APPENDIX AA Useful Information

Just as you need to know your name and address and telephone number and e-mail address to locate yourself in the world, so must you know some basic information to locate yourself in physics. Like competent profession- als in any field, a practicing physicist carries a large amount of factual baggage. Starting out in physics you will need only the small backpack of facts presented in Tables A.1 and A.3. Then there is information that you need occasionally. Some of that is collected here for your convenience. If you don’t find what you want here or in the text, try the library. Ask a reference librarian to help you find what you want to know, or look in the Handbook of Chemistry and Physics. You can also use the World Wide Web to find constants: http://physics.nist.gov/cuu/Constants/index.html will supply you the very latest, most precise values from NIST (National Institute of Standards and Technology).

A.1 SI PREFIXES

You need to know the SI prefixes. They tell you the order of magnitude of the units of whatever physical quantity they are attached to. It is absolutely essential that you know them. They are widely used, and when you are wrong about them, you make mistakes of factors of thousands! Maybe you can absorb them by os- mosis as you use them; maybe you need to get them by heart by the purest of rote learning; maybe you can come up with a clever mnemonic;

633 634 APPENDIX A. USEFUL INFORMATION

TABLE A.1 SI prefixes Factor Prefix Symbol Factor Prefix Symbol 1018 exa E 10−1 deci d 1015 peta P 10−2 centi c 1012 tera T 10−3 milli m 109 giga G 10−6 micro μ 106 mega M 10−9 nano n 103 kilo k 10−12 pico p 102 hecto h 10−15 femto f 101 deka da 10−18 atto a

maybe (and this would be best) you can learn them attached to particular physical situations and quantities, as suggested in Chap. 2. However you do it, learn them! They are listed in Table A.1.

A.2 BASIC PHYSICAL CONSTANTS

You need to know some basic physical constants. These set the scale of the phenomena of the physical world. Which ones are most important depends on the physical situation under consideration. In this book, with its emphasis on atoms and their parts, the elementary charge; the masses of the electron, the proton, and the neutron; and the values of the Planck and Boltzmann constants are very important. When you deal with macroscopic quantities of atoms in the laboratory, Avogadro’s number and Earth’s gravity are important. For convenient reference Table A.2 lists the official values of these constants in SI units. Table A.3 lists the ones you need to know in the units in which you need to know them.

A.3 CONSTANTS THAT YOU MUST KNOW

You need to be able to calculate quickly and easily with these constants. For this purpose, you need the constants expressed as much as possible in terms of units chosen to match the natural scale of atoms. Electron volts (eV) and nanometers (nm) are convenient for atoms, while megaelectron volts (MeV) and femtometers (fm) are a good choice for nuclei. It is also often simpler to work with masses in units of eV/c2. A.3 CONSTANTS THAT YOU MUST KNOW 635

TABLE A.2 Basic physical constants Name of constant Symbol Value −27 Atomic mass unit mu or u 1.661 × 10 kg 23 −1 Avogadro constant NA 6.022 × 10 mol −11 Bohr radius a0 5.292 × 10 m −23 −1 Boltzmann constant kB 1.381 × 10 J·K 8.617 × 10−5 eV·K−1 Charge-to-mass ratio of electron e/m −1.759 × 1011 C·kg−1 9 2 −2 Coulomb constant kc or 8.988 × 10 N·m ·C 1 4π0 −31 Electron mass me 9.109 × 10 kg Elementary charge e 1.602 × 10−19 C Faraday constant F 96485 C·mol−1 Intensity of Earth’s gravitational field g 9.82 N·kg−1 (m·s−2) Molar gas constant R 8.314 J·mol−1·K−1 −27 Neutron mass mn 1.675 × 10 kg Planck constant h 6.626 × 10−34 J·s 4.136 × 10−15 eV·s h × −34 · ¯h = 2π 1.055 10 J s 6.582 × 10−16 eV·s −27 Proton mass mp 1.673 × 10 kg 7 −1 Rydberg constant R∞ 1.09737 × 10 m Speed of light c 2.99792458 × 108 m·s−1

Table A.3 gives constants, combinations of constants, and masses in terms of these more convenient units. The combinations simplify calculations of energies, wavelengths, and frequencies that are frequently made in this course. The Remark column tells you when the constant is one that you absolutely need to know. No kidding! These constants are of fundamental importance. One goal of this book is to show how the constants interrelate and how they specify the scale of observed effects and phenomena. They specify the scales and magnitudes 636 APPENDIX A. USEFUL INFORMATION

TABLE A.3 Constants in convenient energy units Name Symbol Value Remark Planck constant h 4.14 × 10−15 eV·s hc 1240 eV·nm know this one! Reduced Planck h × −16 · constant: 2π ¯h 6.58 10 eV s ¯hc 197 eV·nm know as ≈ 200 eV nm ¯hc 197 MeV·fm know as ≈ 200 MeV fm 2 Coulomb force kce 1.44 eV·nm know this numerator

Thermal energy

at T = 300 K kBT 0.0259 eV remember as ≈ 1/40 eV h¯2 0 2 Bohr radius a = ke me 0.0529 nm ke2 Fine structure α = hc¯ 1/137.036 no units constant

Rydberg energy hcR∞ 13.61 eV know this one 2 Electron mass mec 511 keV know this 2 Proton mass mpc 938.3 MeV know ≈ 938 MeV 2 Neutron mass mnc 939.6 MeV know mn is 1.29 MeV >mp 2 Atomic mass unit u 931.50 MeV/c remember 1 u ≈ mp Speed of light c 3 × 108 m·s−1 know this Elementary charge e 1.6 × 10−19 C know this

of the quantities with which physicists have built a consistent and in- formative picture of the microphysical world and its connection to the macrophysical world where we live and do physics.

