Principles of Modern Physics doc

principles of modern physics principles of modelrn physics NEIL ASHBY STANLEY C MILLER University of Colorado HOLDEN-DAY, INC San Francisco Cambridge London Amsterdam o Copyright 1970 by Holden-Day, 500 Sansome Inc., Street San Francisco, California All rights reserved No part of this book may be reproduced in any form, by mimeograph or any other means, without permission in writing from the publisher library of Congress Catalog Card Number: 71-l 13182 Manufactured in the United States of America HOLDEN-DAY SERIES IN PHYSICS McAllister Hull and David S Saxon, Editors preface This book is intended as a general introduction to modern physics for science and tull year’s engineering students It is written at a level which presurnes a prior course in integral classical physics, and a knowledge of elementary differential and quantum me- calculus The material discussed here includes probability, chanics, atomic physics, statistical mechanics, particles Some of these top&, such as relativity, nuclear physics and elementary statistical mechanics and probability, are ordinarily not included in textbooks at this level However, we have felt that for proper understanding of many topics in modern physics such as chanics and its applications this material is essential It is quaIlturn me- opilnion that our present-day science and engineering students should be able to worlk quanti- tatively with the concepts of modern physics Therefore, we have attempted to present these ideas in a manner which is logical and fairly rigorous A number of topics, especially in quantum1 mechanics, are presented in greater depth than is customary In many cases, unique ways of presentation are given which greatly simplify the discussion of there topics However, few of the developments require more mathematics than elementary calculus and the algebra of complex bers; in a Unifying few places, concepts familiarity which with halve partial differentiation important will applications be nurn- necessary throughout modern physics, such as relativity, probability and the laws of conservation, have been stressed Almost all theoretical developments are linked to examples and data taken from experiment Summaries are included at the end of each chapter, as well as problems with wide variations in difficulty This book was written for use in a one-semester course at the iunior level The course could be shortened by omitting some sophlomore topics; for or example, Chapter 7, Chapter 12, Chapters 13 through 15, and Chapter 16 contain blocks of material which are somewhat independent of each other The system of units primarily used throughout is the meter-kilogram-second system A table of factors for conversion to other useful units is given in Appendix Atomic mass units are #defined with the C” atom as tihe standard We are grateful for the helpful comments of a large number of students, who used the book in preliminary term for a number of years We also thank our colleagues and reviewers for their constructive criticism Finally, we wish to express our thanks to Mrs Ruth Wilson for her careful typing of the manuscript vii contents INTRODUCTION 1 l HISTORICAL SURVEY 1.2 NOTATION AND UNITS 1 1.3 UNITS OF ENERGY AND MOMENTUM 1.4 ATOMIC MASS UNIT 1.5 PROPAGATION OF WAVES; PHASE AND GROUP SPEEDS 1.6 COMPLEX (6 NUMBERS :3 PROBABILITY II 2.1 DEFINITION OF PROBABILITY :2 2.2 SUMS OF PROBABILITIES 2.3 CALCULATION OF