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ICP2000Modern Physics - An Introductory Text
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Table of Contents Part One: The Birth of a New Physics 1 1.1 The Electron 3 1.2 Electromagnetic Waves 9 1.2. I The Production and Properties of Electromagnetic Waves 15 1.2.2 The Limits of Electromagnetic Theory 16 1.3 The Special Theory of Relativity 19 1.3.1 The Principle of Covariance 21 1.3.2 The Newtonian Conception of Motion 26 Example 1. I Example 1.2 The Galilean Transformation The Velocity of Sound Relative to a Moving Observer 1.3.3 The Michelson-Morley Experiment 34 1.3.4 The Postulates of the Special Theory of Relativity 38 1.3.5 Simultaneity and the Relativity of Time 39 1.3.6 The Lorentz Transformation 45 1.3.7 Relativistic Mechanics - Kinematics 47 Example 1.3 Example 1.4 Example 1.5 Example 1.6 The Lorentz Transformation and Special Relativity The Mystery of the Muons Stationary Clocks and Moving Clocks The Minkowski Diagrams of Different Observers - The Twins Paradox Calculations in Relativistic Mechanics The Transformation of Energy and Momentum 1.3.8 Relativistic Mechanics - Dynamics 57 Example 1.7 Example 1.8 1.3.9 Magnetism - A Relativistic Effect 65 1.4 The General Theory of Relativity 71 1.4.1 The Postulates of the General Theory of Relativity 72 1.4.2 Gravitation and the General Theory of Relativity 76 1.4.3 Gravity and Geometry 78 1.5 Appendices to Part One 1.5.1 Velocity Addition in Special Relativity I S.2 The Kinetic Energy of a Particle in Special Relativity 1.5.3 The Total Energy of a Particle 1 S.4 The Transformation of Force 84 84 86 87 88 Questions, Exercises and Problems 89 vii viii Table of Contents Part Two: Quantum Theory 2.1 The Quantum Hypothesis 2.1.1 Radiators and Radiation 2.1.2 Thermal Radiation 2.1.3 Black-body Radiation Example 2. I Wien's Law Example 2.2 Blackbody Radiation and Astronomy 2.1.4 Difficulties in the Classical Theory of Radiation Example 2.3 The Frequencies in Cavity Radiation 2.1.5 Planck's Quantum Hypothesis 2.1.6 Atomic Spectra 2. I .7 The Franck-Hertz Experiment 2.2 The Photoelectric Effect 2.2.1 The Photoelectric Effect - The Problem 2.2.2 Einstein's Equation Example 2.4 Photons and Wavelengths Example 2.5 Counting Photons Example 2.6 Photoelectrons Example 2.7 Minimum X-ray Wavelength Example 2.8 X-ray Crystallography 2.2.3 Planck's Constant 2.2.4 X-rays 2.2.5 X-rays and Crystallography 2.3 Photons 2.3.1 Photon Mass 2.3.2 The Cornpton Effect 2.3.3 Photons - Light Particles 2.3.4 The Locality Paradox The Mechanics of Minute Particles 2.4.1 De Broglie's Hypothesis Example 2.12 Electron Diffraction - Thomson's Experiment 2.4.2 Heisenberg's Uncertainty Principle ExampIe 2. J 3 Heisenberg's Uncertainty Principle 2.4.3 Matter Waves 2.4.4 Wave Functions and Probability Amplitudes 2.4.5 The Wave Function of a Free Particle 2.4.6 Quantum Mechanics - Schrodinger's Equation 2.4.7 Quantum Mechanics - Potential Wells 2.4.8 The Tunnel Effect Example 2.9 Radiation Pressure Example 2.10 The Compton Wavelength Example 2. I I Photons and Interference Patterns 2.4 93 95 95 96 97 103 105 107 112 115 115 116 119 122 