Concepts of Modern Physics
Arthur Beiser
- 8TH
- INDIA MEDTECH 2024
- 623P
Relativity 1 1.1 Special Relativity 2 All motion is relative; the speed of light in free space is the same for all observers 1.2 Time Dilation 5 A moving clock ticks more slowly than a clock at rest 1.3 Doppler Effect 10 Why the universe is believed to be expanding 1.4 Length Contraction 15 Faster means shorter 1.5 Twin Paradox 17 A longer life, but it will not seem longer 1.6 Electricity and Magnetism 19 Relativity is the bridge 1.7 Relativistic Momentum 22 Redefining an important quantity 1.8 Mass and Energy 26 Where E0 mc2 comes from 1.9 Energy and Momentum 30 How they fit together in relativity 1.10 General Relativity 33 Gravity is a warping of spacetime APPENDIX I: The Lorentz Transformation 37 APPENDIX II: Spacetime 46 bei48482_FM 2/4/02 12:12 PM Page iii CHAPTER 2 Particle Properties of Waves 52 2.1 Electromagnetic Waves 53 Coupled electric and magnetic oscillations that move with the speed of light and exhibit typical wave behavior 2.2 Blackbody Radiation 57 Only the quantum theory of light can explain its origin 2.3 Photoelectric Effect 62 The energies of electrons liberated by light depend on the frequency of the light 2.4 What Is Light? 67 Both wave and particle 2.5 X-Rays 68 They consist of high-energy photons 2.6 X-Ray Diffraction 72 How x-ray wavelengths can be determined 2.7 Compton Effect 75 Further confirmation of the photon model 2.8 Pair Production 79 Energy into matter 2.9 Photons and Gravity 85 Although they lack rest mass, photons behave as though they have gravitational mass CHAPTER 3 Wave Properties of Particles 92 3.1 De Broglie Waves 93 A moving body behaves in certain ways as though it has a wave nature 3.2 Waves of What? 95 Waves of probability 3.3 Describing a Wave 96 A general formula for waves 3.4 Phase and Group Velocities 99 A group of waves need not have the same velocity as the waves themselves 3.5 Particle Diffraction 104 An experiment that confirms the existence of de Broglie waves iv Contents bei48482_FM 1/11/02 2:54 PM Page iv 3.6 Particle in a Box 106 Why the energy of a trapped particle is quantized 3.7 Uncertainty Principle I 108 We cannot know the future because we cannot know the present 3.8 Uncertainty Principle II 113 A particle approach gives the same result 3.9 Applying the Uncertainty Principle 114 A useful tool, not just a negative statement CHAPTER 4 Atomic Structure 119 4.1 The Nuclear Atom 120 An atom is largely empty space 4.2 Electron Orbits 124 The planetary model of the atom and why it fails 4.3 Atomic Spectra 127 Each element has a characteristic line spectrum 4.4 The Bohr Atom 130 Electron waves in the atom 4.5 Energy Levels and Spectra 133 A photon is emitted when an electron jumps from one energy level to a lower level 4.6 Correspondence Principle 138 The greater the quantum number, the closer quantum physics approaches classical physics 4.7 Nuclear Motion 140 The nuclear mass affects the wavelengths of spectral lines 4.8 Atomic Excitation 142 How atoms absorb and emit energy 4.9 The Laser 145 How to produce light waves all in step APPENDIX: Rutherford Scattering 152 CHAPTER 5 Quantum Mechanics 160 5.1 Quantum Mechanics 161 Classical mechanics is an approximation of quantum mechanics Contents v bei48482_FM 1/11/02 2:54 PM Page v 5.2 The Wave Equation 163 It can have a variety of solutions, including complex ones 5.3 Schrödinger’s Equation: Time-Dependent Form 166 A basic physical principle that cannot be derived from anything else 5.4 Linearity and Superposition 169 Wave functions add, not probabilities 5.5 Expectation Values 170 How to extract information from a wave function 5.6 Operators 172 Another way to find expectation values 5.7 Schrödinger’s Equation: Steady-State Form 174 Eigenvalues and eigenfunctions 5.8 Particle in a Box 177 How boundary conditions and normalization determine wave functions 5.9 Finite Potential Well 183 The wave function penetrates the walls, which lowers the energy levels 5.10 Tunnel Effect 184 A particle without the energy to pass over a potential barrier may still tunnel through it 5.11 Harmonic Oscillator 187 Its energy levels are evenly spaced APPENDIX: The Tunnel Effect 193 CHAPTER 6 Quantum Theory of the Hydrogen Atom 200 6.1 Schrödinger’s Equation for the Hydrogen Atom 6.2 Separation of Variables 203 A differential equation for each variable 6.3 Quantum Numbers 205 Three dimensions, three quantum numbers 6.4 Principal Quantum Number 207 Quantization of energy 6.5 Orbital Quantum Number 208 Quantization of angular-momentum magnitude 6.6 Magnetic Quantum Number 210 Quantization of angular-momentum direction vi Contents bei48482_FM 1/11/02 2:54 PM Page vi 6.7 Electron Probability Density 212 No definite orbits 6.8 Radiative Transitions 218 What happens when an electron goes from one state to another 6.9 Selection Rules 220 Some transitions are more likely to occur than others 6.10 Zeeman Effect 223 How atoms interact with a magnetic field CHAPTER 7 Many-Electron Atoms 228 7.1 Electron Spin 229 Round and round it goes forever 7.2 Exclusion Principle 231 A different set of quantum numbers for each electron in an atom 7.3 Symmetric