A.4 MISCELLANEOUS

Table A.4 contains some constants used occasionally in this course, including constants having to do with Earth, Moon, and Sun. Table A.5 gives conversion factors between some especially common English units and their metric equivalents. A.5 NAMES OF SOME SI DERIVED UNITS 637

TABLE A.4 Miscellaneous occasionally used constants Name Symbol Value Units Remarks 24 Earth’s mass M⊕ 6 × 10 kg 10 moles of kilograms 11 Earth–Sun distance RES 1.5 × 10 m 1 A.U. 6 Earth radius R⊕ 6.366 × 10 m2πR⊕ =40Mm 8 Earth–Moon distance REM 3.82 × 10 m60R⊕

Moon’s mass M) 0.01234 M⊕ M⊕/81 30 Sun’s mass M 2 × 10 kg 333 000 M⊕ Viscosity of air η 18.3 μPa·sat20◦C −1 ◦ Speed of sound in air vs 343 m s at 20 C

TABLE A.5 Some conversion factors between english and metric units English English metric 1in 2.54cm 1 ft 12 in 30.48 cm 1 mile 5280 ft 1609.3 m 3.28 ft 1 m 0.396 in 1 cm 1 mph 1.467 ft/s 0.447 m/s 0.621 mph 0.911 ft/s 1 km/hr 2.24 mph 3.28 ft/s 1 m/s 1 lb 16 oz 453.5 g 1 oz 28.3 g 2.205 lb 1 kg

A.5 NAMES OF SOME SI DERIVED UNITS

Table A.6 lists some names of composite SI units. There are also a num- ber of non-SI units that are still in use because because they are deeply embedded in engineering practice or every day life (because many peo- ple are unwilling to change their habits of thought). Table A.6 lists some of these non-SI units along with their abbreviations and their SI equiva- lents. The entries in the table are in alphabetical order according to their abbreviations. 638 APPENDIX A. USEFUL INFORMATION

TABLE A.6 Commonly used units and abbreviations quantity Name Abbrev. SI units current ampere A A length Angstrom A10˚ −10 m pressure atmosphere atm 101.3 kPa area barn b 10−24 m2 pressure bar bar 100 kPa energy calorie cal 4.1858 J electric charge coulomb C A·s viscosity centipoise cp 10−3 Pa·s energy electron volt eV 1.602 × 10−19 J magnetic field gauss G 10−4 T frequency hertz Hz s−1 energy joule J kg·m2·s−2 =N·m temperature kelvin K K mass kilogram kg kg volume liter L 10−3 m3 length meter m m pressure millimeters of mercury mm Hg 133.32 Pa volume cubic meter m3 m3 amount mole mol mol force newton N kg·m·s−2 electric field newton per coulomb N·C−1 N·C−1 pressure pascal Pa N·m−2 viscosity pascal seconds Pa·s angle radian rad rad time second s s magnetic field tesla T kg·s−1·C−1 pressure torr torr 133.32 Pa mass atomic mass unit u 1.6605 × 10−27 kg electric potential volt V J·C−1 electric field volts per meter V·m−1 N·C−1 power watt W J·s−1 angle degree ◦ 1.7453 × 10−2 rad A.6 SI BASE UNITS 639

TABLE A.7 SI base units Name Symbol Definition meter m The meter is the length of path traveled by light in vacuum during a time interval of 1/299 792 458 of a second. mass kg The kilogram is the unit of mass. It is equal to the mass of the international prototype of the kilogram. (The international prototype is a platinum–iridium cylinder kept at the BIPM in S`evres (Paris) France.) second s The second is the duration of 9 192 631 770 periods of the radi- ation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom. ampere A The ampere is that constant current that if maintained in two straight parallel conductors of infinite length, of negligible cir- cular cross section, and placed 1 meter apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per meter of length. kelvin K The kelvin is the unit of thermodynamic temperature. It is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water. (The Celsius temperature scale is defined by the equation t = T − T0,whereT is the thermodynamic temperature in kelvins and T0 = 273.15 K.) mole mol The mole is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kg of carbon-12. candela cd The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian.

