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www.elsolucionario.net www.elsolucionario.net www.elsolucionario.net MODERN PHYSICS SIXTH EDITION Paul A Tipler Formerly of Oakland University Ralph A Llewellyn University of Central Florida W H Freeman and Company New York TIPLER_FM_i-xvi-hr.indd 11/4/11 12:06 PM www.elsolucionario.net Executive Editor: Jessica Fiorillo Associate Editor: Brittany Murphy Marketing Manager: Alicia Brady Media and Supplements Editor: Dave Quinn Senior Media Producer: Keri Fowler Photo Editor: Ted Szczepanski Designer: Blake Logan Senior Project Editor: Mary Louise Byrd Senior Illustration Coordinator: Bill Page Production Coordinator: Paul W Rohloff Illustrations and Composition: Preparé Printing and Binding: RR Donnelley Library of Congress Control Number: 2011934108 ISBN-13: 978-1-4292-5078-8 ISBN-10: 1-4292-5078-X © 2012, 2008, 2003, 2000 by W H Freeman and Company All rights reserved Printed in the United States of America First printing W H Freeman and Company 41 Madison Avenue New York, NY 10010 Houndmills, Basingstoke RG21 6XS, England www.whfreeman.com TIPLER_FM_i-xvi-hr.indd 11/4/11 12:06 PM www.elsolucionario.net Contents PART CHAPTER 1-1 Relativity and Quantum Mechanics: The Foundations of Modern Physics Relativity I The Experimental Basis of Relativity Michelson-Morley Experiment CCR 1-2 Einstein’s Postulates 11 1-3 The Lorentz Transformation 17 Calibrating the Spacetime Axes 1-4 Time Dilation and Length Contraction 29 1-5 The Doppler Effect 40 1-6 The TIPLER_FM_i-xvi-hr.indd The Twin Paradox and Other Surprises CCR 44 45 The Case of the Identically Accelerated Twins 48 Superluminal Speeds 51 65 2-1 Relativistic Momentum 66 2-2 Relativistic Energy 70 CCR Transverse Doppler Effect Relativity II CHAPTER The 28 Another Surprise 80 2-3 Mass/Energy Conversion and Binding Energy 81 2-4 Invariant Mass 84 icon indicates material that appears only on the Web site: www.whfreeman.com/tiplermodernphysics6e icon indicates material of high interest to students 11/4/11 12:06 PM www.elsolucionario.net iv Contents 2-5 General Relativity Deflection of Light in a Gravitational Field 103 Gravitational Redshift 106 CCR Perihelion of Mercury’s Orbit 108 CCR Delay of Light in a Gravitational Field 108 Quantization of Charge, Light, and Energy 119 3-1 Quantization of Electric Charge 119 3-2 Blackbody Radiation 123 3-3 The Photoelectric Effect 131 3-4 X Rays and the Compton Effect 137 CHAPTER CCR Derivation of Compton’s Equation 143 The Nuclear Atom 153 4-1 Atomic Spectra 154 4-2 Rutherford’s Nuclear Model 156 CHAPTER 4-3 CCR Rutherford’s Prediction and Geiger and Marsden’s Results The Bohr Model of the Hydrogen Atom Giant Atoms 162 165 174 4-4 X-Ray Spectra 175 4-5 The Franck-Hertz Experiment 180 A Critique of Bohr Theory and the “Old Quantum Mechanics” 182 The Wavelike Properties of Particles 193 5-1 The de Broglie Hypothesis 193 5-2 Measurements of Particle Wavelengths 195 5-3 Wave Packets 204 5-4 The Probabilistic Interpretation of the Wave Function 210 The Uncertainty Principle 213 CHAPTER 5-5 5-6 TIPLER_FM_i-xvi-hr.indd 97 CCR The Gamma-Ray Microscope Some Consequences of the Uncertainty Principle 214 216 11/4/11 12:06 PM www.elsolucionario.net Contents 5-7 Wave-Particle Duality CCR 219 220 The Schrödinger Equation 229 6-1 The Schrödinger Equation in One Dimension 230 6-2 The Infinite Square Well 237 6-3 The Finite Square Well 246 CHAPTER 6-4 6-5 CCR 6-6 Graphical Solution of the Finite Square Well Expectation Values and Operators CCR Transitions Between Energy States The Simple Harmonic Oscillator CCR 249 250 253 253 Schrödinger’s Trick 256 Parity 257 Reflection and Transmission of Waves 258 Alpha Decay 265 NH3 Atomic Clock 267 Tunnel Diode 267 Atomic Physics 277 7-1 The Schrödinger Equation in Three Dimensions 277 7-2 Quantization of Angular Momentum and Energy in the Hydrogen Atom 280 7-3 The Hydrogen Atom Wave Functions 289 7-4 Electron Spin 293 CHAPTER CCR 7-5 Stern-Gerlach Experiment 296 Total Angular Momentum and the Spin-Orbit Effect 298 The Schrödinger Equation for Two (or More) Particles 303 7-7 Ground States of Atoms: The Periodic Table 305 7-8 Excited States and Spectra of Alkali Atoms 309 7-6 CCR Multielectron Atoms 311 CCR The Zeeman Effect 312 Frozen Light 312 TIPLER_FM_i-xvi-hr.indd Two-Slit Interference Pattern v 11/4/11 12:06 PM www.elsolucionario.net vi Contents Statistical Physics 325 Classical Statistics: A Review 326 CCR Temperature and Entropy 329 CCR A Derivation of the Equipartition Theorem 334 CHAPTER 8-1 8-2 Quantum Statistics 338 8-3 The Bose-Einstein Condensation 345 Liquid Helium 8-4 The Photon Gas: An Application of Bose-Einstein Statistics 354 8-5 Properties of a Fermion Gas 361 Applications of Quantum Mechanics and Relativity 373 Molecular Structure and Spectra 375 9-1 The Ionic Bond 376 9-2 The Covalent Bond 381 PART CHAPTER CCR 9-3 9-4 Other Covalent Bonds 387 Other Bonding Mechanisms 387 Energy Levels and Spectra of Diatomic Molecules 392 9-5 Scattering, Absorption, and Stimulated Emission 402 9-6 Lasers and Masers 408 CHAPTER 10 Solid State Physics 427 10-1 The Structure of Solids 427 10-2 Classical Theory of Conduction 437 10-3 Free-Electron Gas in Metals 440 10-4 Quantum Theory of Conduction 444 448 CCR Thermal Conduction—The Quantum Model 10-5 Magnetism in Solids 448 451 Spintronics 10-6 Band Theory of Solids 452 Quantum Wells 459 Energy Bands in Solids—An Alternate Approach 460 TIPLER_FM_i-xvi-hr.indd 346 CCR 11/4/11 12:06 PM www.elsolucionario.net Contents 10-7 Impurity Semiconductors 460 463 Hall Effect 10-8 Semiconductor Junctions and Devices 467 472 CCR How Transistors Work 10-9 Superconductivity 472 Flux Quantization 477 Josephson Junction 482 CHAPTER 11 Nuclear Physics 494 11-2 Ground-State Properties of Nuclei 496 Liquid-Drop Model and the Semiempirical Mass Formula 505 11-3 Radioactivity 508 511 CCR Production and Sequential Decays 11-4 Alpha, Beta, and Gamma Decay 511 514 CCR Energetics of Alpha Decay 11-5 The Nuclear Force 522 528 Probability Density of the Exchange Mesons 11-6 The Shell Model 529 11-7 Nuclear Reactions 533 11-8 Fission and Fusion 542 CCR Nuclear Power 546 CCR Interaction of Particles and Matter 552 11-9 Applications 553 566 CCR Radiation Dosage CHAPTER 12 Particle Physics TIPLER_FM_i-xvi-hr.indd 493 11-1 The Composition of the Nucleus CCR 579 12-1 Basic Concepts 580 12-2 Fundamental Interactions and the Force Carriers 588 595 A Further Comment about Interaction Strengths vii 12-3 Conservation Laws and Symmetries 598 CCR When Is a Physical Quantity Conserved? 601 CCR Resonances and Excited States 609 11/4/11 12:06 PM www.elsolucionario.net I-8 Index Helix nebula, 663 Helmholtz, Hermann von, 113, 145, 598 Hermite polynomials, 255, 269 Hermitian operators, 631 Herriott, D.R., 413 Hertz, Gustav L., 175, 180, 186, 609 Hertz, Heinrich R., 131, 132, 137, 145, 186 Hertzsprung-Russell (H-R) diagrams, 661, 661–663 Hess, Victor, 569 Heteropolar (heteronuclear) molecules, 421 Hexagonal close-packed (hcp) crystal symmetry, 433, 433 Higgs bosons, 586, 599, 621 Higgs field, 621 High-temperature superconductivity, 481– 482, 481t Hipparchus, 653, 697 Hofstadter, Robert, 497, 569 Holes, 457, 462 Holography, electron, 447 Homopolar (homonuclear) molecules, 421 Hooke, Robert, 119 Horizontal branch, in stellar evolution, 663 Hosono, H., 481 Hounsfield, Godfrey, 557, 570 Hoyle, Fred, 697 Hubble, Edwin P., 43, 675, 676, 678, 686, 697 Hubble constant (H0 ), 679–680, 682, 685 Hubble Space Telescope, 639, 651, 666, 668, 670, 680 Hubble time, 680 Hubble’s law, 678–683, 679, 679, 684 Hulse, R.A., 109 Hybridization of orbitals, 435, 486 Hydrogen (H) atoms binding energy of, 84 Bohr model of, 165–175, 182* energy-level diagrams for, 169, 286, 288, 288t excited states