124 129 129 132 137 144 147 147 154 159 161 164 165 167 171 Table of Contents iX 2.5 Appendices to Part Two 2.5.1 The Kinetic Energy and Linear Momentum of a Particle 2.5.2 The Wave Function of a Trapped Particle Questions, Exercises and Problems Part Three: The Nuclear Atom 3.1 The Structure of the Atom 3.1.1 The Thomson Model of the Atom 3.1.2 The Nuclear Atom Example 3. I The Bohr Model of the Atom 3.2.1 The Hydrogen Atom The Atomic Nucleus 3.2 Example 3.2 Spectral Transitions Example 3.3 The Correspondence Principle Example 3.4 3.2.2 The Zeeman Effect - Space Quantisation 3.2.3 Moseley's Experiment Example 3.5 The Quantum Mechanical Model of the Atom 3.3.1 The Hydrogen Atom The Bohr Atom and De Broglie's Principle The Characteristic X-ray Spectrum of Copper 3.3 Example 3.6 Example 3.7 3.3.2 Atomic Spectra and Quantum Mechanics The Average Distance of the Electron from the Hydrogen Nucleus The Probability of Finding an Electron 3.4 Electron Spin 3.4.1 Electron Spin 3.4.2 The Stern-Gerlach Experiment Example 3.8 Electron Spin Resonance 3.4.3 Spin-Orbit Coupling 3.4.4 The Pauli Exclusion Principle and the Periodic Table 3.4.5 Spin, Identical Particles and the Pauli Principle 3.4.6 Total Spin 3.4.7 The Energy Levels in Multi-electron Atoms 3.4.8 Total Spin and the Energy Levels in Molecules 3.5 Appendices to Part Three 3.5.1 The Energy of an Orbiting Charged Particle 3.5.2 The Schrodinger Equation for the Hydrogen Atom 3.5.3 The Angular Momentum of an Orbiting Particle Questions, Exercises and Problems 174 174 174 177 183 185 185 187 193 195 204 207 215 215 226 231 23 1 23 3 23 6 238 243 247 249 254 262 262 263 270 272 X Table of Contents Part Four: Interactions of Electromagnetic Radiation and Matter 4.1 The Passage of Radiation through Matter 4.1.1 The Attenuation of Radiation by Matter Example 4.1 4.1.2 Mechanisms of the Absorption of Radiation 4.1.3 Quantum Electrodynamics The Attenuation of Ultra-violet Radiation 4.2 Molecular Spectra 4.2.1 Molecular Energies 4.2.2 Rotational Spectra Example 4.2 4.2.3 Vibrational Spectra Example 4.3 4.2.4 Electronic Spectra Example 4.4 4.2.5 Raman Spectra The Interatomic Distance in the HCl Molecule Vibrational Spectrum of CO The Excitation of x Electrons 4.3 Fluorescence and Phosphorescence 4.4 Appendices to Part Four 4.3.1 Fluorescence in Biological Systems 4.4.1 Raleigh Scattering 4.4.2 Moment of Inertia of a Diatomic Molecule Questions, Exercises and Problems Part Five: Nuclear Physics 5.1 The Structure of the Nucleus 5.1.1 Nucleons 5.1.2 Nuclear Nomenclature 5.1.3 Nuclear Masses; Isotopes 5.1.4 Nuclear Binding Energy Example 5. I Example 5.2 Example 5.3 Nuclear Magic Numbers The Density of Nuclear Material Binding Energy per Nucleon 5.1.5 The Nuclear (‘Strong’) Force 5.1.6 Nuclear Models 5.1.7 The Elementary Particles of Matter 5.2 Nuclear Radiations 5.2.1 The Nature of the Nuclear Radiations 5.2.2 Mechanisms of Nuclear Radiation Attenuation 277 279 28 1 282 287 295 295 296 300 3 04 307 309 311 318 318 318 320 323 325 325 326 328 330 333 336 337 345 345 347 Table of Contents xi 5.3 5.2.3 Detectors of Ionising Radiation 5.2.4 The Biological Effects of Nuclear Radiation