A.6 SI BASE UNITS

There are seven units that form the basis of the SI. In this book we use six of them. Table A.7, which gives their names, symbols, and definitions, is provided here just for your general information. You will find it more useful and informative to remember the looser definitions that are given in the chapters where they are introduced. 640 APPENDIX A. USEFUL INFORMATION

TABLE A.8 Some chemical atomic masses Element Symbol Z Mass Phase Density (u) (g cm−3)

hydrogen H 1 1.00797 gas H2 helium He 2 4.0026 gas He lithium Li 3 6.939 solid 0.534 beryllium Be 4 9.0122 solid Be 1.848 boron B 5 10.811 crystalline B 2.34 carbon C 6 12.01115 amorphous C ≈ 2.0

nitrogen N 7 14.0067 gas N2

oxygen O 8 15.9994 gas O2

fluorine F 9 18.9984 gas F2 aluminum Al 13 26.981538 solid 2.6989 silicon Si 14 28.0855 solid 2.33 iron Fe 26 55.844 solid 7.874 cobalt Co 27 58.93320 solid 8.9 nickel Ni 28 58.69 solid 8.902 copper Cu 29 63.546 solid 8.96 zinc Zn 30 65.40 solid 7.133 tantalum Ta 73 180.9479 solid 16.6 silver Ag 47 107.8681 solid 10.5 gold Au 79 196.96654 solid 19.32 lead Pb 82 207.2 solid 11.35 uranium U 92 232.0289 solid 18.95

A.7 ATOMIC MASSES

Table A.8 lists some useful chemical atomic masses and densities of el- ements that are solids at room temperature. If you need to know the density of any gaseous element, you can calculate it. There is a periodic table on p. 643. A.8 MASSES OF NUCLIDES 641

TABLE A.9 Masses of some Nuclides Name of Symbol Z Nuclide Mass % Natural Half-life Nuclide (u) Abundance hydrogen 1H 1 1.007825 99.985 deuterium 2H or D 1 2.01410 0.015 tritium 3H or T 1 3.016050 12.26 y helium-3 3He 2 3.016030 0.00013 helium-4 4He 2 4.002603 100.0 lithium-6 6Li 3 6.015125 7.42 lithium-7 7Li 3 7.016004 92.58 beryllium-9 9Be 4 9.012186 100. boron-10 10B 5 10.012939 19.78 boron-11 11B 5 11.009305 80.22 carbon-12 12C 6 12.000000 98.89 carbon-13 13C 6 13.003354 1.11 carbon-14 14C 6 14.003242 5730 y nitrogen-14 14N 7 14.003074 99.63 nitrogen-15 15N 7 15.010599 0.37 oxygen-16 16O 8 15.994915 99.759 oxygen-17 17O 8 16.999133 0.037 oxygen-18 18O 8 17.999160 0.204 fluorine-19 19F 9 18.998405 100.0

A.8 MASSES OF NUCLIDES

For determining how nuclei will behave, the difference between masses of atoms may be important. When this is the case, you need to know the individual atomic masses quite precisely. Table A.9 lists some of the more important elements and their nuclides and their masses. 642 APPENDIX A. USEFUL INFORMATION

A.9 PERIODIC TABLE OF THE CHEMICAL ELEMENTS

The periodic table of the elements is the basic map of the material world. Since Moseley’s work made clear the structure of the table, chemists and physicists have used it as a guide for searching for new elements. The table succinctly shows which elements are likely to have analogous chemical properties, and it provides practical help for making and understanding new chemical compounds. A.9 PERIODIC TABLE OF THE CHEMICAL ELEMENTS 643 , 293 948 798 180 . . . . 2 0026 . 36 54 18 neon 10 86 [222] [297] argon Ar Kr radon Xe xenon He Ne Rn helium 4 39 83 20 118 krypton 131 Uuo Pure Appl. Chem. ununoctium 904 453 904 998 . . I . . 9 F 17 Cl 35 53 85 [210] [294] Br At iodine 35 79 18 117 fluorine chlorine astatine 126 bromine Uus ununseptium 60 96 . 054 065 999 . . . . 8 S O 16 34 52 84 Se [209] [293] Te 70 sulfur [259] 78 Po 32 No 127 15 Yb oxygen 116 102 173 selenium tellurium Uuh polonium nobelium ytterbium ununhexium 760 980 934 974 921 007 ...... 7 P N 15 Bi 33 51 83 [289] 69 Sb [258] As 30 74 14 arsenic 115 101 Md Tm 121 208 bismuth thulium nitrogen 168 Uup antimony phosphorus ununpentium mendelevium alone.pl?ele=&ascii=html&isotype=some. 2 . 710 64 259 086 011 . . . . . 6 tin C Si lead 14 32 50 82 [289] 68 Sn [257] 72 207 Er silicon Ge Pb 28 12 carbon 114 erbium Fm 100 118 167 fermium Uuq erl and Michael Berglund, germanium ununquadium 818 383 930 982 723 811 ...... 5 B 13 In Al Tl 31 49 81 [286] 67 99 [252] Es boron Ga 26 69 Ho 10 indium gallium 113 114 204 thallium Uut 164 holmium aluminum ununtrium einsteinium 59 411 38 . 500 . . . zinc 30 48 80 [285] 66 98 Cf 65 [251] Zn Cd Hg Cn Dy 200 112 112 mercury 162 cadmium californium dysprosium copernicium 868 967 925 546 . . . . gold 29 47 79 [272] silver 65 97 [247] Ag Rg Cu Au Bk Tb copper 63 111 107 196 terbium 158 berkelium roentgenium 42 08 25 . . . 693 . 28 46 78 [281] Ni Pt 64 96 [247] nickel Ds Pd 58 106 195 Gd 110 157 curium Cm platinum palladium gadolinium darmstadtium ta are from Michael E. Wies 906 217 964 933 . . . . Ir 27 45 77 [268] 63 95 [243] Co cobalt Rh Eu Mt 58 iridium 109 102 192 Am rhodium 151 europium americium meitnerium 07 23 36 . . . 485 . iron 26 Fe 44 76 [277] 62 94 Os [244] Hs Ru Pu 55 101 190 108 Sm 150 osmium hassium ruthenium samarium plutonium 207 938 . . [98] 25 43 75 [264] Tc 61 93 [145] [237] Re Bh 54 Np Mn 107 Pm 186 rhenium bohrium manganese technetium neptunium promethium ements as of 2010. Da 84 96 . 242 029 996 . . . . U 24 42 74 [266] W Sg Cr 95 60 92 51 183 Mo Nd 106 144 238 tungsten uranium chromium seaborgium neodymium molybdenum 948 908 036 942 906 . . . . . V 23 41 73 [262] Ta 59 91 Pr Pa Nb Db 50 92 105 niobium 180 140 231 dubnium tantalum vanadium protactinium praseodymium 49 . 116 038 867 224 . . . . Ti 22 40 Zr 72 [261] Rf Hf 58 90 Ce 47 91 178 Th 104 cerium hafnium titanium thorium 140 232 zirconium rutherfordium 967 905 956 906 . . . . Y 21 Sc 39 71 Lr [262] 57 89 Lu [227] La Ac 44 88 103 yttrium 174 lutetium 138 scandium actinium lawrencium lanthanum PERIODIC TABLE OF THE CHEMICAL ELEMENTS * ** (11), 21312156 (2009) and from http://physics.nist.gov/cgi-bin/Compositions/ stand 57-70 89-102 81 From top to bottomelements in that each box do are not the occur element in name, nature its the atomic atomic number, mass its of atomic the symbol, longest and its lived atomic isotope weight. is For given radioactive in square brackets. . Periodic table of the chemical el Actinide series 327 62 078 . 305 . 012 . . 4 . Sr 56 88 20 38 12 [226] 87 9 Lanthanide series Be Ba Ca Ra ∗∗ 40 24 barium radium Mg calcium 137 beryllium ∗ strontium magnesium 905 098 468 990 . 941 . . . 3 1 0079 . K H Li . Fr 55 87 19 37 11 [223] Cs 6 Na Rb 39 85 22 1 cesium lithium sodium 132 francium rubidium hydrogen potassium Index