of, 291–293, 328 fine-structure splitting in, 301, 301–302 probability density (P(x,t)) in, 290–292, 291, 292, 293 quantization of angular momentum in, 283–285 quantization of energy in, 286–287 radial functions for, 287t Schrödinger equation, 280–282 size of, 217–218 spectra of, 155, 156 in sun’s core, 644 wave functions for, 289–293, 297–298 wavelength of, 170–171 Hydrogen bonds, 388–389, 389 Hydrogen (H2 ) molecules escape of, from Earth’s atmosphere, 333–334 in interstellar medium, 673–674 TIPLER_INDEX_001-018hr.indd wave functions for, 381–384, 384 Hypercharge (Y ), 603–605, 605, 606 and group theory, 610 Hyperfine splitting, 322, 507, 507 and interstellar dust, 673–674, 674 and masers, 409, 409–410 Hyperfine structure, 312, 495, 505 I Ice, dipole-dipole bonds in, 388, 389 Ice Cube experiment, 133 Ideal blackbodies, 124 Imaginary numbers See Complex numbers Impact parameters (b), 160, 160 Impurity semiconductors See under Semiconductors Incident photon intensity, 136 Index of refraction, 104 Indistinguishable particles, 303–304, 338, 339, 340–342 Inelastic collisions and relativistic energy, 76, 76–77, 82 Inelastic scattering, 404 Inertial confinement, 549 Inertial reference frames, 4, 4–6#, 24 and simultaneity, 14–17 and special relativity, 12, 12–14, 46, 49 Infinite square wells, 237–246, 238 complete wave function, 242–246 energy levels of, 238–240, 240 and free-electron gas in metals, 440, 441 and line of stability, 503 minimum energy of, 216–217 in three dimensions, 278–279 Inflation, 690 Insulators, and band theory of solids, 455, 456 Integral quantized Hall effect (IQHE), 466 Intensity (I), 418, 537 of electron diffraction, 197, 199 and photoelectric effect, 135 Interaction times, 589 Interactions See also Fundamental interactions and Feynman diagrams, 584 Interference See also Diffraction; Superposition double-slit, 210–211, 211, 220* by electrons, 194, 196–198, 197, 211 fringes produced by, 9#, 10 and linear equations, 229 quantum, 312–313, 313 Interferometers, Michelson, 7, 9, 9–11, 10, 109, 110 Internal conversion, 521–522 Internal quantum numbers, 601, 601t International Thermonuclear Experimental Reactor (ITER), 548, 549 Interstellar dust, 673–674 Interstellar medium (ISM), 673–674 Intrinsic semiconductors See under Semiconductors Invariance, and conservation laws, 66, 73, 598 and gauge theories, 632 interval and gravitational interactions, 100–102, 101 of masses, 84–97 TCP, 607–608 Inverse beta decay, 666, 668 Ionic bonds, 376–381 vs covalent bonds, 386–387 Ionic solids, 429–436 Ionization energy, 170 and ionic bonds, 307–309, 308, 376–377, 377t, 378 Ionization potential, 307–309 Ionizing radiation, 552*, 566* IQHE See Integral quantized Hall effect (IQHE) Irregular galaxies, 675–676, 676 Island of stability, 504, 532 ISM See Interstellar medium (ISM) Isobars, 496 Isomers, 521 Isospin (I), 603, 605, 608t and group theory, 610 weak (Tz ), 586, 587t, 588 Isotones, 496, 530 Isotope effect, 478 Isotopes, 171, 478, 496 ITER See International Thermonuclear Experimental Reactor (ITER) J J/c puzzle, 615–617 Javan, Ali, 413 Jefferson National Accelerator Facility, 613 Jensen, Johannes Hans Daniel, 530, 532, 569 Jin, Deborah, 364 Josephson, Brian D., 483, 486 Josephson effect ac, 483 dc, 483 Josephson junctions, 482–483, 483, 484 Joule, James, 113, 598 Junction lasers, 418 Junctions Josephson, 482–483, 483, 484 semiconductors, 467, 467 K K series, 176–178, 177 K shell, 177 Kamerlingh Onnes, Heike, 345, 346, 346, 366, 472, 473 Kant, Emmanuel, 675 Kaons (K 0), 590, 608 Keesom, William H., 345, 347 Kelvin, William Thompson, Lord, 316, 644 11/2/11 3:26 PM www.elsolucionario.net Kepler, Johannes, 666 Ketterle, Wolfgang, 353, 416 Kilowatt-hours, 546 Kinematic states, 85 Kinetic energy (Ek ) Maxwell distributions of, 333, 333–334 minimum, 216–217 negative, 248, 262 nonrelativistic, 95–96 in nuclear reactions, 538 and photoelectric effect, 132 relativistic, 71–72, 72 of rotation, 392–393 vs potential energy, 81–83 Kinetic energy operators, 252t Kinetic theory, 326#, 329#, 330#, 333# and blackbody radiation, 123–125 of gases, 119, 329–330 and Planck’s law, 127 Klein, Oskar, 528 Klein-Gordon relativistic wave equation, 582, 595 Klitzing, Klaus von, 455–456, 486 Knowledge creation paradox, 54, 54 Kronig-Penney model, 452, 452–455, 453, 485 Kündig, Walter, 45 Kusch, P., 332, 332 L L series, 176–177, 177 Laboratory frames of reference, 535, 535, 536 Lagrangian points, 664, 664 Laguerre polynomials, 287, 287t, 290, 292 Lamb, W., 315 Lamb, Willis, 303 Lamb shift, 302–303 Lambda points, 345, 346, 347, 347 Landé, Alfred, 316 Landé factor (gN ), 506 Langevin, Paul, 222 Laplace, Pierre, 109 Large Hadron Collider (LHC), 581, 583, 586, 621, 624, 659 Laser Interferometer Gravitational-Wave Observatory (LIGO), 109–111, 110, 111 Lasers, 408–419 applications of, 416–419 atomic, 353, 353 blue, 417 continuous wave, 312 diode, 418, 418, 471, 471 gas, 418 helium-neon, 413, 413–415, 414 liquid, 418 other types of, 417–418 parameters, 415t ruby, 409, 410–413, 411 semiconductor, 418 TIPLER_INDEX_001-018hr.indd Index tunable dye, 418 Late type stars, 653 Latitude, 656, 656 Lattice energy, 431 Lattice ions, 446, 446 Laue, Max von, 80, 138 Laue patterns, 139, 200, 202, 432 Laughlin, R.B., 486 Law of atmospheres, 327–328 Law of inertia, Lawrence, Ernest O., 532 Lawrence Berkeley Laboratory, 602 Lawrence Livermore Laboratory, 581 Laws of motion, Newtonian, 4–6 Lawson, J.D., 548 Lawson’s criterion, 548 LEDs See Light-emitting diodes (LEDs) Lee, David M., 348 Lee, T.D., 606, 607, 608 Left-handed coordinate system, 607, 607 Legendre polynomials, 282 Lego plots, 593 Lenard, Philipp, 131, 132 Lenard-Jones potential, 425 Length, proper (Lp ), 33, 34, 85 Length contraction, 33–36, 34 gravitational, 102 Lepton era, 693 Lepton number conservation of, 599–600 nonconservation of, 625 Leptons, 516, 586, 587t, 616, 617, 631 and weak interaction, 592 Leptoquarks, 625 Leucippus, 119 Lever paradox, 80, 80–81 LHC See Large Hadron Collider (LHC) Libby, Willard F., 570 Lie, S., 610 Life, extraterrestrial, 651 Lifetime (t), 218, 509 of excited energy states, 406 and force ranges, 590 of protons, 615–616 of quasars, 681 for spontaneous emission (tp ), 412–413 of strange particles, 602 and tunneling, 266 Light See Electromagnetic radiation; Speed of light (c) Light clocks, 29, 30 Light curves, 660 Light-emitting diodes (LEDs), 470, 470–471, 471, 472 Lightlike spacetime intervals, 37, 38–39 LIGO See Laser Interferometer Gravitational-Wave Observatory (LIGO) Limbs, solar, 641, 642 Linac Coherent Light Source (LCLS), 419 I-9 Lindblad, Bertil, 658 Line of stability, 502, 503 and fission, 544, 545 Line spectra, 153–154, 154 Linear combinations, 231 Liquid-drop model, 505* and fission, 543, 543 Liquid lasers, 418 Liquids helium, 346–351, 348, 349, 351 structure of, 427 surface tension of, 390 Little Ice Age, 649 Livingston, M.S., 532 Livingston Observatory, 109 Local clocks, 15 London, Fritz, 345, 390 London dispersive forces, 390 See also van der Waals attraction Longitude, 656, 656 Lorentz, Hendrik A., 34, 104, 222, 315 and coordinate transformations, 18 and electrons, 122, 145 and Michelson-Morley experiment, 57 and Zeeman effect, 302, 316 Lorentz, Henrik A and conduction, 437 Lorentz-FitzGerald contraction, 34 Lorentz transformation, 17 and dynamics, 65, 73, 73–76 of four-vectors, 84–85 of mass-energy, 88 and nuclear reactions, 535 of space and time coordinates, 17–29 Luminosity (L), 640, 659–660 of galaxies, 675 and Hertzsprung-Russell diagrams, 661, 661–663 Lyman, Theodore, 156, 170 Lyman series, 156, 169, 170 M Macroscopic quantum wave functions, 353, 353 Madelung constant (a), 380, 429, 430t, 433, 434, 484 Magic numbers, 504, 529–530 Magnetic confinement, 548 Magnetic fields (B) charged particles in, 120–121 critical (Bc ), 473, 473t, 474, 476 and fine-structure splitting, 301–302 inhomogeneous, 296, 296 at the nucleus, 506t relativistic electrons in, 94–95, 95 solar, 627, 629, 647, 647–648, 648 Magnetic levitation, 475, 482 Magnetic moment (m), 294–297, 449 nuclear, 505–508 quantization of, 295 11/2/11 3:26 PM www.elsolucionario.net I-10 Index Magnetic monopoles, 626–627, 690 Magnetic quantum number (m), 284, 506 Magnetic resonance imaging (MRI), 507, 556 and superconductivity, 473 Magnetic susceptibility (x), 449 Magnetic traps, 352 Magnetic tunnel junction, 451, 451 Magnetism, 295, 448–451 Magnetization (M), 492 Magnetons Bohr (mB ), 189, 295 nuclear (mN ), 323 Magnetoresistance, giant (GMR), 451 Magnetoresistive random access memory (MRAM), 451 Magnitude, stellar absolute (M), 654 apparent (m), 653–654, 698 Maiman, Theodore, 410 Main sequence dwarfs, 661, 661 Main sequence stars, 661, 661 Majorana neutrinos, 586 Marsden, Ernest and nuclear charge, 178 and Rutherford scattering, 157–159, 158, 161, 161–162, 165, 493 and size of nucleus, 163 Masers, 408, 409, 409–410 See also Lasers Mass (m) conversion from energy, 91–92 effective (m*), 458, 461 gravitational vs inertial, 98–99, 99 and Higgs boson, 621 invariance of, 84–97 of the Milky Way, 658–659 of neutrinos, 516, 552, 599–600, 626–629, 633 of nuclei, 504–505, 505 reduced (m), 171–172 relativistic (m(u)), 67–70, 68 rest (m), 78 stellar, 644, 661–662 units of, 78, 83, 393, 694 Mass number, 496 Massless particles, 89–90 See also Gluons; Gravitons; Photons Mather, Frank C., 697 Mather, John C., 690 Matter-antimatter asymmetry and CP violations, 608 Matter waves, 195–204 Maunder minimum, 649 Max Planck Institute, 670 Maxwell, James Clerk, 6, 326, 329, 588 Maxwell-Boltzmann distributions and diode currents, 468 and fusion, 552 and Planck’s law, 127–128 TIPLER_INDEX_001-018hr.indd 10 Maxwell distributions and Bose-Einstein condensates, 352 and electromagnetism, 588 and fusion, 548, 645 of kinetic energy, 333, 333–334 of molecular speeds, 329–332, 330, 330, 370 Maxwell’s equations, 6, 6, 11, 141 Mayer, M., 530, 532 Mean free path (l), 439, 445 Mean lifetime, 509 Mediation of forces, 588–598 and Feynman diagrams, 584–585, 585 and the uncertainty principle, 526 Medicine nuclear, 483, 494, 545, 556–558, 631 and x rays, 138, 141 Meissner, H Walther, 474 Meissner effect, 474, 474–477, 476 Mendeleev, Dimitri, 176, 610 Mercury [element], spectra of, 155, 181 Mercury [planet], precession of orbit of, 102–103, 108* Meson fields, 526 Meson octet (nonet), 605, 610, 610 Mesons, 526, 526, 587, 589, 591t, 606–607, 612t, 615 as force mediators, 622 probability density of, 528–529, 529 supermultiplets of, 616 Metallic bonds, 376, 387, 429, 436–437, 484 Metals, free electron gases in, 361, 440–444, 443, 485 Metastable states, 303, 521 and lasers, 409, 409, 410, 413 Michelson, Albert A., 7, 7, 9, 10, 11, 131 Michelson interferometer, 7, 9, 9–11, 10 and gravity waves, 110, 110–111 Michelson-Morley experiment, 7–11* Microscopes gamma-ray, 214–216, 215 photoelectric-effect, 137 resolving power of, 222 scanning tunneling (STMs), 264, 264–265 Mikheyev, S., 626 Milky Way, 627, 651, 654, 655, 677, 689 See also Galaxies mass of, 658–659 structure of, 654, 654–655 Miller, R.C., 332, 332 Millikan, Robert A., 131, 145, 697 and electron charge, 120, 122–123 and photoelectric effect, 134, 134, 579 Millikan oil-drop experiment, 122–123#, 123 Minimum time interval, 20 Minkowski, Hermann, 113 Mirror nuclides, 496, 497 Missing mass See Dark matter Mitchell, John, 697 Molecular orbitals See Orbitals Molecules, 375–426 and covalent bonds, 381–392 energy levels and spectra of, 392–402 and ionic bonds, 376–381 and lasers and masers, 408–420 and other bonds, 387–390 polar, 388–389, 389 and scattering, absorption, and simulated emission, 402–408 Moment of inertia (I), 394 and rotational spectra, 392, 393 Momentum (p) of electromagnetic radiation, 141 Lorentz transformation of, 73–76, 74 relativistic (p), 66–70, 67, 68, 82, 94–95, 95 Momentum operators (pop ), 251, 252t MORE See also Classical Concept Reviews; Exploring alpha-decay energetics, 514* Bohr atomic model, 182* conservation laws, 601* delay of light in a gravitational field, 108* derivation of Compton’s equation, 143* double-slit interference, 220* energy bands, 452*, 460* entropy, 329* equipartition theorem, 334* graphical solution of the finite square well, 249* ionization radiation, 552* liquid-drop model, 505* Michelson-Morley experiment, 11* Mössbauer effect, 521* multielectron atoms, 311*, 413* nuclear power, 546* other covalent bonds, 387*, 435* perihelion of Mercury’s orbit, 108* radiation dosages, 566* radioactive decay, 511* relativity of simultaneity, 48* resonances and excited states, 609* Rutherford scattering, 162* Schrödinger’s differential equation trick, 256* shell model, 533* temperature, 329* theories of everything, 629* thermal conduction, 448* transistors, 472* transitions between energy states, 253*, 405*, 406* tunnel diodes, 267* twin paradox, 48* wave-particle duality, 220* Weizsäcker formula, 505* Zeeman effect, 312* Morley, Edward W., 9, 11, 56 Moseley, Henry G.-J., 175, 175–178, 185, 188, 494, 558 11/2/11 3:26 PM www.elsolucionario.net Moseley plots, 176, 177 Mössbauer, Rudolf Ludwig, 521*, 569 Mössbauer effect, 219, 521*, 575 measuring gravitational red- and blueshift with, 102, 108, 521 measuring natural line widths with, 218 measuring transverse Doppler effect with, 45, 521 Most probable speed (vm ), 330, 330 Mott, M.F., 451 Mourou, Gérhard, 417 Moving square, shape of, 36 MRAM See Magnetoresistive random access memory (MRAM) MRI See Magnetic resonance imaging MSW effect, 626 Muller, H., 431 Muller, Karl A., 481 Multielectron atoms, 307, 311*, 413 Multiplets, charge, 590, 603, 625 Muons (mu (m) mesons), 516, 569, 579 decay of, 36, 36–37 mass of, 78 Myhres, F., 614 N N galaxies, 676 n-type semiconductors, 462, 462, 467 NAA See Neutron activation analysis (NAA) Nanostructures, 459, 459 Natural line width (G0), 218–219 and gamma decay, 520–521 and nuclear resonances, 570 Neel temperature (TN ), 450 Ne’eman, Yuval, 609 Neon, 308 Neutral current, 592 Neutral weak force, 492 Neutralinos, 658, 659 Neutrinos (n), 90 as dark matter, 659 and density parameter, 688 discovery of, 516, 579 Majorana, 586 mass of, 516, 552, 599–600, 626–629, 658 oscillations of, 600, 627–629, 658 in proton-proton cycle, 552, 646 and solar-neutrino problem, 552, 625, 625–626 from supernovae, 666 types of, 516, 586, 587t Neutron activation analysis (NAA), 494, 539, 553–555, 554 Neutron capture, 530, 530–531 cross section for, 530, 530, 540 Neutron number, 495 Neutron stars, 109, 109, 362, 500, 668–670, 669 TIPLER_INDEX_001-018hr.indd 11 Index Neutrons (n), 495t decay of, 597 diffraction, 201, 202 discovery of, 493, 495, 495t, 579 reactions of, 539–540 thermal, 540 Newton, Isaac, 3, 4, 153, 366, 686 Newtonian physics, 4–6, 70–71 See also Classical physics Nichols, Ernest F., 141 Nicholson, J.W., 167 Nishijima, K., 602 NMR See Nuclear magnetic resonance Noether, Emmy, 598, 631 Nondispersive media, 207 Nonpolar molecules, 389–391, 390 Normalization of Bose-Einstein distribution, 349 and hydrogen atom wave functions, 290 of Maxwell-Boltzmann distribution, 128 of probability amplitude, 233, 235, 236, 239–240, 247, 529 Novae, 664, 664 npn transistors, 471, 471 Nuclear binding energy (B), 504–505, 505 and driplines, 511, 511 and shell model, 529, 529–530 Nuclear exchange force, 525–527 Nuclear force See Strong interaction Nuclear magnetic moment, 505–508 Nuclear magnetic resonance (NMR), 486, 555–556 See also Magnetic resonance imaging (MRI) Nuclear magneton (mN ), 323 Nuclear physics, 493–578 applications of, 553–566 and composition of the nucleus, 