PROBABILITIES BY COUN’TING :3 2.4 PROBABILITY OF SEVERAL EVENTS OC:CUF!RING TOGETHER PROBABILITIES 14 1:s FUNCTIONS FOR COIN FLIPPING 16 2.5 SUMMARY OF RULES FOR CALCULATINIG 2.6 DISTRYBUTION 14 2.7 DISTRIBUTION FUNCTIONS FOR MORE THAN TWO POSSIBLE 2.8 OUTCOMES EXPECTATION VALUES 2.9 19 20 NORMALIZATION ‘I 2.10 EXPECTATION VALUE OF THE NUMBER OF HEADS ‘I EXPERIWIENTAL PROBABILITY 22 2.12 EXPERIMENTAL ERROR 2.1 DETERMINATION OF 24 2.13 RMS DEVIATION FROM THE MEAN 2.114 RMS DEVIATION FOR 24 FLIPPING 25 2.15 ERRORS IN A COIN-FLIPPING EXPERIMENT 27 2.16 ERRORS IN AVERAGES OF REPEATED EXPERIMENTS 2.17 PROBABILITY DENSITIES 28 2.18 EXPECTATION VALUES FROM PROBABILITY DENSITIES 3:! 2.19 DISTRIBUTION 34 2.20 EXPECTATION VALUES USING A GAUSS1A.N DISTRIBUTION 35 SUMh\ARY 37 GAUSS1A.N COIN PROBLEMS SPECIAL THEORY OF RELATIVITY 3.1 CONFLICT BETWEEN ULTIMATE SPEED AND NEWTON’S LAWS 30 3Ei 421 42 ix 3.2 CLASSICAL MOMENTUM AND EINERGY CONSERVATION- COINFLICT WITH EXPERIMENT 43 WITH EXPERIMENT 44 47 3.5 INERTIAL SYSTEMS 47 3.6 NON-INERTIAL SYSTEMS 49 3.7 AXES RELATIVE TO FIXED STARS CONSERVATION OF MASS-COlNFLICT 3.4 CORRESPONDENCE PRINCIPLE 3.3 50 GALILEAN 3.8 3.9 THIRD 51 VELOCITY TRANSFORMATIONS 52 GALILEAN 3.10 SECGND 3.11 TRANSFORMATIONS LAW LAW OF MOTION UNDER GALILEAN UNDER :3.12 GALILEAN TRANSFORMATIONS TRANSFORMATIONS MICHELSON-MORLEY 53 54 EXPERIMENT 54 RELATIVITY 55 3.14 EXPERIMENTAL EVIDENCE FOR THE SECOND POSTULATE 57 3.13 POSTULATES OF 3.15 GALILEAN TRANSFORMATIONS AND THE PRINCIPLE OF RELATIVITY 3.16 TRANSFORMATION OF LENGTHS PERPENDICULAR TO THE 59 RELATIVE VELOCITY 59 DILATION 60 CONTRACTION 64 TRANSFORMATIONS 65 3.20 SIMULTANEITY TRANSFORMATION OF VELOCITIES 67 71 SUMMARY 74 PROBLEMS 76 TRANSFORMATIONS 79 79 3.17 3.18 3.19 3.21 TIME LENGTH LORENTZ RELATIVISTIC MECHANICS AND DYNAMICS 4.1 4.2 DISCREPANCY BETWEEN LORENTZ EXPERIMENT AND NEWTONIAN MOMENTUM 80 EXPERIMENT 81 EXPERIMENTAL VERIFICATION OF MASS FORMULA 4.5 RELATIVISTIC SECOND LAW OF MOTION 83 4.3 4.4 MOMENTUM FROM A THOUGHT 85 4.6 THIRD LAW OF MOTION AND CONSERVATION OF MOMENTUM RELATIVISTIC ENERGY 85 4.8 ENERGY 87 4.9 POTENTIAL ENERGY AND CONSERVATION OF ENERGY 88 4.7 KINETIC 86 4.10 EXPERIMENTAL ‘VERIFICATION OF EQUIVALENCE OF MASS AND ENERGY 89 MOMENTUM 89 4:12 R E S T M A S S (OF ilo F R O M E X P E R I M E N T 4.11 90 RELATIONSHIP 4.13 BETWEEN TRANSFORMATION ENERGY PROPERTIES AND OF ENERGY AND MOMENTUM 96 500 Appendix i! Element 51 Sb 52 Te 53 54 55 56 I Xe cs Ba 57 La 58 Ce 59 60 Pr Nd 61 Pm A - 116 117 118 119 120 122 124 121 123 120 122 123 124 125 126 128 130 127 124 126 128 129 130 131 132 134 136 133 130 132 134 135 136 137 138 138* 139 136 138 140 142 141 142 143 144* 145 146 148 150 147 N Atomic Mass - _ 66 67 68 69 70 72 74 70 72 68 70 71 72 73 74 76 78 74 70 72 74 75 76 77 78 80 82 78 74 76 78 79 80 81 82 81 82 78 80 82 84 82 82 83 84 85 86 88 90 86 115.901745 116.002958 117.901606 118.903313 119.902198 121.903441 123.905272 120.903816 122.904213 119.904023 121.903066 122.904277 123.902842 124.904418 125.903322 127.904426 129.906238 126.904470 123.90612 125.90429 127.90354 128.90478 129.90351 130.90509 131.90416 13390540 135.90722 132.90536 129.90625 131.90512 133.90461 134.90555 135.90430 136.90550 137.90500 137.90691 138.90614 135.90710 137.90583 139.90539 141.90914 14Cl.90760 141.90766 14:!.90978 143.91004 144.91254 14Li.91309 147.91687 149.92092 14t5.91511 Spin I ~(nuclear magnetons) - -0.99983 l/2 -1.04621 5/2 