A, see logic, 612 amplitude probability, 578 Absolute zero, 102 amplitude of a wave, 324 absorption spectrum, 529 angle, 26 activity, 481 degrees, 26, 28 and radioactive decay, 489 arc seconds, 28 radioactivity, 481 minutes, 28 standards of, 483 seconds, 28 units sexagesimal system, 28 curie (Ci), 488 radians, 26, 29 SI: becquerel (Bq), 488 rays, 27 age and death small-angle approximation, 30, 32 of nuclei, 492 subtend, 27 radioactive decay, 492 vertex, 27 of people, 493 angstrom, see length of stars, 493 angular momentum, 524 alpha particles quantization of, 517, 524 are helium ions, 483 anions, 230 radioactive radiations, 483 anode, 230 scattering, 494 antiproton, 399 apparatus of Geiger and approximations Marsden, 497 by binomial expansion, 344 from atoms, 494 mathematical tool for, 340 alpha rays non-relativistic, see non-relativistic alpha particles, 509 approximations radioactive radiations, 483 of binomial functions, 344 AM radio frequencies, 289 small-angle, 346 American adults straight-line, 341 heights, 21 atom of charge, see electron, masses, 21 elementary charge

645 646 INDEX

atomic collisions effective collision cross section, 123 collision mean free path, 122 hard-sphere model, 110 atomic hypothesis, 9 mean free path, 122, 131 atomic mass unit, 71 mean square velocity, 112, 114 in MeV/c2, 391 number density, 113 atomic masses, 640 at STP, 113 atomic nucleus, 501, 509 pressure, 110 discovery from radioactivity, 509 root mean square velocity, 114 nucleus, 501 viscosity, 131 atomic number Z, 502, 507, 509 average nucleus computation of, 135 electric charge of, 502 of a distribution, 139, 140 atomic spectroscopy, 318 average force, 43 atomic spectrum, 319 Avogadro’s constant, 75 atomic weights, 70 atomic masses, 76 chemical scale Avogadro’s number, 252 of some elements, 73 sizes of atoms, 76 isotopes, see isotopes Avogadro’s number, 75 atoms, 5 Avogadro’s principle, 70 absorption of photons by, 529 Avogadro, Amadeo, 69 diffraction of, 467 diatomic molecules, 69 early history, 63 electrical nature, 229 emission of photons by, 522 Babinet’s principle, 323 energy levels in, 529 backscatter peak, 445, see scintillation energy levels of, 524 counter energy states of, 522, 524, 526 Bainbridge apparatus, see energy transitions in, 527 charge-to-mass ratio, electron evidence for, 64 Bainbridge, K. T., 209 hard-sphere, 5, 135 Balmer series, see hydrogen atom integers, 64 Balmer,J.J.,519 internal structure deduced from bandwidth, 585 emitted light, 309, 518 Barkla, Charles (1877–1944) made of + and − charges, 6 characteristic x-rays, 537 mass of, 76 barometer equation, 86 not well localized, 7 battery, 272 nuclear model, 6, 503 beam splitter, 572 nuclei of, 501 polarizing, 615 shell structure of, 542 beam-splitting polarizer, 614 size, 133 Becquerel, Henri, 479 sizes, 5, 21 discovers radioactivity, 421, 479 spectra of, 325 experiments on radioactivity, 480 transmutation of, 485 measures e/m of radioactive atoms of gases radiations, 481 average force, 110, 111 Bell’s inequalities, 598 average kinetic energy, 134 Bell, John (1928–1990), 598 at room temperature, 118 Bertsch, G. F., 515 average square speed, 112 Berzelius, Jons, 69 INDEX 647 beta rays, 509 of hydrogen atom, 234 radioactive radiations, 483 of proton, 234 binomial expansion, 344 Charles’ Law binomial function, 344 see Gay-Lussac’s Law, 89, 100 bins, see distribution Chart of the Nuclides, 509, 512 bins of a distribution, 137 circuit velocity, 142 see electric circuit, 185 Bohr atom, see Bohr model circumference of a circle, 15 Bohr model, 517 coherence length, 584 and hydrogen-like ions, 535 coherence time, 584 and x-ray lines, 542 coincidence counting, 572 energy states, 525 collision mean free path first Bohr-orbit radius, 525 seemeanfreepath,122 limitations of, 545 collisional mean free path three assumptions, 544 seemeanfreepath,122 Bohr radius, see Bohr model color, see light, wavelength Bohr, Niels (1885–1962), 517 common, see electric ground Boltzmann’s constant, 117 Compton edge, 445, see scintillation Boyle’s law, 91 detector, 445 Boyle, Sir Robert, 89 Compton effect, 401, 435, 438, 447 experiment on gases, 89 data, 438 Brackett series, see hydrogen atom, frequency shift in, 441 spectrum wavelength shift in, 443 Bragg Law, 426 Compton scattering, 436, 438, 553 Bragg law of crystal diffraction, see equation for, 442 Bragg law of x-ray reflection Compton, A. H., 435 Bragg spectrometer, 432 conductor, see electrical conductor Bragg, W. H., 406, 425 conservation of energy, 47, 49 Bragg, W. L., 425 conversion of gravitational buoyancy force, 107 potential energy into kinetic energy, 51 conservation of momentum, 40 Cathode, 230 constants of physics, 634 cathode rays from NIST on the Web, 633 electrons, 236 that you must know, 634 cations, 230 Coolidge tube, 422, see x-rays, Celsius temperature scale, 95 production of Celsius, Anders, 95 correlations, 609 Chadwick, J. Coulomb’s law, 159 discovered the neutron, 507 force constant, 159 characteristic x-rays, 539, 542, 545 Coulomb, Charles Augustin, 157 characteristic x-rays crystal spectrometer, see x-rays, see x-rays, characteristic, 538 spectrometer charge-to-mass ratio crystals of electron lattice spacings of common, 431, Bainbridge method, 240 460 significance of, 242 Miller indices, 459, 461 value, 241 ordered arrays of atoms, 424, 447 648 INDEX