494–495 and fission and fusion, 542–552 and ground properties of nuclei, 496–508 history of, 493–494 and nuclear decay, 511–522 and nuclear reactions, 533–541 and radioactivity, 508–511 and the shell model, 529–532 and the strong interaction, 522–529 Nuclear power, 493, 546* Nuclear radii, 496–500 Nuclear reactions, 533, 533–541 Nuclear reactors fission, 81, 542, 546, 547 fusion, 549, 550 natural, 570 Nuclear spectra, 496, 539 Nuclear spin angular momentum (I), 312, 505, 508 Nuclear weaponry, 494, 546 Nucleons, 495, 525, 531 mass differences between, 542, 542 Nucleosynthesis period, 693 I-11 Nucleus composition of, 494–495 compound, 533, 537–538, 538 decay of, 508–509 density of, 500, 505 discovery of, 159–162 excited states of, 538, 538–539 ground state of, 496–508 radius of, 165 shape of, 501 size of, 163–164, 496–500 stability of, 502, 502–504 structure of, 199 Nuclides, 496, 559t fissile, 544 mirror, 496, 497 Null interval, 38–39 Number density, 441–442, 443t Nurmia, M., 513 Nuttall, John Mitchell, 512 O Observers in special relativity, 13–14 and wave-particle duality, 220 Occupation probability (fFP (E)), 445 Ochsenfeld, Robert, 474 Ohm’s law, 437, 438, 439, 484 and Josephson junction, 482 Oil-drop experiment See Millikan oil-drop experiment Olbers, Wilhelm, 686 Olber’s paradox, 686 OLEDs See Organic semiconductor lightemitting diodes (OLEDs) Oort, Jan, 658 Open clusters, 651 Open universe, 688 Operators, 250–251, 252t Oppenheimer, J Robert, 108 Optical barrier penetration, 264 Optical pumping, 409 Optical traps, 416 Optical tweezers, 417 Orbital quantum number See Angular momentum quantum number Orbitals, 375, 384, 421, 485 bonding vs antibonding, 385, 385 elliptical atomic, 285 hybridization of, 435 Orbits circular atomic, 165–166, 166 elliptical atomic, 173–174 Ordinary spiral galaxies, 675–676, 676, 677 Organic semiconductor light-emitting diodes (OLEDs), 471, 471 Oscillators, number of, 360 Oscilloscopes, 121 Osheroff, Douglas D., 348 Ötzi the Iceman, 565, 565 11/2/11 3:26 PM www.elsolucionario.net I-12 Index P P branches, 421 p mesons See Pions (p) p-type semiconductors, 462, 462, 467, 467 Pair production of particles, 90–93, 91, 92, 581, 581, 582, 585 Paradoxes in relativity See Gedanken experiments Parallax angles (u), 660, 660 Paramagnetism, 449, 492 Parity (P), 606–607, 607 nonconservation of, 606 Parity operations, 257–258, 606 Parsecs (pc), 654, 655, 660 Partial cross sections, 537 Particle-in-a-box See Infinite square wells Particle-induced x-ray emission (PIXE), 565–566, 566 Particle physics, 579–637 basic concepts for, 580–588 conservation laws and symmetries in, 598–609 fundamental interactions and force carriers in, 588–598 and grand unified theories, 623–630 history of, 579–580 Standard Model of, 609–617 Particle waves, 193–227, 195 and the de Broglie hypothesis, 193–195 measurements of, 195–196 probabilistic interpretation of, 210–213 and the uncertainty principle, 207–209 and wave packets, 204–210 and wave-particle duality, 219–221 Particles See also Alpha particles (a); Antiparticles; Beta particles (b); Virtual particles annihilation of, 90–93, 91, 583–584, 584 indistinguishable, 303–304, 338, 339, 340–342 macroscopic, 217 massless, 89–90 pair production of, 90–93, 91, 92, 581, 581, 582, 585 predicting properties of, 614–617 Paschen, Friedrich, 156, 170 Paschen series, 156, 169, 170 Pauli, Wolfgang, 307, 312, 315 and electron spin, 293 and neutrinos, 516, 626 Pauli exclusion principle, 303, 304–305 and baryons, 614 and bosons, 340 and fermions, 363, 382, 445, 495 and line of stability, 503 and neutron stars, 667 and white dwarfs, 668 Pauli paramagnetism, 449 Penzias, Arno Allan, 131, 690, 697 Perfect cosmological principle, 686 TIPLER_INDEX_001-018hr.indd 12 Periodic table, 175 and ground states of atoms, 305–309 Perl, M., 631 Perrin, Jean-Baptiste, 120, 195, 222 Perturbation theory, first-order, 306 PET See Positron emission tomography (PET) Petit, A., 337 Pfund, A.H., 170 Phase transitions, 345, 693 Phase velocity (vp ), 204, 207 for particle waves, 209 Phonons, 478–480, 526 Photodisintegration, 666 Photoelectric effect, 129, 131–137, 147, 403, 405 and de Broglie wavelength, 198 in potassium, 135 Photomultiplier, 133 Photon gases, 354–361 Photons, 89–90, 133, 145, 579 as force mediators, 591t, 592 incident intensity, 136 and Schrödinger equation, 230–231 sensitivity of the human eye, 136–137 time lag, 135–136 virtual, 526 Photosphere, 640–641, 642 Photovoltages, 470 Photovoltaics See Solar cells Pickering, Edward, 653 Pions (p), 527, 579, 582, 584, 587 in Feynman diagrams, 584 virtual, 614, 619 PIXE See Particle-induced x-ray emission (PIXE) Plages, solar, 649, 649 Planck, Max K.E.L., 145, 222, 269 and energy distribution, 127–129, 354–355 and energy quantization, 133–134, 154, 165, 233, 256, 355, 579 and fundamental constants, 694–695 Planck’s constant (h), 128, 129, 166 Planck’s law, 127, 127–131, 128, 130 and stellar temperatures, 641 and stimulated emission, 407 Planetary nebula, 663, 663 Plasma, 548 confinement of, 548–549 metals as, 486 solar, 644–645, 647 structure of, 427 Plato, 650 pn junctions, 467, 467 pnp transistors, 471, 471 Polar coordinates, 104 Polar molecules, 388–389, 389 Polaris, 652, 697 Polarizability (a), 389 Pole and barn paradox, 48–50, 49 Polycrystalline solids, 428 Polyelectrons, 113 Polynomials Hermite, 255, 269 Lagendre, 282 Laguerre, 287, 287t Population densities (n), 412 Population I stars, 651 Population II stars, 651 Population inversions, 409, 413–414, 414 critical density (Dnc ), 412, 415–416 Positron emission tomography (PET), 494, 517, 558 Positronium, 113, 188 Positrons (e +), 16, 90–91, 91 discovery of, 493, 580 Potassium photoelectric effect in, 135 Potential energy (U), 81 See also Finite square wells; Infinite square wells; Simple harmonic oscillators and alpha decay, 512, 512 and coupling constants, 589, 595 and covalent bonding, 382–386, 384, 385 of electric dipoles, 386, 387 gravitational, 644 and ionic bonding, 378, 378–379 Kronig-Penney, 452, 452–453 Lenard-Jones, 425 of massless particles, 90 of moving objects, 85–86, 88 for quarks, 619, 619 and Schrödinger equation, 232, 237–238 and solids, 429–432 of strong interaction, 495, 522, 524, 531 and vibrational energy levels, 395, 395– 396, 396 vs kinetic energy, 81–83 Pound, R.V., 102, 108, 569 Pregnant elephant, 32 Primitive vertices, 580, 580, 585 Principal quantum number (n), 167, 286 Principle of equivalence, 98–100, 99, 100 and gravitational redshift, 106–107 Probability, and particle waves, 204, 210– 213, 232–233 Probability amplitude (C (x, t)), 233 Probability density (P(x,t)), 233 in band theory of solids, 455 for electron solids, 436, 436–437 of exchange mesons, 528–529, 529 in finite square wells, 244, 244 for the hydrogen atom, 290–292, 291, 292, 293 and indistinguishable particles, 303–304, 338, 339, 340–342 in infinite square wells, 241, 242, 243– 244, 244 in simple harmonic oscillators, 255, 256 11/2/11 3:26 PM www.elsolucionario.net Probability distribution functions (P(x)), 211–213, 254 for exchange mesons, 528–529, 529 for infinite square wells, 243–244, 244 Promethium, 179, 179 Prominences, solar, 649, 649 Proper frequency ( f0 ), 42 Proper Length (Lp ), 33, 48 as four-vector, 85 Proper time interval, 30, 33, 38 as four-vector, 85 Proper time interval (t), 20–21, 23–24 Proportionality constant, 126 Proton-proton cycle, 551–552, 645–646, 646, 647t Proton spin, 613–614 Proton spin crisis, 614 Protons ( p), 96–97, 495t, 579 decay of, 625–626 diffraction of, 201, 202 in interstellar medium, 673 strong interaction, 523–524 Proxima Centauri, 660 Ptolemy, 656 Pulsars, 109, 669, 669 Pulsed lasers, 418 Pump level in lasers, 410, 411 Purcell, E.M., 486 Pure rotational spectra, 393 Q Q branches, 402 