7/2 +3.3590 +2.547 l/2 -0.73585 l/2 -0.88715 5/‘2 +2.8091 l/2 -0.77686 3/2 +0.69066 7/2 +2.5789 3/2 +0.83718 3/2 +0.93654 712 +3.7071 +2.7781 512 +4.3 7/2 -1.064 7/2 -0.653 Appendix Z Element 62 Sm 63 Eu 64 Gd 65 66 Tb OY 67 68 HO Er 69 70 Tm Yb I 71 Lu 72 Hf 73 74 Ta w A 144 147* 148 149 150 152 154 151 153 152 154 155 156 157 158 160 159 156 158 160 161 162 163 164 165 162 164 166 167 168 170 169 168 170 171 172 173 174 176 175 176* 174 176 177 178 179 180 181 180 182 N 82 85 86 87 88 90 92 88 90 88 90 91 92 93 94 96 94 90 92 94 95 96 97 98 98 94 96 98 99 100 102 100 98 100 101 102 103 104 106 104 105 102 104 105 106 107 108 108 106 108 AtomicMass 143.91199 146.91487 147.91479 148.91718 149.91728 151.91976 lS3.92228 l!iO.91984 152.92124 1511.91979 1513.92093 15~4.92266 155.92218 156.92403 157.92418 159.92712 158.92539 155.92392 157.92445 159.92520 160.92695 161.92680 162.92876 163.92920 164.93042 161.92874 16.3.92929 16.5.93031 166.93206 1617.93238 16'?.93556 1613.93425 167.9342 169.93502 170.93643 17'1.93636 17:!.93806 173.93874 Spin I p(nuclear maqnetons) 712 -0.8 7/l 0.65 S/2 5/2 +3.465 +1.52 312 7/2 7,/2 l/2 l/2 +0.4930 5/2 -0.678 7/2 +2.23 712 +0.61 912 -0.47 712 +2.35 175.94268 174.94064 17S.94266 173.94036 17S.94157 176.94340 177.94388 17E1.94603 179.94682 180.94801 179.94700 181.94830 501 502 Appendix Z Element 7!5 Re 74 OS 77 Ir 78 Pt 79 80 Au b 81 TI 82 Pb 83 Bi A 183 184 186 185 187* 184 186 187 188 189 190 192 191 193 190* 192 194 195 196 198 197 196 198 199 200 201 202 204 203 205 206* 207* 208* 209* 210* 204 206 207 208 209 210* 211* 212* 214* 209 210* 211* 212* 213* 214* N Atomic Mass 109 182.95032 110 183.9!5103 112 185.9.5444 110 184.95306 112 186.95583 108 183.95275 110 185.95387 111 186.95583 112 187.95608 113 188.95830 114 189.95863 116 191.96145 114 190.96064 116 192.96301 112 189.95995 114 191.96115 116 193.96272 117 194.96481 118 195.96497 120 197.96790 118 196.96654 116 195.96582 118 197.96676 119 198.96828 120 199.96833 121 200.97031 122 201.9'7064 124 203.97349 122 202.972353 124 204.974442 125 205.976104 126 206.977450 127 207.982813 128 208.985296 129 209.990054 122 203.973044 124 205.974468 125 206.975903 126 207.976650 127 208.981082 128 209.984187 129 210.988742 130 211.991905 132 213.99977 126 208.980394 127 209.984121 128 210.987300 129 211.991279 130 212.994317 131 213.998686 Spin I ~(nuclearmagnetons) l/2 +0.117224 5,/2 5,/2 +3.1718 +3.2043 312 3/2 +0.16 +0.17 l/2 +0.60602 312 +0.74485 l/2 +0.502702 3/2 -0.556701 l/2 l/2 +1.61169 +1.62254 l/2 +0.5895 9/2 +4.0802 Appendix 503 Element a4 PO 85 At 86 Rn 87 Fr 88 Ra 89 AC 90 Th 91 Pa 92 U 93 94 95 NP Pu Am - A 209* 210* 211* 212* 213* 214' 215* 216* 218* 215* 216* 217* 218* 219* 220* 222* 221' 223* 223* 224* 225* 226* 228* 225* 227' 228* 227* 228* 229* 230* 231* 232* 231* 233* 234* 233' 234* 235* 238* 237* 240* 241' N 125 126 127 128 129 130 131 132 134 130 131 132 133 133 134 136 134 136 135 136 137 138 140 136 138 139 137 138 139 140 141 142 140 142 143 141 142 143 146 144 146 146 Atomic Mass 208.982426 209.982876 210.986657 211.988866 212.992825 213.995201 214.999423 216.001922 218.008930 214.998663 216.002411 217.004648 218.008607 219.009481 220.011401 222.017531 221.014183 223.019736 223.018501 2'24.02021 2'25.02352 2'26.02536 2'28.03114 2'25.02315 2t27.02775 2t28.03108 2Y27.02771 2t28.02875 2t29.03165 230.03309 231.03629 232.03812 231.03588 233.04013 234.04330 233.03952 234.04090 235.04392 238.05377 