational Motion Separation of Variables Angular Momentum Quantum Numbers Parity Quantization of Energy Observables in Spherical Coordinates 308 313 320 325 328 333 341 CHAPTER SEVEN THE ONE-ELECTRON ATOM 344 7-1 7-2 7-3 74 7-5 The Radial Differential Equation Solutions of the Radial Equation Degeneracy ' Probability Distributions Electric Dipole Selection Rules 345 348 357 360 366 373 CHAPTER EIGHT SPIN AND MAGNETIC INTERACTIONS 375 8-1 8-2 8-3 84 8-5 8-6 8-7 8-8 8-9 8-10 8-11 8-12 Atoms and Light in a Magnetic Field Orbital Magnetic Moments The Normal Zeeman Effect The Stern Gerlach Experiment The Properties of Electron Spin Magnetic Resonance Spin4 Thought Experiments Addition of Orbital and Spin Angular Momenta The Spin-Orbit Interaction Results from Reiativistic Quantum Mechanics The Zeeman Effect Hyperfine Structure - 376 380 385 390 394 397 400 405 410 416 425 431 437 CHAPTER NINE COMPLEX ATOMS 440 9-1 9-2 9-3 94 9-5 9-6 9-7 The Central-Field Model The Exclusion Principle The Ground States of Atoms and the Periodic Table X-Ray Spectra ElBdron Antisymmetry The Helium Atom Alkali Atoms 440 446 449 457 464 469 476
xvi Contents 9-8 Angular Momentum Coupling 481 9-9 Spectroscopic Aspects of LS Coupling 488 498 CHAPTER TEN MOLECULES soi 10-1 + Binding by Quantum Tunneling: H 2 502 10-2 Covalent Bonding: H 2 508 10-3 Ionic Bonding: LiF 512 104 Van der Waals Interaction 5/7 10-5 Polyatomic Molecules: H 2 0 and CH 4 521 10-6 Rotation 522 10-7 Vibration 524 10-8 Spectra 527 533 CHAPTER ELEVEN QUANTUM STATISTICAL PHYSICS 538 11-1 Particle Indistinguishability 539 11-2 Thermal Distribution Functions 543 11-3 High-Temperature. Low-Density Limit 554 114 Photon Statistics 559 11-5 Phonons 560 11-6. Low-Temperature Fermi-Dirac Systems 567 57/ CHAPTER TWELVE SOLIDS 575 12-1 The Structure of Solids 576 12-2 Bragg Scattering 584 12-3 The Free-Electron Theory of Metals 587 124 Energy Bands in Solids 596 12-5 The Band Theory of Metals. Insulators, and Semiconductors 606 12-6 Semiconductors 608 12-7 Semiconductor Devices 6/5 12-8 Phonon Dynamics 621 12-9 Magnetism in Solids 627 631
Contents xvii CHAPTER THIRTEEN SUPERFLUIDS AND SUPERCONDUCTORS 634 13-1 Experimental Characteristics of Superfluids 635 13-2 Experimental Characteristics of Superconductors 638 13-3 Superfiow and the Energy Gap 640 134 The Bose-Einstein Condensation 643 13-5 The Two-Fluid Model of Superfluid Helium 647 13-6 Cooper Pairs and the BCS Theory 650 13-7 Theoretical Interpretation of Superconducting Experiments 654 13-8 The Josephson Effect 658 13-9 Other Superfluid Systems 664 665 CHAPTER FOURTEEN PROPERTIES AND MODELS OF THE NUCLEUS 667 14-1 Nuclear Particles 668 14-2 Nuclear Systematics 673 14-3 Electron Scattering and the Nuclear Radius 678 14-4 Nuclear Mass and Binding Energy 682 14-5 The Semiempirical Mass Formula - 689 14-6 The Fermi Gas Model 695 14-7 The Nucleon-Nucleon Interaction 699 14-8 A Simple Model of the Deuteron 705 14-9 Magic Numbers 710 14-10 The Nuclear Shell Model 714 14-11 Spins and Moments in the Shell Model 720 14-12 Charge Independence and Isospin Symmetry 728 736 CHAPTER FIFTEEN NUCLEAR PROCESSES 740 15-1 15-2 15-3 15-4 15-5 15-6 15-7 15-8 15-9 Radioactivity The Exponential Decay Law a Decay P Decay The Weak Nuclear Interaction Y Decay Resonance Radiation Introduction to Nuclear Reactions Nuclear Reactions and Nuclear Structure 741 745 751 759 767 773 779 783 789
xviil Contents 15-10 Nuclear Fission 796 15-11 Fusion and Thermonuclear Energy 804 811 CHAPTER SIXTEEN ELEMENTARY PARTICLES sis 16-1 16-2 16-3 164 16-5 16-6 16-7 16-8 16-9 16-10 16-11 16-12 16-13 16-14 16-15 16-16 16-17 Introduction to High-Energy Physics Particles and Fields Mesons and the Nuclear Force Muons and Pions Neutrinos Nonconservation of Parity The Weak Interaction Strangeness Neutral K Decay and CP Symmetry Isospin Baryon and Meson Resonances Quarks The Electromagnetic and Weak Interactions of Quarks The Electroweak Interaction Color and the Strong Interaction Gauge Symmetries Grand Unification 816 821 826 830 834 837 842 848 852 870 875 881 902 APPENDIX A TABLE OF NUCLEAR PROPERTIES A-I BIBLIOGRAPHY A-8 ANSWERS A-12 PHOTO CREDITS NAME INDEX A-IS i-i SUBJECT INDEX i-3