Q-switching, 411 Q values, 534–536, 539, 551 QED See Quantum electrodynamics (QED) QSOs See Radio-quiet quasars (QSOs) QSRs See Radio-loud quasars (QSRs) Quality factors (Q), 411 Quantization, 119–152 of angular momentum, 167, 283, 283–285 and blackbody radiation, 123–131 and the Compton effect, 141–144 of electric charge, 119–123, 146 of energy, 128–129, 132, 233, 239, 241, 286–287 of energy states of matter, 355–358 of magnetic flux, 477 of magnetic moment, 295 and the photoelectric effect, 131–137 Quantum chromodynamics (QCD), 609, 617–619, 618, 659 and dark matter, 659 failures of, 614 and Feynman diagrams, 584 Quantum computers, 264, 451, 460 Quantum dots, 247, 459, 460 Quantum electrodynamics (QED), 295–296, 582 and antiparticles, 582 and interaction strengths, 595–596 TIPLER_INDEX_001-018hr.indd 13 Index and mediation of forces, 592 Quantum fluctuations, 210 Quantum gravity, 627, 692, 695 Quantum Hall effect, 465, 465 Quantum interference, 312–313, 313 Quantum mechanics, 229 Quantum numbers, 167, 240, 278, 287–289 angular momentum (l), 284 energy (n), 167, 243 internal, 601, 601t magnetic (m), 284, 288 in particle physics, 598–609 and Pauli exclusion principle, 304–305 principle (n), 286 rotational (O), 392 spin (ms ), 293 total angular momentum (j), 299 vibrational (y), 395 Quantum statistics, 338–345 Quantum wells, 459, 459 Quantum wires, 459, 460 Quark confinement, 596, 618, 621 Quark model of hadrons, 609–613 Quarks, 90, 495, 527, 586–588, 587t, 611, 616, 620t antiquark combinations, 612t, 613 discovery of, 160, 579 internal quantum numbers of, 601, 601t naming of, 631 and quantum chromodynamics, 617–620 up-type vs down-type, 587t, 588 and weak interaction, 592 Quartz, 428 Quasars, 677, 681 Quiet galaxies, 675 Quiet Sun, 641 R R branches, 421 Radial Schrödinger equation, 281 Radiant flux (F), 640, 654, 659 of quasars, 677 Radiation, 130, 508 See also Blackbody radiation; Cosmic background radiation; Electromagnetic radiation; Emission; Radioactivity coherent, 403, 406 dispersion, 124 Hawking, 672, 697 ionizing, 552*, 566* radio-frequency (RF), 556 resonance, 403, 406 thermal, 123 Radiation dosages, 566* Radiation era, 693 Radio-frequency (RF) radiation, 556 Radio galaxies, 677, 677 Radio-loud quasars (QSRs), 677 Radio-quiet quasars (QSOs), 677 Radioactivity, 508–511, 569 I-13 counting rate of, 510 dating, 558–563 decay modes of, 265–267, 511–522 discovery of, 493 statistical nature of, 36–37, 508–510 units of, 509 Radiography, 556–558, 557, 558 Radioisotopes, 564 Radiometric dating, 558–560, 559 RAM See Random access memory (RAM) Raman spectra, 404, 404 Raman, Chandrasekhara V., 404, 421 Raman scattering, 403, 404, 404–405, 421 Raman spectra, 404, 404 Ramsauer-Townsend effect, 267 Random access memory (RAM), 451 Rayleigh, John W Strutt, Lord, 126, 127, 145, 338, 403 Rayleigh-Jeans equation, 126, 127, 128 Rayleigh scattering, 403, 403 Rayleigh’s criterion, 222 Reactors See Nuclear reactors Rebka, G.A., 569 Recurrent novae, 664 Red giants, 663 Red subgiants, 663 Red supergiants, 663 Redshift, 42, 43–44 cosmological, 681–683 of galaxies, 677, 678 of gamma-ray bursts, 672 gravitational, 102, 106–108, 107, 107, 670 and Hubble’s law, 678–680, 679 of quasars, 681 Reduced mass (m), 171–172 in moments of inertia, 393, 394 in Schrödinger equation, 279 in simple harmonic oscillators, 393 Reference clocks, in special relativity, 13, 14 Reference frames, 58, 99, 99–100 center-of-mass, 535, 576 inertial, 4, 4–6# laboratory, 535, 535, 536 non-inertial, 97, 98 rest, 688 zero momentum (S'), 74 Reflection of wave functions, 258–268 Refraction by electromagnetic waves, 153 index of, 313 Reines, Frederick, 516 Relative boiling points, 390–391 Relativistic force (F), 70–71 Relativistic Heavy Ion Collider (RHIC), 114, 580, 583 Relativistic kinetic energy (Ek ), 71–72, 72 Relativistic mass (m(u)), 67–70, 68 Relativistic mechanics, 230, 293 and de Broglie relations, 194 11/2/11 3:26 PM www.elsolucionario.net I-14 Index Relativistic momentum (p), 66–70, 67, 68 and fine-structure splitting, 173 Relativistic multiplier (g), 19 Relativistic speed ratio (b), 21, 43 Relativistic wave equations, 295, 507, 528, 580, 582 Relativity, 3–64 classical, 4–6#, 7–10, 11 and coordinate transformations, 17–29 and the Doppler effect, 40–45 and dynamics, 65–97 and Einstein’s postulates, 11–17 and energy, 70–81 experimental basis of, 4–11 and Gedanken experiments, 45–51 general, 33, 47, 97–108, 108* and invariant mass, 84–97 and the Lorentz transformation, 17–29 and mass/energy conversion, 81–84 and momentum, 66–70 and motion, 3–64 of simultaneity, 14–17, 15, 16, 17, 48*, 49 special, 3–97 and time dilation and length contraction, 29–40 Relaxation time (t), 439 Residual strong interaction, 622 Resistance (R), 439 standard of, 466 Resistivity (r), 439 and superconductivity, 472 temperature dependence of, 447, 447–448, 457 Resonance absorption, 406 Resonance radiation, 403, 406 Resonances, 538–539, 539 of hadrons, 591, 605, 609*, 617 Response time-bandwidth relation, 207 Rest energy (mc 2), 72–73 Rest mass (m), 78 and conservation of energy, 81–83 of moving objects, 85–86 Reverse biasing, 467, 467, 468 RHIC See Relativistic Heavy Ion Collider (RHIC) Richardson, Robert C., 348 Richter, Burton, 615, 631 Right ascension (a), 656, 656, 697 Right-handed coordinate system, 607, 607 Rindler, W., 48, 50 Ritz, Walter, 156 Roche, Edouard A., 697 Roche lobes, 664, 664, 665 Rocks, radiometric dating of, 559–560, 562–563 Roentgen, Wilhelm K., 138, 145, 493, 556 Rohrer, Heinrich, 264 Roosevelt, Franklin D., 547 Rotational energy levels, 358, 392–395, 393 Rotational quantum number (l), 392 TIPLER_INDEX_001-018hr.indd 14 Rubbia, Carlo, 593, 631 Ruby lasers, 409, 410–413, 411 Rumford, Benjamin Thompson, Count, 89 Rutherford, Ernest, 157, 185, 186 and atomic model, 145, 156–159, 158, 162, 270 and the atomic model, 165 and the nucleus, 163, 163–164, 493, 495, 496, 508, 533 and radiation, 512 Rutherford Appleton Laboratory, 418 Rutherford scattering, 159–162*, 164 Rydberg, Johannes R., 156 Rydberg atoms, 174, 174–175 Rydberg constant (R), 156, 168, 171–172 Rydberg-Ritz equation, 168 Rydberg-Ritz formula, 156 Ryle, Martin, 689, 697 S s-bonding, 385 Sagittarius A*, 655, 670–671, 672 Salam, Abdus, 588 Satellites BeppoSAX, 672 Cosmic Background Explorer (COBE), 131, 685, 690 geosynchronous, Saturated bonds, 385 Saturated forces, 504, 523, 525 Scale factor (R(t )), 688 Scanning tunneling microscopes (STMs), 264, 264–265 Scattered fraction ( f ), 161 Scattering, 402–405 See also Collisions deep inelastic, 611 elastic, 402, 403, 533–534, 534 and the nucleus, 524 Scattering angles (u), 159, 160, 164 Schrieffer, J Robert, 478, 486 Schrödinger, Erwin R.J.A., 231, 256, 269 and de Broglie relations, 194 and wave equation, 229–230, 253, 280, 295 Schrödinger equation, 229–275, 452–453 See also Wave equations and acceptable wave functions, 235–237 and expectation values and operators, 250–253 and the finite square well, 246–249 and the infinite square well, 237–246 for multiple particles, 303–305 in one dimension, 230–237 radial, 281 and reflection and transmission of waves, 258–268 and the simple harmonic oscillator, 253–257 in spherical coordinates, 279–280, 280 in three dimensions, 277–280 time-independent, 233–235 and wave equations, 232–233 and wave-particle duality, 220 Schwarzschild radius (RG ), 109, 670 and limits of knowledge, 695 Schwinger, Julian, 631 Scissors paradox, 52, 52 SDSS See Sloan Digital Sky Survey (SDSS) Search for Extraterrestrial Intelligence (SETI), 651 Seasons, 657 Second-order Doppler effect, 44 Segrè, Emilio, 547, 558, 570, 582, 631 Selection rules, 255 for hydrogen atoms, 288 and molecular spectra, 393, 395, 396, 398 for nuclear transitions, 506, 601 for simple harmonic