and Antisymmetric Wave Functions 233 Fermions and bosons 7.4 Periodic Table 235 Organizing the elements 7.5 Atomic Structures 238 Shells and subshells of electrons 7.6 Explaining the Periodic Table 240 How an atom’s electron structure determines its chemical behavior 7.7 Spin-Orbit Coupling 247 Angular momenta linked magnetically 7.8 Total Angular Momentum 249 Both magnitude and direction are quantized 7.9 X-Ray Spectra 254 They arise from transitions to inner shells APPENDIX: Atomic Spectra 259 CHAPTER 8 Molecules 266 8.1 The Molecular Bond 267 Electric forces hold atoms together to form molecules Contents vii bei48482_FM 1/11/02 2:54 PM Page vii 8.2 Electron Sharing 269 The mechanism of the covalent bond 8.3 The H2 Molecular Ion 270 Bonding requires a symmetric wave function 8.4 The Hydrogen Molecule 274 The spins of the electrons must be antiparallel 8.5 Complex Molecules 276 Their geometry depends on the wave functions of the outer electrons of their atoms 8.6 Rotational Energy Levels 282 Molecular rotational spectra are in the microwave region 8.7 Vibrational Energy Levels 285 A molecule may have many different modes of vibration 8.8 Electronic Spectra of Molecules 291 How fluorescence and phsophorescence occur CHAPTER 9 Statistical Mechanics 296 9.1 Statistical Distributions 297 Three different kinds 9.2 Maxwell-Boltzmann Statistics 298 Classical particles such as gas molecules obey them 9.3 Molecular Energies in an Ideal Gas 300 They vary about an average of 3 2 kT 9.4 Quantum Statistics 305 Bosons and fermions have different distribution functions 9.5 Rayleigh-Jeans Formula 311 The classical approach to blackbody radiation 9.6 Planck Radiation Law 313 How a photon gas behaves 9.7 Einstein’s Approach 318 Introducing stimulated emission 9.8 Specific Heats of Solids 320 Classical physics fails again 9.9 Free Electrons in a Metal 323 No more than one electron per quantum stat 9.10 Electron-Energy Distribution 325 Why the electrons in a metal do not contribute to its specific heat except at very high and very low temperatures 9.11 Dying Stars 327 What happens when a star runs out of fuel CHAPTER 10 The Solid State 335 10.1 Crystalline and Amorphous Solids 336 Long-range and short-range order 10.2 Ionic Crystals 338 The attraction of opposites can produce a stable union 10.3 Covalent Crystals 342 Shared electrons lead to the strongest bonds 10.4 Van der Waals Bond 345 Weak but everywhere 10.5 Metallic Bond 348 A gas of free electrons is responsible for the characteristic properties of a metal 10.6 Band Theory of Solids 354 The energy band structure of a solid determines whether it is a conductor, an insulator, or a semiconductor 10.7 Semiconductor Devices 361 The properties of the p-n junction are responsible for the microelectronics industry 10.8 Energy Bands: Alternative Analysis 369 How the periodicity of a crystal lattice leads to allowed and forbidden bands 10.9 Superconductivity 376 No resistance at all, but only at very low temperatures (so far) 10.10 Bound Electron Pairs 381 The key to superconductivity CHAPTER 11 Nuclear Structure 387 11.1 Nuclear Composition 388 Atomic nuclei of the same element have the same numbers of protons but can have different numbers of neutrons 11.2 Some Nuclear Properties 392 Small in size, a nucleus may have angular momentum and a magnetic moment 11.3 Stable Nuclei 396 Why some combinations of neutrons and protons are more stable than others 11.4 Binding Energy 399 The missing energy that keeps a nucleus together 11.5 Liquid-Drop Model 403 A simple explanation for the binding-energy curve 11.6 Shell Model 408 Magic numbers in the nucleus 11.7 Meson Theory of Nuclear Forces 412 Particle exchange can produce either attraction or repulsion CHAPTER 12 Nuclear Transformations 418 12.1 Radioactive Decay 419 Five kinds 12.2 Half-Life 424 Less and less, but always some left 12.3 Radioactive Series 430 Four decay sequences that each end in a stable daughter 12.4 Alpha Decay 432 Impossible in classical physics, it nevertheless occurs 12.5 Beta Decay 436 Why the neutrino should exist and how it was discovered 12.6 Gamma Decay 440 Like an excited atom, an excited nucleus can emit a photon 12.7 Cross Section 441 A measure of the likelihood of a particular interaction 12.8 Nuclear Reactions 446 In many cases, a compound nucleus is formed first 12.9 Nuclear Fission 450 Divide and conquer 12.10 Nuclear Reactors 454 E0 mc2 $$$ 12.11 Nuclear Fusion in Stars 460 How the sun and stars get their energy 12.12 Fusion Reactors 463 The energy source of the future? APPENDIX: Theory of Alpha Decay 468 CHAPTER 13 Elementary Particles 474 13.1 Interactions and Particles 475 Which affects which 13.2 Leptons 477 Three pairs of truly elementary particles 13.3 Hadrons 481 Particles subject to the strong interaction 13.4 Elementary Particle Quantum Numbers 485 Finding order in apparent chaos 13.5 Quarks 489 The ultimate constituents of hadrons 13.6 Field Bosons 494 Carriers of the interactions 13.7 The Standard Model and Beyond 496 Putting it all together 13.8 History of the Universe 498 It began with a bang 13.9 The Future 501 “In my beginning is my end.” (T. S. Eliot, Four Quartets) APPENDIX