rock salt lattice spacing, 430 deuteron, 512 spacing between atom planes in, mass of, 512 460 diffraction spacing between planes of atoms of atoms, 467 in, 429 of electrons, 458 curie of neutrons, 467 activity diffraction grating, 309, 325 units, 488 multi-slit interference, 316 Curie, Marie, 479, 482 principal maximum and radioactivity of thorium, 482 order number, 325 discovers polonium, 482 resolution, 317 discovers radium, 482 spectrometer, 318 Curie, Pierre, 479, 482 dimensions current, see electric current consistency, 26 cutoff of x-ray spectrum, see x-rays, discharge tube, 320 continuous spectrum disintegration constant, 489 cyclotron, 223 radioactive decay, 490 displacement in a wave, 324 Dalton, John, 65 distance of closest approach model of atom, 66 Rutherford scattering, 501 Davisson and Germer distribution, 137, 559 apparatus, 463 bins, 137, 559 verify wave nature of electrons, 463 histogram, 139 Davisson, C. J., 462 of velocities, 140, 141 Davy, Sir Humphrey, 65 standard deviation of, 560 de Broglie wavelength, 455 Doppler effect, 368 equation for, 469 red shift, 369 implies large energies to probe double-slit interference, 309, 325 small objects, 470 effect of single-slit diffraction on, implies particles are not sharply 315 localized, 471 maxima, 325 de Broglie, Louis, 455 of electrons, 465 Debye-Scherrer diffraction rings, 427, down converter, 572 see x-rays, powder diffraction, dynodes, see photomultiplier tube 446 decay constant, 489 Earth radioactive decay, 490 average density, 34 density, 17 circumference, 15, 21 Earth’s crust, 34 magnetic field, 201 iron, 34 mass, 21 mercury, 34 efficiency of a gas, 76 of a detector, 574 of some gases, 73 of coincidences, 574 water, 16, 34 efficiency of photon detector, 572 detector efficiency, 572, 574 Einstein, Albert, 339, 360 deuterium, 508, 641 Einstein, Podolsky, Rosen deuterium: mass-2 isotope of incompleteness of quantum hydrogen, 208 mechanics, 611 INDEX 649 electric charge, 152 electromagnetic radiation probing forces between, 154 atoms with, 285 negative, 154 electromagnetic spectrum, 317 neutral, 154 electromagnetic waves, 324 positive, 154 frequencies of, 288 units electron SI: coulomb (C), 160 average speed in an electric current, electric circuit, 185 164 electric current, 163 charge, 252 direction, 161, 162 component of every atom, 6, 229, source of magnetic field, 207 447 units elementary charge, 229 SI: ampere (A), 161 energy of interaction with atom, electric deflection 253 ∝ 1/kinetic energy, 239 mass, 253 control of charged particles, 239 in keV/c2, 379, 395 inkjet printer, 254 in MeV/c2, 391 quark hunting, 257 rest energy, 379 electric field, 169 electron diffraction, 458, 463 constant in space, 172 Debye-Scherrer rings, 458 direction, 172 electron interference, 465 magnitude, 190 electron volt, 118, 188 of a point charge, 171 electrons strength, 170 diffraction of, 463 units discovery, 236 SI: newtons per coulomb electroscope, 152 (N C−1), 170 elementary charge, 188, 233, 243, 252 electric force value, 249 negative derivative of electric elements, 63, 64 potential energy, 176 number of, 77 electric ground, 192 Elster and Geitel, 402 electric potential, 173, 179 energy, 44 and potential energy, 179 and mass equivalence, 375, 378 different from electric potential gravitational potential energy, 48 energy, 179 kinetic energy, 48 equipotential surfaces, 186, 187 units electric potential energy, 173 electron volt, 118 electrical conductor, 157 electron volt (eV), 188 electrode, 230 kilowatt-hour (kW-h), 47 electrolysis, 230 SI: joule (J), 45 Faraday’s law of, 231 energy costs, 47 electrolyte, 230 energy levels, 529 electromagnetic radiation see atoms, 524 polarization, 600 energy states, 522 wavelengths see atoms, 524 and structure of atoms, 309 energy-level diagrams, 526, see atoms, x-rays, 422 energy states of 650 INDEX