oscillators, 255–256, 256 Semiconductor lasers, 418 Semiconductors devices of, 467–472 impurity, 460, 460–463, 484 intrinsic, 456, 456–459, 457 junctions of, 467, 467 n-type, 462, 462, 467 p-type, 462, 462, 467, 467 Semimetals, 455 Separation of variables, 234–235, 269, 281 constant for (C), 234–235 Series limits, 155, 155, 169, 169 SETI See Search for Extraterrestrial Intelligence (SETI) Seyfert, Carl, 676 Seyfert galaxies, 676 Shapiro, I.I., 103 Shapley, Harlow, 655, 697 Shells electronic, 300, 307, 308 nuclear, 497, 529–532, 533* Shielding, 307 Shock waves, 643 Shockley, William B., 471, 486 Short-range forces, 525 Shroud of Turin, 565 Signal processing, 207 Silicon (Si), and impurity semiconductors, 456, 456–468 Simple cubic (sc) crystal symmetry, 433, 433 Simple harmonic oscillators, 253, 253–257 and correspondence principle for, 255, 255 and equipartition theorem, 334* and heat capacities, 356–358, 358 and Planck’s law, 127 and vibrational energy levels, 395 Simultaneity relativity of, 14–17, 15, 16, 17, 48*, 49 in spacetime, 28, 28 Single-cell biological lasers, 418 11/2/11 3:26 PM www.elsolucionario.net Single-photon emission computer tomography (SPECT), 558 Sinusoids, 206 Sirius, 651 SLAC See Stanford linear accelerator (SLAC) Sloan Digital Sky Survey (SDSS), 677 Smirnov, A., 626 Smoke detectors, 512 Smoot, George F., 690, 697 SN1987A [supernova], 633, 663, 663 Snell’s law, 222 SNO neutrino observatory, 90, 133 Snyder, H., 108 Socrates, 631 Sodium (Na) and band theory of solids, 455, 455 spectra of, 310–311, 311, 506, 507 Soft superconductors, 475, 475 Solar cells, 469, 470 Solar constant ( f ), 147, 640, 659 Solar flares, 648, 649 Solar irradiance, 640 Solar-neutrino problem, 552, 626, 645–646 Solar wind, 643 Solid angle (V), 185 Solid state physics, 427–492 and band theory of solids, 452–460 and conduction, classical, 437–440 and conduction, quantum, 444–448 and the free-electron gas in metals, 440–444 and impurity semiconductors, 460–463 and magnetism, 448–451 and semiconductor junctions and devices, 467–472 and the structure of solids, 427–437 and superconductivity, 472–484 Solids amorphous, 428 covalent, 429–436 heat capacities (Cv ), 337, 337–338 ionic, 429–436 magnetism in, 448–451 polycrystalline, 428 structure of, 427–437 Solstices, 657, 657, 697 Sommerfeld, Arnold, 173, 222, 293, 448 Southern Cross, 651 sp 2 and sp 3 hybridization, 435 Spacelike spacetime intervals, 37, 38 Spacetime, 13 simultaneity in, 28, 28 worldlines in, 24–28 Spacetime diagrams, 23–29, 24, 32, 46 See also Feynman diagrams calibrating axes of, 27, 28–29 Spacetime intervals (Ds), 37–40, 40 as four-vector, 84–85 lightlike, 37, 38–39 TIPLER_INDEX_001-018hr.indd 15 Index spacelike, 37, 38 timelike, 37–38, 39 Special relativity, 3–64, Specific heat See Heat capacities (Cv ) SPECT See Single-photon emission computer tomography (SPECT) Spectra, 153 absorption, of diatomic molecules, 398– 402, 400, 401 ammonia inversion, 405 atomic, 154–156, 155 band, 153 continuous, 153–154 emission, of diatomic molecules, 397, 397–398, 399 line, 153–154, 154 nuclear, 496, 539 pure rotational, 393 and supernovae, 665 vibrational-rotational, 398, 399 x ray, 175–179, 179 Spectral distributions, 124–125, 125 Spectral lines, 120 Doppler broadening of, 338, 675 and Hubble’s law, 679 natural width (G0 ) of, 218–219, 520–521, 538 and stellar classification, 653 Spectroscopic notation, 300*–301 Spectroscopy, 153 accelerator mass (AMS), 553, 562, 563– 565, 564, 565 atomic beam fluorescence, 506 electron energy loss (EELS), 182–183, 183 Speed See also Velocity of a fast electron, 86–88 Fermi (mF ), 445, 447 molecular, 329–332 superluminal, 51–54, 52, 53 Speed of light (c), 6–7 and the Doppler effect, 41 and ether, 6–11 slowing of, 102–103, 312–313, 313 and special relativity, 12 and time dilation, 30–31 and worldlines, 24–25, 25 Spherical coordinates, 279–280, 280, 290 Spherical harmonic functions, 289 Spherical harmonics, 282, 282t Spin, 174 Spin angular momentum (S), 293–298 of antineutrinos, 602 of hadrons, 591t, 604t and magnetism, 449–451 nuclear (I), 312, 505 of protons, 613–614 of quarks, 587t Spin Hall effect, 451, 466, 466–467 Spin-orbit coupling, 301–302 I-15 Spin-orbit effect, 298–302, 310 nuclear, 531, 532 Spin quantum numbers (ms ), 293 Spin valves, 451 Spintronics, 451, 451 Spontaneous emission, 406 vs stimulated emission, 408 Spontaneously broken symmetry, 620 Spring equinox, 657, 657 SQUIDs See Superconducting quantum interference devices (SQUIDs) Standard candles, 660, 665, 668, 685 Standard Model, 552, 579, 580, 609–617 and conservation laws, 599, 608 failures of, 623 and mass, 621 and mediation of forces, 589, 621 and quarks and gluons, 586, 588 summary of, 621–622 Standard model of the universe, 689 Standing waves and de Broglie relations, 194, 194 and lasers, 410, 410 and Planck’s law, 127 and Schrödinger equation, 229 Stanford linear accelerator (SLAC), 116, 497, 613 Star clusters, 651 Stars, 651–663, 653t See also Astrophysics; Cosmology; Galaxies; Sun and cataclysmic events, 664–666 classification of, 653, 653t composition of, 155, 310 constellations of, 651, 652 evolution of, 659–663 final states of, 667–673 and Hertzsprung-Russell diagrams, 661, 661–663 magnitude of, 653–654 neutron, 668–670, 669 populations of, 651–653 surface temperature of, 125, 659, 661, 661 Stationary states, 166, 233 Statistical mechanics, 325 Statistical physics, 181, 240, 325–371 and atomic spectra, 309–311, 311 and Bose-Einstein condensates, 345–353 classical, 326–338 and fermion gases, 361–365 of the hydrogen atom, 291–293 and nuclear reactions, 538–539 and photon gases, 354–361 quantum mechanical, 338–345 Stefan, Josef, 124, 366 Stefan-Boltzmann law, 124, 130 and stellar temperatures, 641 Stefan’s constant (s), 124, 130, 640 Stellar aberration, 60 Stellar populations, 651–653 Step potentials, 258–262, 259, 261, 262, 263 11/2/11 3:26 PM www.elsolucionario.net I-16 Index Stern, Otto, 201, 294, 296–297, 315, 370 Stern-Gerlach experiment, 294, 296, 296– 298, 297, 298 Stimulated emission, 403, 406–408 See also Lasers vs spontaneous emission, 408 STMs See Scanning tunneling microscopes (STMs) Stoney, George J., 120, 145 Stopping potential (V0 ), 132–134, 133 Stormer, H.L., 486 Strange particles, 602 Strangeness (S), 582, 601–603, 601t, 602, 604t Strassmann, Fritz, 543, 546, 570 String theories, 624 Strong force, 495 Strong interaction, 522–529, 589–592, 591t, 594t See also Fundamental interactions alpha decay, 265–267 and beta decay, 517 and cosmology, 692 range of, 500, 527, 594t, 598 residual, 622 transmission of, 90 Strutt, John W Lord Rayleigh, 126, 127, 145, 338, 403 SU(2) group theory, 610 SU(3) group theory, 610, 610–612, 611 Sudbury Neutrino Observatory, 552, 600, 625, 626 Summer solstice, 657, 657 Sun, 639–651 See also Astrophysics; Stars active, 647–649 change in mass of, 79 chromosphere of, 642, 642, 643 core of, 643 corona of, 642–643 energy source of, 551–552, 644–646 interior of, 643–644 limbs of, 641, 642 magnetic field of, 643, 647, 647–648, 648 mass of, 79, 643 photosphere of, 640–641, 642 proton-proton cycle in, 551–552, 645–646, 646, 647t quiet, 641 rotation of, 43 spectrum of, 338 surface and atmosphere of, 129, 640–643, 641, 642 x rays from, 641, 643 Sunspot cycle, 647–648, 648 Sunspots, 642, 648, 648, 649 Super-Kamiokande Neutrino Observatory, 90, 133, 552, 600, 625, 625, 626, 666 Superclusters, 682, 683 Superconducting energy gaps (Eg ), 479–480, 480 TIPLER_INDEX_001-018hr.indd 16 Superconducting quantum interference devices (SQUIDs), 483, 484 Superconductivity, 472–484 BCS theory of, 477–480, 478 high-temperature, 481–482, 481t type I vs type II, 475, 475 Supercurrents, 473 Superfluids, 346–351, 348, 349 Superleaks, 366 Superluminal speeds, 51–54, 52, 53 