Radioactivity 5.3.1 The Disintegration of Unstable Nuclei Example 5.4 Disintegration Energy 5.3.2 The Kinetics of Radioactive Disintegration Exumple 5.5 Radioactive Disintegration 5.3.3 Age Determination with Radio-isotopes Example 5.6 Carbon 14 Dating 5.3.4 Uses of Radio-isotopes Example 5.7 Dosimetry 5.3.5 The Factors Affecting Nuclear Stability Example 5.8 5.3.6 The Mechanism of 01 Decay 5.3.7 The Mechanism of p Decay - Weak Charge Disintegration Modes of Heavy Nuclei 5.4 Nuclear Reactions and Nuclear Energy 5.4.1 Nuclear Reactions 5.4.2 The Discovery of the Neutron 5.4.3 Nuclear Cross-sections Example 5.9 Nuclear Cross-sections 5.4.4 Nuclear Energy - Fusion and Fission Exumple 5.10 Endoergic Nuclear Reactions 5.4.5 Nuclear Fusion 5.4.6 Nuclear Fission 5.4.7 Nuclear Chain Reactions 5.4.8 Fission by Fast Neutrons - Bombs 5.4.9 Fission by Slow Neutrons - Nuclear Reactors Example 5.11 The Slow Neutron Chain Reaction of Natural Uranium 5.4.10 Nuclear Engineering: The Chernobyl Catastrophe 5.5 Appendices to Part Five 5.5.1 The Mean Lifetime of a Radioactive Nucleus 5.5.2 Radioactive Decays of the Type A + B + C Questions, Exercises and Problems Part Six: Selected Applications 6.1 TheLaser 6.1.1 The Spontaneous and Stimulated Emission of Radiation 6.1.2 Laser Action 6.1.3 The Ruby Laser 6.1.4 The Helium-Neon Laser 6.1.5 Laser Applications 350 353 359 359 3 62 364 366 368 371 373 385 386 388 3 90 393 396 399 403 407 413 419 424 424 424 426 429 431 43 1 433 43 5 43 7 43 8 xii Table of Contents 6.2 The Mossbauer Effect 6.2,l The Width of Spectral Lines Example 6. I The Width of Spectral Lines 6.2.2 The Mechanics of Photon Emission and Absorption 6.2.3 Recoilless Emission and Absorption 6.2.4 The Gravitational Shift - Black Holes 6.3 Nuclear Magnetic Resonance 6.3.1 Magnetism and Angular Momentum 6.3.2 Nuclear Magnetic Moments 6.3.3 Nuclear Magnetic Resonance 6.3.4 Observing Nuclear Magnetic Resonance 6.3.5 Chemical Shift 6.3.6 Applications of Nuclear Magnetic Resonance The Conduction of Electricity Through Solids 6.4.1 The Electrical Conductivity of Solids 6.4.2 The Electron Gas Example 6.2 6.4.3 Energy Levels in Solids - Band Theory 6.4.4 Insulators 6.4.5 Metallic Conductors 6.4 The Relaxation Time of Conduction Electrons Example 6.3 Example 6.4 6.4.6 Superconductivity 6.4.7 Semiconductors 6.4.8 The p-n Junction 6.4.9 Semiconductor Devices Invariance, Symmetry and Conservation Laws 6.5.1 The Symmetry of the Laws of Physics 6.5.2 Group Theory 6.5.3 Noether’s Theorem 6.5.4 The Conservation Laws of Particle Physics 6.6 Appendices to Part Six 6.6.1 The Probabilities of Stimulated and Spontaneous Emission Questions, Exercises and Problems Supplementary Topics The Velocity of Conduction Electrons The Mean Path-length of the Conduction Electrons 6.5 A B C The Greek Alphabet The Mathematical Description of Wave Motion List of Physical Constants and Conversion Factors Answers to the Numerical Exercises and Problems Index 443 443 446 448 450 455 455 456 459 46 1 465 468 471 47 1 47 3 475 477 478 483 485 489 493 50 1 5 02 503 506 508 514 514 517 519 519 527 527 528 53 1 |
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