entangled state, 610 Franck-Hertz experiment, 531 entanglement, 597, 609, 610 apparatus, 532 EPR data, 533 see Einstein, Podolsky, Rosen, 611 significance of, 534 Estermann, I., 467 Fraunhofer, J. v., 519 ether, 351 frequency, 324 event, 362 bandwidth, 585 event generator, 361 units exclusion principle SI: hertz (Hz), 288 see Pauli exclusion principle, 542 frequency of a wave, 288 Friedrich, W., 423 Faraday, 230, see mole of charges fringe pattern Faraday’s law of electrolysis, see photon counts, 576 electrolysis fringes, 353, 354 Faraday, M., 229 Frisch, O., 467 federal budget, 32 fusion, 400 deficit, 33 Feynman, Richard P., 9, 45 Galilean relativity, 351 energy analogy, 45 Galileo, 1, 4, 52 field, see electric field, see magnetic Dialogues Concerning Two New field Sciences, 1 fission, 400 gamma in relativity, 363 fluorescence, 480 gamma rays FM radio frequencies, 289 radioactive radiations, 484 force, 37, 54 Gas Laws F = ma, 39 see Boyle’s Law, Gay-Lussac’s Law, average force, 60 Charles’ Law, Ideal Gas Law, rate-of-change of momentum, 37, 89 39 gauge pressure, 88 spatial variation of potential Gay-Lussac’s Law, 100, 101 energy, 53 Gay-Lussac, Joseph Louis, 67 units Geiger, Hans, 494, 500 SI: newton (N), 38 Germer, L. H., 462 fractional difference, 392 gram atomic weight, 75 fractional error, see precision gram molecular weight, 75 fractional precision, see precision gravitation, 1 frame of reference, 347 gravitational potential energy, 48 description of motion depends on, depends only on vertical distance, 348 50 Galilean relativity, 351 ground, see electric ground inertial frame, 350 laboratory, 386 Half-life, 488 no special, 350 radioactive decay, 488 rest, 386 Hall effect, 227 transform from one to another, 351 Hallwachs, W., 402 Franck, J., 532 photoelectric effect, 402 INDEX 651 harmonic waves, see waves, sinusoidal from two slits, see double-slit Heisenberg uncertainty principle, 554, interference 558, 570 in 2-D, 307 estimating average kinetic energy of a particle with itself, 554, 591 with, 561 of light estimating force with, 562 fringes, 308 estimating size with, 563 patterns Heisenberg, Werner, 558 sizes and structures determined helium from, 325 discovered in Sun, 319 U. of Rochester apparatus for, 588 discovered on Earth, 320 interference patterns, 307 Hertz, G., 532 reveal structure, 321 Hertz, Heinrich, 401 interferometer discovers photoelectric effect, 402 fringes, 353, 354 generates radio waves, 401 Mach-Zehnder, 575 hidden variables, 598, 618 interferometer histogram, 139 Michelson, 352 hydrogen atom ions, 230 Bohr model of, 517 isotope, 507, 509 energy states of, 525 notation for, 509 mass isotopes, 208, 487 in MeV/c2, 391 of carbon, 208 spectrum of chlorine, 208 Balmer series, 519, 520, 527 of hydrogen, 208 Brackett series, 528 of lead, 215 Lyman series, 528 of oxygen, 208 Paschen series, 528 relative abundances of, 214 Pfund series, 528 hydrogen-like ions, 535 Joint probability, 578 jumps, see atoms, energy transitions in Ideal gas, 100, 103 ideal gas law, 102 K x-rays, 544, see x-rays, line spectra, indistinguishability, 588, 590 545 in quantum theory, 582 and the Bohr Model, 544 inkjet printer, 254 Kashy, E., 515 insulator, see electrical insulator Kaufmann, W., 379 interference, 296, 325 measures e/m of beta rays, 481 coherence length, 584 Kelvin temperature scale, 101 coherence time, 584 Kelvin temperature scale constructive, 297 absolute zero, 102 defining property of waves, 296 kinetic energy, 54 destructive, 298 relativistically correct, 384 from many slits, see multi-slit Kirchhoff, G. R., 519 interference Knipping, P., 423 from one slit, see single-slit K radiation diffraction see x-rays, 538 652 INDEX