237.04806 240.05388 241.05671 Spin I ~(nuclearmagnetons) l/2 7/2 S/2 l-l.4 appendix SOME PHYSICAL CONSTANTS AND CONVERSIONS’ Table of physical constants S p e e d o f l i g h t , c = 9 x lO*m/sec P l a n c k ’ s c o n s t a n t , h = 6.626 x 10eZ4 j o u l e - s e c If = h,‘2r = 5 x 10e3” j o u l e - s e c Reciprocal of fine structure constant, /tr = /( e2/4rcohc) Gravitational constant, G = 6.67 x Bolltzmann lo-” c o n s t a n t , ks = 1.381 x 10 m23 = 137.04 nt-m2/kg2 joule/K A v o g a d r o ’ s n u m b e r , Ne =: 6.022 x 1023/mole Gas constant, R = Noks = j o u l e / K - m o l e = 9 c a l o r i e s / K - m o l e Electron: Charge, ) e / = 1.602 x lo-l9 c o u l o m b s ; M a s s , m, = x 110-3’ kg = 0.5 110 MeV; M a g n e t i c m o m e n t (Bohlr magneton:!, ps = eh/lm, = 9.273 x 1O-24 joule/(weber/m2:); C o m p t o n w a v e l e n g t h , X, = h/m.c = 2.426 x lo-l2 B o h r r a d i u s , a = 4*coli/m,e2 = 5.2917 x lo-” m; m; R y d b e r g c o n s t a n t , R, == % m,e4/hf:(4rQi)2 = 7 x lO’/m Pro’ton: Nuclear M a s s , mpmag~i~~,3 ;, ll~~~~:,9,= MeV = 1!:6.1 m , ; = := x lo- ioule/(weber/m2) I C o n s t a n t i n C o u l o m b ’ s l a w , l/( 47rti) = 8.987 x lo9 nt-m2/cou12 Stefan-Boltzmann constant a = 2r5k;/15c3h3 in black = 5.67 x 10 body radiation, -s watts/m2-K4 Table of conversions radian = 57.3 degrees; degree = 0.01745 radians almu = 6 x 10m2’kg = 931.48MeV eV = x lo-l9 i; i = x 1O’seV NeV = x 10-13i f e r m i = 10-l’ m A n g s t r o m = lo- lo m foot = 0.3048 m; m == 3.281 ft m i l e = k m ; k m = ml1 b u r n = 10m2*m2 d a y = 0 set year = x 107sec curie = 3.7 x lO”disintegrations,‘sec ’ IReference: N Taylor, W H Parker, D N Langenberg, Reviews of Modern Physics 41,375,(1969) 504 bibliography of Modern Physics, McGraw-Hill Book Company, New York, [l] B e i s e r , A C o n c e p t s 1967 [2] C h e w , G F , M American, Gell-Mann, February 1964, W A Rosenfeld, H “Strongly and Freeman Interacting Company, Reprint Particles,” Scientific 296 131 E i s b e r g , R F u n d a m e n t a l s o f M o d e r n P h y s i c s , J o h n W i l e y S o n s , I n c , N e w Y o r k , 1961 The A t o m i c N u c l e u s , M c G r a w - H i l l B o o k C o , N e w Y o r k , 5 [4] E v a n s , R [5] F e l l e r , W A n lnfroducfion to Probability T h e o r y (and Ifs Applicafions, 3rd Ed., John Wiley Sons, Inc., New York, 1968 T h i r t y Years That S h o o k P h y s i c s , the Story of t h e Q u a n t u m Theory, [6] G a m o w , G Doubleday 171 Company, Inc., Garden City, New York, 1965 Goble, A., and P Baker, Efemenfs of Modern Physics, Ronald Press Co., New York, 1962 [8] G o l d w o s s e r , E O p t i c s , W a v e s , A f o m s , a n d N u c l e i , W A B e n j a m i n , I n c , N e w Y o r k , 1965 191 Herzberg, G Atomic Specfrc ond Atomic Sfrucfure, Dover Publications, Inc., New York, 1944 [lo] K i t t e l , C I n t r o d u c t i o n t o S o l i d S t a t e P h y s i c s , r d E d , J o h n W i l e y & S o n s , I n c , New York, 1966 [l l] L e e , J F , F W S e a r s , a n d D T u r c o t t e , Sfofisfical T h e r m o d y n a m i c s , Addison- Wesley Publishing Company, Inc Reading, Moss., 1963 [12] Leighton, R B Principles of Modern Physics, McGraw-Hill Book Company, Inc., New York, 1959 [13] Pouling, L., and E B Wilson, fnfroducfion to IQuonfum Mechanics, McGraw-Hill Book Company, New York, 1’335 [14] R e i f , F F u n d a m e n t a l s o f Sfc~fisficaf o n d Jhermol Physics, McGraw-Hill