Supermultiplets, 609, 610, 610 Supernovae, 500, 663, 665–666, 666 as standard candles, 660, 665, 668, 685 Superpartners, 586, 623–624, 624t and dark matter, 659 Superposition See also Diffraction; Interference and stationary states, 243, 269 and wave packets, 205, 205 Superstring theories, 624, 627 Supersymmetry (SUSY), 586, 623–625 and wave-particle duality, 193 Surface-barrier detectors, 469 Surface tension, 390 Symmetry breaking of, 620–621, 621 and conservation laws, 66, 598–609 and crystallography, 429, 429–436, 430t, 434, 435 and three-dimensional square wells, 279, 279 Synchronization, in special relativity, 13, 14, 14–15 T Taagepera, B., 513 Tachyons, 53–54, 54 Tarantula nebula, 663 Taylor, E.E., 48 Taylor, J.H., 109 TCP invariance, 607–608 Temperature (T ), 329* critical (Tc ), for Bose-Einstein condensates, 350–351 critical (Tc ), for superconductivity, 472, 473t, 474, 476, 481t Curie (Tc ), 450 Debye (TB ), 357, 358 Einstein (TE ), 357, 357, 446–447 Fermi (TF ), 443, 444 fusion, 551 Neel (TN ), 450 stellar, 653, 659, 661, 661–662 of the Sun, 125, 641, 641–642, 642 Thales, 650 Theories of everything, 629* Thermal conduction, 347, 448* Thermal equilibrium, 123–124 Thermal neutrons, 540 Thermal radiation, 123 Thermochemical effect, 348, 349 Thomas, A., 614 Thompson, Benjamin, Count Rumford, 89 Thompson, C., 558 Thompson, William, Lord Kelvin, 316 Thomson, George P., 200, 222 Thomson, Joseph J., 121, 145, 185, 200 and atomic model, 156–157 and discovery of electrons, 120–121, 131, 222, 437, 579, 586 and polyatomic molecules, 386 Thomson experiment, 120, 120–122, 121, 122 Thought experiment, 214 Time See also Clocks absolute direction of, 608 interaction, 589 relativistic, 17–21 relaxation (t), 439 Time dilation, 29–33, 30, 30, 31, 32 and the Doppler effect, 42 gravitational, 100 Time-independent Schrödinger equation, 233–235, 251 Time intervals, proper (t), 20–21 Timelike spacetime intervals, 37–38, 39 Timelike worldlines, 37 Ting, Samuel Chao Chung, 615, 631 Tokamaks, 548, 549 Tomography, 569 See also Computer assisted tomography (CAT); Positron emission tomography (PET); Singlephoton emission computer tomography (SPECT) Tomonaga, Sin-Itiro, 631 Top (T ), 587t, 588 Torque (t) and magnetic moments, 295, 295 and precession, 298 relativisitic, 80–81 Total angular momentum quantum numbers (j), 299, 299 Totalitarian principle, 598 Townes, Charles, 409 Townsend, John S.E., 122 Tracers, isotopic, 186 Transcendental equations, 249* Transformation of coordinates See also Coordinate systems; Lorentz transformation Galiliean, 4–6#, 6, 18 Transistors, 471, 471–472, 472* Transition elements, 309 Transitions between energy states, 253*, 405*, 406* Transmission coefficient (T ), 513 Transmission of wave functions, 258–268 Tritium, 543, 547, 549 Tsui, Daniel C., 465, 466, 486 Tunable dye lasers, 418 11/2/11 3:26 PM www.elsolucionario.net Tunnel diodes, 264, 267*, 468, 469, 469 Tunneling, 248, 264, 264–265 and alpha decay, 266–267, 513, 513 and fission, 544 and fusion, 548, 645 and Josephson junctions, 482–483 and scanning tunneling microscopes (STMs), 264, 264–265 and semiconductor devices, 468, 469, 469 Tunneling current, 469, 469 Turning points, 253 Twin paradox, 45–48*, 46 Two-slit interference experiment, 210–211, 211 Type I superconductors, 475, 475 Type I supernovae, 665 Type II superconductors, 475, 475 Type II supernovae, 665–666, 666 U Uhlenbeck, George E., 293, 315 Ultraviolet catastrophe, 126 Uncertainty principle, 213–216 angular momentum, 285, 299 classical, 207–209, 208 consequences of, 216–219 and finite square wells, 248 and infinite square wells, 241 and limits of knowledge, 694 and mediation of forces, 526 Unified mass unit (u), 393 Unit cells, 428, 484 Universe See also Big Bang acceleration of expansion of, 660, 680 critical energy density of, 684–685 evolution of, 310, 691 expansion of, 680–681, 687 geometry of, 687 history of, 690–693 photon density of, 355 Up (U), 587t, 588, 601 Up-type quarks, 587t, 588 Uranium diffusion of, 330 fission of, 543, 544–546, 545 Urey, Harold C., 171, 185 V Vacuum polarization, 596, 596, 618 Valence bands, 455, 455, 456 Van de Graaff generators, 493, 534 and accelerator mass spectroscopy, 564, 564 van der Meer, Simon, 631 van der Waals, Johannes D., 346, 387, 390, 421 van der Waals attraction, 387, 390, 421 Vector models, 284, 285, 299 Velocity See also Speed drift (vd) , 438, 438–439 TIPLER_INDEX_001-018hr.indd 17 Index escape (ve ), 109, 333–334, 670, 697 group (vg ), 205, 206, 210 nonrelativistic, 96 phase (vp ), 204, 209 relativistic transformations of, 21–23 Velocity distribution function, 330–331, 331 Vernal equinox, 657, 657 Very Large Array, 655 Very Large Telescope (VLT), 672 Vessot, R.F.C., 108 Vibrational energy levels, 360, 395, 395–397 Vibrational quantum numbers (v), 395 Vibrational-rotational spectra, 398, 399 Virtual particles, 214 and exchange forces, 525–526 Feynman diagrams for, 584, 585, 592 and vacuum polarization, 596, 596 Virtual photons, 526 VLT See Very Large Telescope (VLT) von Fraunhofer, Joseph, 153, 185, 405, 653 von Helmholtz, Hermann, 113, 145, 598 von Klitzing, Klaus, 455–456, 486 von Klitzing constant (Rk ), 465–466 von Laue, Max, 80, 138 Vortices, 475, 476, 477 W W; bosons, 593, 593, 594t Walsh, D., 105 Walton, Ernest T.S., 493, 532, 569 Wave equations, 230 See also Schrödinger equation classical, 204, 210, 220 relativistic, 230, 297–298, 507, 528, 580, 582 Wave functions (c (x, t)), 209 and alpha decay, 513, 513 for barrier potentials, 263, 263–264 and covalent bonding, 381, 381–382 for finite square wells, 247, 247–249, 248 for the hydrogen atom, 289–293 for hydrogen molecules, 382–386, 384 for infinite square wells, 237–240, 241, 242–246, 244 macroscopic, 353, 353 for neutrinos, 628 probabilistic interpretation of, 210–213 reflection and transmission of, 258–268 for simple harmonic oscillators, 254–256, 255 and step potentials, 258–263, 259, 262 and TCP invariance, 607–608 Wave mechanics, 229 Wave number (k), 204, 205, 206, 213, 222 Wave packets dispersion of, 212, 212 for particles, 204–210 reflection and transmission of, 261 for waves (c (x, t)), 204–207, 205, 206 I-17 Wave-particle duality, 193, 219–220 and Compton effect, 142 and photon gases, 355 and uncertainty principle, 214 Wave vectors (k), 455 Wave velocity See Phase velocity (vp ) Wavelength, 43–44 Waves See also Particle waves gravitational, 106, 106–108 harmonic, 204, 230, 232 matter, 195–204 shock, 643 Weak charge, 588, 592, 594t Weak interaction, 517, 592–594, 594t See also Fundamental interactions and beta decay, 517 charged vs neutral, 592 and cosmology, 692 Feynman diagrams for, 592 mediation, 592 range of, 594 Weak isospin Tz , 586, 587t, 588 Weakly interacting massive particles (WIMPs), 658–659 Weight diagrams, 610, 610, 611 Weinberg, Steven, 588 Weizsächer semiempirical binding-energy formula, 505*, 505 Weizsächer semiempirical mass formula, 518, 518, 577 Wheeler, John A., 48, 543, 697 White dwarfs, 663, 667–668, 668 Wieman, Carl E, 351, 353 Wien, Wilhelm, 125 Wien’s displacement law, 125, 128 Wigner, Eugene, 569 Wilczek, Frank, 697 Wilkinson Microwave Anisotropy Project (WMAP), 131, 680, 685, 690, 697 Wilson, Robert Woodrow, 131, 690, 697 WIMPs See Weakly interacting massive particles (WIMPs) Winter solstice, 657, 657 WMAP See Wilkinson Microwave Anisotropy Project (WMAP) Wolfenstein, L., 626 Wolfke, Miwczyslaw, 345 Wollaston, William H., 185 Work and relativity, 72, 79–80 and torque, 298 Work function (f), 133, 134, 135t, 140 World Wide Web, 592 Worldlines, 24–28, 25, 27, 28, 46 and event analysis, 26 of tachyons, 54 timelike, 37 Wu, C.S., 606, 607 11/2/11 3:26 PM www.elsolucionario.net I-18 Index X X rays, 137–141, 138, 139 discovery of, 493 and particle-induced x-ray analysis (PIXE), 