L x-rays, 544, see x-rays, line spectra, longitudinal wave, 293, 325 545 Lorentz contraction, 365, 367 measured by Moseley, 551 Lorentz force, see magnetic force Large Hadron Collider (LHC), 215 Lorentz, H. A., 242 lattice constant, 460 Loschmidt, J. J., 132 Laue Lyman series, see hydrogen atom, see von Laue, 423 spectrum Laue diffraction, 446 Lyman, T., 520 Laue pattern, 424 L radiation Laue spots, 424 see x-rays, 538 Lavoisier, 64 law of combining volumes, 68 M law of constant proportions, 65 ach-Zehnder interferometer, 575 law of large numbers, 579 magnetic deflection ∝ law of multiple proportions, 66 1/momentum, 239 Lenard, Philipp, 402 control of moving charges, 215, measures charge-to-mass ratio 219, 239 of charges emitted in discovery of isotopes, 208 photoelectric effect, 402 magnetic field, 199, 200 length, 14 constant units moving charge in, 204 angstrom, 430 uniform circular motion of a SI: meter (m), 14 charge in, 204 light direction, 200, 201, 217 “atomicity” of, 411 outside a long straight current, intensity of, 376 207 polarization, 598, 600 exerts a force only on moving pressure from, 375 charges, 217 speed of, 395 magnitude, 201 constancy of, 351 of Earth, 201 limiting velocity, 7 outside a long, straight current, 207 wavelength and color, 308 produced by electric currents, 207 light clock, 361 source of, 200, 217 light waves, 286 strength electromagnetic waves, 288 outside a long straight wire, 207 sinusoidal uniform, 208 pure color, 286 momentum of charged particle velocity in a vacuum, 287 in, 205 same for moving and stationary units observers, 325 gauss, 201 line spectra, 318 SI: tesla (T), 201 linear approximation, see used to measure momentum of a approximations, straight-line charged particle, 204 linear polarization, 654 magnetic force, 217 localization, 556 direction, 199, 217 connected to measurement, 556 right-hand rule, 202 logic on a moving charge, 199 A means ‘not A’, 612 Lorentz force, 203 INDEX 653 magnetic mass spectrometer, 209 Moon Bainbridge design, 209 3.8 × 108 mfromEarth,33 mass doublets, 213 60 Earth radii distant from Earth, Malus’s law, 603 32 Mandel, L., 588 Morley, E. W., 352 Marsden, E., 497, 500 Moseley’s law, 541 Mass data for, 540 familiar objects, 16 significance of, 546 liter, 16 Moseley, Henry J. G. (1887–1915) mass, 15 atomic number, 537 and energy equivalence, 375, 376, Moseley, Henry J. G. (b. 1887, d. 378 1915), 502 dependence on velocity, 379 multi-slit interference units diffraction grating, 316 eV/c2, 387 principal maxima, 316, 325 SI: kilogram (kg), 15 secondary maxima, 316 mass doublets magnetic mass spectrometer, 213 Negative derivative of electric mass number A, 507, 509 potential energy mass spectrometer see electric force, 176 magnetic mass spectrometer, 209 neutron, 467, 507 Maxwell, James Clerk, 131 and isotopes, 508 mean free path, 122 diffraction of, 467 of N2 at STP, 124 half-life, 507 2 2 mass of O and N molecules, 131 2 medium, 286 in MeV/c , 391 Mendeleev, Dimitri (1834–1907), 536 properties of, 507 Michelson interferometer, 352, 353, neutron number N, 507, 509 359 Newton, 1, 7, 10 Michelson, A. A., 322, 352 Newtonian physics microwave oven frequencies, 289 low speed limiting case of relativistic physics, 340 Miller indices, 459, 461 non-locality, 597 Millikan, Robert A., 229, 243 non-relativistic approximations oil-drop experiment, 243 how good?, 392 photoelectric effect experiment, 408 rule of thumb, 393 model, 109 rules of thumb, 395 Modern Introductory Physics nuclear force, 507, 510 atoms, 5 nuclear model of the atom, 503 mole, 75 hydrogen, 517 Avogadro’s number, 75 nucleons in nucleus, 509 of charges, 230, 232 nucleus, 6, 498 molecules, 66, 69 atomic number of, 507 momentum, 36, 54, 56 electric charge of, 502 relativistically correct, 383 electrostatic potential energy of an units alpha particle in, 506 eV/c, 387 mass number of, 507 SI: newton-seconds (N s), 39 neutrons in, 507 654 INDEX