Book Com- pany, Inc., New York, 1965 [15] R e s n i c k , R lntroducfion to Special Relativity, John Wiley Sons, Inc., New York, 1968 [16] Saxon, S Elementary Quantum Mechanics, Holden-Day, Inc., San Francisco, [17] T a y l o r , E F , a n d J A W h e e l e r , S p o c e f i m e P h y s i c s , W H Freemon San [ 181 Francisco, 1968 and Company, 1966 Tipler, P A Foundations of Modern Physics, Worth Publishers, Inc., New York, 1969 [19] W e i d n e r , R T , a n d R L S e l l s , E l e m e n t a r y M o d e r n P h y s i c s , Allyn Boston, and Bacon, Inc., 1960 5 index Absolute space, 53 Accelerators, Band, 364,366,367 402 conduction, 370 Acceptor, 373 valence, 370 Acoustic branch, 356 Band spectra, 246 Actinium series, 440 Barn, unit, 391 Alkali metals, 256 Barrier penletration, Alpha decay, 441 Boryon, theory, 443 Beta decay, 43 1,447 Alpha particle, 391 theory, 450 model, 425 scattering, 190, 443 467 Beta particle, 391 393 Binding energy amu, definitiorl, Angular momentum deuteron, 415 conservation, intrinsic, 230 hydrogen atom, 230 240 operator, impurity, 231,232,488 quantization, 218 373 nuclear, 422 per nucleon, 424 quantum number, 218, 232, 234, 244 spin, 240 Black body radiation, 328 Bloch theorem, 365 total, 233,243 Annihilation, 230 Bohr magneton, 237 123 Bohr model, hydrogen, 17 Anomalous Zeeman effect, 243 Bohr radius, 221 Antineutrino, 447, Antiparticle, 464 Boltzmann (constant, ks, 4, 289, 504 Antisymmetric 464 Boltzmann ‘distribution, 335 function, 258 Atomic mass Boltzmann ,factor, 238, 312 Bench-Bruevich experiment, 58 number, 409 Bond table, 495 covalent, 346 unit, ionic, 34t5 Atomic number, 401 metallic, 347 Average lifetime, 461 Bose-Einstein Average value, 20 Boson, 312 momentum, 296 Avogadro’s number, distribution, 335 Boundary conditions, 170, 192, 316 6,504 Azimuthal quantum number, 232, 235 Brackett series, 217 Bragg formula, 148 Bravois lattice, 341 Balmer formula, 15 Brillouin zone, 367 Balmer series, 217 Biicherer experiment, 83 507 Index c, speed of light, 43,504 Carbon based amu, beta, 447 fission, Carbon dating, 458 457 gamma, 454 Center of mass system, 220 Decay constant, 432 Charge independence, 417 Dee, 402 Classical statistical mechanics, 279 Degeneracy Collision, 43 eigenvolues, 226, 256 Complex numbers, statistics, 16, 336 Compound nucleus, 455 Density of states, 288 Compton effect, 119 Compton wavelength, 12:3, 504 Conduction band, 370 electron, Deuteron, 262 414 Diatomic molecule, 244 Conservation laws baryons, momentum, 295,316,318 Detailed balance, 305,314,321,335 Conductors, 370, 371 Configurations, energy, 299,321 Diffraction, 468 electron, 148 Dilation, time, 61 energy, 43,88 Dipole moment, magnetic leptons, 465 electron, 236 mass, 44 nuclei, 413 mass-energy, a8 Discrete medium, 349 momentum, 43,83 Disintegration constant, 431 strong interactions, 469 Dispersion relation, 6, 352 Constant potential, 169 Distribution Contraction, lengths, 64 function, Bose-Einstein, Conversion of units, 504 energy, Coordinate tronsformatic~ns 16 335 300 Fermi-Dirac, 315 Galilean, 51 ideal gas, 291 Lorentz, 65 Maxwell-Boltzmann, ICorrespondence principle, 47 momentum, quantum theory, 207 291 295,299 phase space, 285 (Coulomb barrier, 443 Donor, (Coupling, S 1, 241 Doppler effect, 100 ICovalent binding, 346 Double-slit ‘Cross-section differential, 397 total, e, electron charge, 504 Effective mass, 368 Crystal binding force, 346 Eigenfunction, Crystal classification, 