565–566, 566 from solar corona, 641, 643 spectra of, 141, 175–179, 179 TIPLER_INDEX_001-018hr.indd 18 Y Yang, C.N., 606, 607, 608 Yukawa, Hideki, 569 and exchange forces, 525–527, 584, 589 Z Z 0 bosons, 593, 593, 594t, 595 Zeeman, Pieter, 56, 120, 122, 302, 316 Zeeman effect, 120, 288, 302, 312* nuclear analog of, 507 Zener breakdown, 468, 468 Zener diode, 468, 468 Zero momentum frames (S¿), 76–77 Zero point energy, 216–217, 341, 380 Zweig, George, 611 Zwicky, Fritz, 658 11/2/11 3:26 PM www.elsolucionario.net The Greek Alphabet Alpha A a Iota i Rho r Beta Gamma Delta Epsilon Zeta Eta G D b g d z x Kappa Lambda Mu Nu Xi Omicron L J l m n j Sigma Tau Upsilon Phi Chi Psi S F C s t x c Theta u Pi P p Omega V v Prefixes for Powers of 10 Multiple 18 10 1015 1012 109 106 103 102 101 1021 1022 1023 1026 1029 10212 10215 10218 Mathematical Symbols Prefix Abbreviation exa peta tera giga mega kilo hecto deka deci centi milli micro nano pico femto atto E P T G M k h da d c m m n p f a is equal to Dx change in x is not equal to absolute value of x is approximately equal to n! 0x0 is of the order of sum is proportional to is greater than lim Dt S limit Dt approaches zero is greater than or equal to derivative of x with respect to t partial derivative of x with respect to t integral is less than dx dt 0 x 0 t is less than or equal to W is much greater than n1n - 121n - 22 g V is much less than Tipler_Endpaper_1-hr.indd 11/4/11 10:43 AM www.elsolucionario.net Abbreviations for Units A ampere 210 keV kilo-electron volts L liter Å angstrom (10 atm atmosphere m meter Btu British thermal unit MeV mega-electron volts Bq becquerel minute C coulomb mm millimeter °C degree Celsius ms millisecond cal calorie N newton Ci curie nm nanometer (1029 m) cm centimeter rev revolution eV electron volt R roentgen °F degree Fahrenheit Sv seivert s second m) 215 m) fm femtometer, fermi (10 G gauss T tesla Gy gray u unified mass unit g gram V volt H henry W watt h hour Wb weber Hz hertz y year J joule mm micrometer (1026 m) K kelvin ms microsecond kg kilogram mC microcoulomb km kilometer V ohm Some Useful Combinations hc 1.9864 10225 J # m = 1239.8 eV # nm Uc = 3.1615 * 10-26 J # m = 197.33 eV # nm Bohr radius a0 = 4p0U2 = 5.2918 * 10-11 m m ee2 ke2 1.440 eV # nm Tipler_Endpaper_1-hr.indd Fine structure constant = e2 = 0.0072974 4p0Uc 137 kT = 2.5249 * 10-2 eV 40 eV at T = 293 K 11/4/11 10:43 AM www.elsolucionario.net Some Physical Constants Avogadro’s number Boltzmann’s constant Bohr magneton (See Appendix D for a complete list of Coulomb constant fundamental constants.) Compton wavelength Fundamental charge Gas constant NA k m B = eU>2m e k = 1>4p0 lc = h>m ec e R NAk Gravitational constant Mass, of electron G me of proton mp of neutron mn Permeability of free space m 0 Planck’s constant h U Speed of light Unified mass unit Some Conversion Factors Some Particle Masses and Rest Energies Tipler_Endpaper_2-hr.indd c u yr 3.156 107 s light-year 9.461 1015 m cal 4.186 J MeV>c = 5.344 * 10-22 kg # m>s eV 1.6022 10219 J kW # h 3.6 MJ Electron Muon Proton Neutron Deuteron a particle W Z° 6.022142 * 1023 particles>mol 1.380650 * 10-23 J>K 9.2740095 * 10-24 J>T 8.987551788 * 109 N # m2 >C 2.42631024 10212 m 1.602176 10219 C 8.31447 J>mol # K = 1.987 22 cal>mol # K = 8.20578 * 10-2 L # atm>mol # K 6.6742 * 10-11 N # m2 >kg 9.109382 10231 kg = 510.9989 keV>c 1.672622 10227 kg = 938.2722 MeV>c 1.674927 10227 kg = 939.5653 MeV>c 4p * 10-7 N>A2 6.626069 10234 J # s 4.135667 10215 eV # s 1.054572 10234 J # s 6.582119 10216 eV # s 2.99792458 * 108 m>s 1.660539 10227 kg = 931.49401 MeV>c T 104 G Ci 3.7 1010 Bq barn 10228 m2 u 1.66054 10227 kg parsec 3.26 light-years rad 57.30° kg MeV>c u 9.1094 10231 1.8835 10228 1.6726 10227 1.6749 10227 3.3436 10227 6.6447 10227 1.43 10225 1.63 10225 0.51100 105.66 938.27 939.57 1875.61 3727.38 80 103 91.2 103 5.4858 1024 0.11343 1.00728 1.00866 2.01355 4.00151 85.9 97.9 11/4/11 10:44 AM Tipler_Endpaper_2-hr.indd 10 11 12 C Carbon 12.0107(8) B Boron 10.811(7) 13 Be Beryllium 9.012 182(3) Li Lithium 6.941(2) Y Yttrium 88.905 85(2) 57-71 Strontium 87.62(1) Rubidium 85.4678(3) Barium Cesium Radium [226] Francium [223] 15 16 17 Niobium Thorium Nd 60 [266] Seaborgium Sg 106 183.84(1) Tungsten W 74 95.94(2) Molybdenum 91 Protactinium Pa Uranium U 92 144.242(3) 232.038 06(2) 231.035 88(2) 238.028 91(3) Actinium [227] 90 Th 89 140.116(1) 140.907 65(2) Ac 138.905 47(7) Pr 42 Mo Manganese Pm 61 [264] Bohrium Bh 107 186.207(1) Rhenium Re 75 [97.9072] Technetium Tc 43 54.938 045(5) [237] Neptunium Np 93 [145] Praseodymium Neodymium Promethium Ce Cerium La Lanthanum [262] Dubnium Db 105 180.947 88(2) Tantalum Ta 73 92.906 38 (2) 59 [261] Rutherfordium Rf 104 178.49(2) Hafnium Hf 72 91.224(2) Zirconium 41 Nb 58 57 Actinoids 89-103 40 Zr Chromium 51.9961(6) Iron [244] Plutonium Pu 94 150.36(2) Samarium Sm 62 [277] Hassium Hs 108 190.23(3) Osmium Os 76 101.07(2) Ruthenium Ru 44 55.845(2) Cobalt Nickel Copper Gold Au 79 107.8682(2) Silver Ag 47 63.546(3) Ds 11 Rg 111 195.084(9) 196.966 569(4) Platinum Pt 78 106.42(1) Palladium Pd 46 58.6934(2) [243] Americium Am 95 151.964(1) Europium Eu 63 [268] [247] Curium Cm 96 157.25(3) Gadolinium Gd 64 [271] [247] Berkelium Bk 97 158.925 35(2) Terbium Tb 65 [272] Meitnerium Darmstadtium Roentgenium Mt 109 192.217(3) Iridium Ir 77 102.905 50(2) Rhodium Rh 45 58.933 195(5) [251] Californium Cf 98 162.500(1) Dysprosium Dy 66 [277] Cn 112 200.59(2) Mercury Hg 80 112.411(8) Cadmium Cd 48 65.409(4) Zinc Zn Silicon 31 32 Erbium Er 68 [289] Uuq 114 207.2(1) Lead Pb 82 118.710(7) Tin Sn 50 72.64(1) Germanium Ge [252] Einsteinium Es 99 [257] Fermium Fm 100 164.930 32(2) 167.259(3) Holmium Ho 67 [284] Uut 113 204.3833(2) Thallium Tl 81 114.818(3) Indium In 49 69.723(1) Gallium Ga llurium Te Polonium Po 84 127.60(3) Te 52 78.96(3) Selenium Se 34 32.065(5) Sulfur S 16 15.9994(3) Oxygen O [258] Mendelevium Md 101 168.934 21(2) Thulium Tm 69 [288] Uup 115 [259] Nobelium No 102 173.04(3) Ytterbium Yb 70 [292] Uuh 116 208.980 40(1) [208.9824] Bismuth Bi 83 121.760(1) Antimony Sb 51 74.921 60(2) Arsenic As 33 30.973 762(2) Phosphorus P 15 14.0067(2) Nitrogen N [262] Lawrencium Lr 103 174.967(1) Lutetium Lu 71 [294] Uub 117 [209.9871] Astatine At 85 126.904 47(3) Iodine I 53 79.904(1) Bromine Br 35 35.453(2) Chlorine Cl 17 18.998 4032(5) Fluorine F Helium [294] Uuo 118 [222.0176] Radon Rn 86 131.293(6) Xenon Xe 54 83.798(2) Krypton Kr 36 39.948(1) Argon Ar 18 20.1797(6) Neon Ne 10 4.002 602(2) - Symbols for elements 112 through 118 are temporary placeholders The corresponding Latin names are, using 115 as an example, Ununpentium, meaning element one, one, five Notes 88 Ra 87 Fr 132.905 451 (2) 137.327(7) 56 Ba 55 Cs Lanthanoids 39 38 Sr 37 Vanadium 50.9415(1) Cu 30 Rb Titanium 47.867(1) Ni 29 Scandium Co 28 44.955 912 (6) Fe 27 Calcium Mn 26 40.078(4) Cr 25 Potassium V 24 39.0983(1) Ti 23 21 Sc 20 Ca 19 K 22 Aluminum Si 26.981 538 6(8) 28.0855(3) Magnesium Sodium 22.989 769 28(2) 24.3050(6) Al 12 Mg 11 Na 14 14 13 1.007 94(7) Hydrogen He 18 H Periodic Table www.elsolucionario.net 11/4/11 10:44 AM ... www.elsolucionario.net MODERN PHYSICS SIXTH EDITION Paul A Tipler Formerly of Oakland University Ralph A Llewellyn University of Central Florida W H Freeman and Company New York TIPLER_ FM_i-xvi-hr.indd... They great work! Paul A Tipler Berkeley, CA TIPLER_ FM_i-xvi-hr.indd 15 Ralph A Llewellyn Oviedo, FL 11/4/11 12:06 PM www.elsolucionario.net this page left intentionally blank TIPLER_ FM_i-xvi-hr.indd... better understanding of the concepts of modern physics, we have included the Classical Concept Review on the book’s Web site As you proceed through Modern Physics, the icon CCR in the margin will
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