341 158, 162 Eigenvalue, 158 Curie, unit, 504 Einstein photoelectric equation, 17 402 Electrostatic D state, 255 Coulomb potential, Electron Daughter nucleus, 433 Davisson-Germer 130 Dulong-Petit law, 302, 361 387 Cyclotron, diffraction, Duane-Hunt law, 115 388 Rutherford, 373 experirnent, De Broglie relations, 145 charge, 504 146 magnetic moment, 504 mass, 504 De Broglie wave, 141,218 Electron capture, 453 De Broglie wavelength, ;!I Electron Decay Electron diffraction, 148, 151 alpha, 441 configuration, 262 Electronic specific heat, 324 424,443 Index Electron lepton number, 465 Electron-positron pair, 123 Electrons in metals, 323 Fermion, 3’12 Fermi, unit, 384 Fine structure Electron spin, 240 constant, 219, 504 Electron volt, splitting, Elementary particles, 16 x-ray, Elements, periodic table, 266 Emission stimulated, Fractional error, 26 332 Endothermic reaction, 456 Energy Frequency, energy relation, 13 Frequency, wave vector transformation, 139 Fusion, nucllear, conservation, 43,88 frequency relation, photon, 113 kinetic, 87 lattice vibrations, 357, 359 mass relation, 87 momentum relationship, 90 momentum transformation, 97 operator, 164,482 band, Gamma decay, Gamma rays, Gaussian distribution, 34 Gaussian packet free-particle, 179 Energy eigenfunction, 158 302 Energy level, 194 Energy level diagram, 195 Energy, probability function, 280, 300 Energy quantization, 193 Equal a priori probabilities, 12 Equiportition of energy, 302 Errors repeated experiments, 28 rms, 25 Exclusion principle, 254, 258 and statistics, 313 h, Planck’s constant, 1 1, 13, 15, 13 1, 150 ti, , Hadron, 467 Half-life, 433 Hall effect, 373 Halogens, 265 Hard sphere scattering, 389 Harmonic oscillator average energy, 302 distributi’on function, 301 energy eigenvalues, 198 quantum, 196 Heat capacity Exothermic reaction, 456 electron gas, 325 Expectation value, 20,32 lattice, 302, 364 energy, 164 distribution, 35 momentum, 160 Heisenberg uncertainty principle, 152, 154 Helium, liquid, 321, 336 Hole, 371 Experimental error, 24,28 Hydrogen Exponential function, Extrinsic semiconductor, 373 F state, 255 Bohr model, 217 energy levels, 15, 226 ortho-, pow-, distribution, rule, 447 Group speed, 6, 141 Energy density of states, 300, 32 equipartition, 436,454 123,436 Ground state, 194, 197, 16, 260 364,365 Energy, binding, 230 Fermi-Dirac transformations, 51 velocity, 52 Geiger-Nuitall rest, 86 gaussian Golilean 457 harmonic oscillator, 205 rdlativistic, 86 Energy Fission, nuclear, 457 Flux, particle, 386 spontaneous, 331 Energy 240 272 315 Fermi energy, 315,322,324 275 Schrb;dinger equation, 222 wavefunctions, 226 509 510 Index Hlyperchorge, 470 Lorentz force, isotopic spin plot, 473 Lorentz Ideal gos energy-momentum, distribution function, 291 wove vector, 139 in gravitational field, 294 Lyman series, 217 Impact porometer, 394 Impurities in semiconductors, 373 Incident flux, 386 Indistinguishability of particles, 256 Inert gases, 263 Inertial frame, 48 system, 48 IInsulator, 371 IInterferometer, hnternol Michelson, 54 conversion, 454 IIntrinsic semiconductor, 373 Inversion symmetry, 344 Itonic binding, 346 fonizotion energy, 230 Isomer, 436,454 Isotope, 411 j, angular momentum quantum number, 243 k:s, Boftzmann constant, 4, 289 li:, wave number, K, x-ray line, 271 Kinetic energy, 87 168,222,483 K meson, 467 ,e, angular momentum quantum number, 234,235 Lambda particle, 90, 468 Laser, 333 Lattice specific heat, 364 ILattice vector, 341 vibrations, 351 energy, 357 quantizotion, ltepton, moment, 360 polynomials, 234 464 Linear accelerator, 403 Linear chain of atoms, 350,354 Liquid drop model, 421 Longitudinal Doppler effect, 102 236,413 Bohr, 237 nuclear, 413 Moss conservation, 44 MOSS effective, 368 relatiwstic, 83 rest, 83 Moss-energy conservation, 87 Moss, atomic, 409 Moss number, 409 distribution, verification, 288 298 ideal gas, 291 Mesons, 419,466 Meson theory of Yukawa, 418 Metallic binding, 347 MeV, MeV/c, Michelson K capture, 453 ILegendre Magnetic Magneto” experimental Isotopic Spin, 469 ILattice Magic number, 425 Maxwell-Boltzmonn Isotone, 411 operator, 96 velocity, 71 energy, 288 IInertial transformations coordinate, 65 interferometer, Michelson-Morley Miller-Kusch 54 experiment, experiment, 54 296 Minimum uncertainty, 181, 197 MKS units, Molecular rotation, 244 Momentum conservation, 43 energy relationship, 90 energy transformation, operator, 98 162 relativistic, 83 Momentum density of states, 295 Momentum distribution function, 295, 299 Momentum eigenfunction, 159 Mosely low, 271 Most probable value energy, 300 momentum, mm, 218,232,235 296,299 Index Mu meson, 63, 383, 464 Particle accelerators, 402 Muon, 464 Particles, elementary, 464 Mvonic lepton number, 465 Particle in a box, 190, 13 n, principal qvontvm number, 226, 235 n-type semiconductor, 373 Natural Pfvnd serie’s, 464 410,411, 54 Nondegenerate statistics, 316, 336 Non-inertial system, 49 35 193, 204 Nuclear binding energy, 422 Nuclear fission, 457 Nuclear forces, 416,418 Nuclear fusion, 457 Nuclear magnetic moment, 413 Nuclear magneton, 413 Nuclear masses, 409 Nuclear models, 421 Nuclear radius, 384, 394 Nuclear reactions, 454 Nuclear spin, 413 Phase, wave, 136, 138 Phonon, 361 Photodisintegration, 415 Photon,5,ll12,113,116,119 distribution, 328 Pi meson, 19,467 Planck energy-frequency relation, 13 Planck rod&ion formula, 329 Planck’s constant, 11, 113, 115, 13 1,504 Positron, 124, 464 Postulates of relativity, 55 Potential energy, 88 Primitive laitice vector, 341 Probability, 11 amplitude, 130, 157 density, 30 distribvtison function, 16 Nucleon, 41 conservation, 284, 450 Photoelectric effect, 15 Normal Zeeman effect, 239 21, 448 Nvclide, 427, 431 equal a priori, 12 products of, 14 sums of, ‘I Number of modes Probability, bond, 367 wavefunction, sound, 354,356 156 mass, 504 Proton-protean cycle, 457 band, 367 Principal quantum number, 226, 235 shell, 256 Principle Optical branch, 356 exclusion,, 254, 258 Orbital angular momentum, 231, 232, 233 relativity, Orthogonolity, superposition, 491 273 56 130, 163 uncertainty, 152, 154 Products of probability, 14 P state, 255 p-type semiconductor, 373 Q, reaction energy, 441 Pair annilhilation, Quanta, 11 I 126 Pair production, 123 Parahydrogen, 130, Proton, 411,467 Number of states Orthohydrogen, 273 Parent nucleus, 433 366 Phase speed, 6, 137, 141 Newton’s laws of motion, 42,53, Normalization, 316,353, volume element, 286, 287 467 distribution, conditions, 217 Phase spacte, Neutron number, 41 Normal boundary Periodic table, 266 flux, 458 Neutron, Pavli exclusion principle, 254, 258 Periodic radioactivity, 431 Neptunium series, 438 Nevtrino, Paschen series, 217 Qvantization Bohr model, 218 lattice vibrations, 360 51 512 I n d e x Quantum mechanics, 167 Scattering, Quantum theory of radiation, 329 Quark, 474 Rutherford, Schrodinger R, gas constant, 302, 504 examples, Radial momentum operator, 224 Semiconductor, 371 Radioactive decay Shell model, 425 laws, 432,433 Sigma particle, 468 table, 437 Simple harmonic oscillator Radioactive series, 436 average energy, 302 Radius distribution function, 301 Bohr, 221 energy eigenvalues, 198 nucleur, , Rayleigh-Jeans radiation formula, 329 Redshift, 103 Sound Reflection plane, 344 347,349 solid lattice, 302, 362 Spectral series, 17 Lorentz, 65 Speed time, 60 group, 6, 141 transverse length, 60 phase, 6, 141 velocity, 71 Speed of light, 43,504 kinetic energy, 137 Spherical polar coordinates, 222, 23 1,483 Relativistic mass, 83 Spin, 240, 24 Relativistic mechanics, 85 Spin magnetic quantum number, 240 Relativistic momentum, 88 Spin orbit interaction, 241 Relativistic postulates, 57 Spontoneous emission, 33 Relativistic wave equation, 169 Spreading of packet, 182 Rest energy, 87 Square potential barrier, 188 Rigid rotator, 244 Root mean square deviation, 24 Rotation axis, 342 Rotational quantum number, 244 Rotational spectrum, 245 symmetry, Stationary state, 195,213 Statistical mechanics, 279, 312 Stern-Gerloch constant, 504 experiment, 242 Stimulated emission, 332 397 Stirling Rutherford scattering, 393 215,219, formula, 35 Strangeness quantum number, 470 394 s, electron spin, 240 Standing wave, 192 Step potential, 183, 187 atomic model, 393 constant, Stability line, 447 Stefan-Boltzmann 342 Rutherford 5; state, 255 waves, electron gas, 325 transformations longitudinal length, 64 Rydberg 153 Specific heat Reflection symmetry, 344 theory, 67 diffraction, Solid state, 341 Reflection coefficient, 186 cross-section, quantum, 196 Simultaneity, Single-slit Reduced mass, 220 Rotational 178 Selection rule, 239, 244 Radioactive carbon dating, 458 R’elativistic 396 equation, 166, 167 hydrogen, 222 Radiation, black body, 329 Relativistic 385 Scattering angle, 387 221,504 Sums of angular momenta, 242 Sums of probabilities, 13 Superposition, 130, 163 of lattice modes, 359 Index Surface energy, nuclear, 423 Symmetric function, 258 Symmetries of crystals, 341 Temperature, 280 Thermal equilibrium, 280 Thorium series, 437 Threshold energy, 125,415,456 Time dilation, 61 Time reversal, 305 phase, 68, 141 Velocity transformations, 52, 71 Vibration, lattice, 349 Volume energy, nuclear, 423 Volume element energy, ,300 momentum space, 295 phase space, 287 Van Laue diffraction, 149 Transformation Wave equation, sound Galilean, 51 Lorentz, group, 6, 141 65 continuous medium, 349 Transition probability, 314 Transitions, 214 discrete Imedium, Wavefunction, Translational symmetry, 341 Transmission coefficient, 187 350 130 free pariicle, 159 hydrogen, 226 Transverse Doppler effect, 101 Wavelength, Tunneling, Wave mechanics, 167 188,443 Uncertainty, minimum, 181, 197 Uncertainty principle energy-time, 152 light waves, 127, 128 momentum, position, 154 Wave packets, 179,205 Wave vector, frequency transformation, 140 Weak interaction, 465 Work function, 16, 326 Work, relativistic, 86 Xi particle, 468 Unit cell, 341 X rays, 14, 270 Units, conversion, 504 Universal gas constant, R, 302, 504 Uranium series, 439 Young’s momdulus, 348 Yukawa force, 421 Zeeman effect, 236 Valence band, 370 anomalous, Valence crystal, 346 normal, 239 Van der Waals Velocity force, 347 243 Zero point energy, 197, 206 Zero rest mass particle, 11 ... 474 477 478 479 483 491 496 504 505 507 principles of modern physics introduction I HISTORICAL SURVEY The term modern physics generally refers to the study