nuclides, 508 some work functions for, 411 protons and neutrons in, 509 work function, 406, 407 radius of, 502, 509 photoelectrons, 402, see photoelectric by proton scattering, 514 effect, 403 random decay of, 492 emitted with no time delay, 405 nuclides, 508 maximum kinetic energy of, 404 chart of, 509 photomultiplier tube, 412 masses of, 641 anode of, 413 notation for, 509 dynodes of, 413 number of stable, 508 photocathode of, 413 radioactive, 508 quantum efficiency of, 414 number density, 76, 113 photon, 407, 411, 415, 553 x-rays, 433 Optical spectroscopy, 318 photopeak, 444, see scintillation order of magnitude, 151 detector physical dimensions Paschen series, 520, see hydrogen M, L, T—mass, length, time, 25 atom, spectrum Physics and Astronomy Classification Paschen, F., 520 Scheme (PACS), 2 Pauli exclusion principle, see atoms, URL, 2 shell structure of pion pendulum, 51 lifetime, 397 conversion of kinetic energy into rest mass, 396, 400 gravitational potential energy, Planck constant, 407, 415, 522 51 ¯h (h bar), 517 Galileo, 52 Planck, Max (1858–1947) period of a wave, 288, 324 start of quantum theory, 569 periodic table of the elements, 536 plum-pudding model, 494 permittivity of free space: 0, 160 polarization, 598 Pfund series, see hydrogen atom, horizontal and vertical, 600 spectrum Malus’s law, 603 phase, 324 polarization, linear, 654 phase constant, 293 polarized light photocathode, see photomultiplier production, 601 tube polarized light, 600 photocurrent, see photoelectric effect polarizer, 601 effects of light frequency on, 404 extinction axis, 601 effects of light intensity on, 404 transmission axis, 601 photoelectric effect, 401, 402, 553 two-beam, 614 alkali metals, 402 polarizing beam splitter, 615 Bragg on the strangeness of, 406 pole-in-the-barn puzzle, 370 discovered, 402 positron, 398 Einstein equation for, 407 radioactive decay, 508 emitted charges are electrons, 402 potential, see electric potential Millikan’s data on, 409 powder diffraction patterns, 427 Millikan’s experiment on, 408 power photoecurrent, 402 units photoelectrons, 402 SI: watt (W), 45 INDEX 655 precision, 212 and activity, 489 pressure, 83 causeless randomness in, 493 force per unit area, 85 decay chains, 485 of enclosed gases, 89 decay constant, 490 of fluid, 84 decay constant or disintegration units, 87 constant, 489 SI: pascal (Pa), 88 disintegration constant, 490, 510 primary x-rays, 538 half-life, 488, 510 principal quantum number, 525 half-life data for UX1, 491 principle of relativity, 339, 350 half-life of thorium-234 (UX1), 489 examples, 349, 365 law of, 489, 490, 510 probability positron emission, 508 joint of independent events, 578 radioactive series, 485 law of large numbers, 579 relation between decay constant mutually exclusive events, 579 and half-life, 492 probability amplitude, 578 radioactive elements, 487 proper length, 367 emanation (radon), 485 proper time, 363 polonium, 482 proton radium, 482 mass, 21 radon, 485 in MeV/c2, 391, 395 thorium, 482 Proust, J.-L., 65 uranium, 481 uranium-x UX1 234Th, 485 Quantization, 411 radioactive radiations, 484 quantum, 407, 415 alpha rays, 483 quantum efficiency, see beta rays, 483 photomultiplier tube energies of, 509 quantum eraser, 607 gamma rays, 484, 510 Quantum mechanics large energies of, 503, 505 correlations, 609 their e/m, 481 quantum mechanics, 321, 510, 545, radioactivity, 380, 479, 480 554 activity of, 481 claimed to be incomplete, 611 related to internal structure of hidden variables, 618 atoms, 482 quantum mechanics used to identify new elements, 482 entanglement, 610 widespread phenomenon, 482 hidden variable theories, 598 rainbow, 317 non-locality, 597 ray, 426 quantum number, 524 reference frame, see frame of reference quantum theory, 321 Relativistic Heavy Ion Collider indistinguishability, 582 (RHIC), 216 quark hunting, see electric deflection relativity quarks, 257 and Newtonian physics, 340 constancy of c, 339 Radial quantum number, 525 correct transformation of velocities, radioactive decay, 379, 488 370 a purely random process, 492, 510 event, 362 alpha particles, 509 event generator, 361 656 INDEX

gamma, 363 shell structure, 545 invariance of laws of physics, 339 SI multipliers, 23 light clock, 361 SI prefixes, 14, 55, 633 of simultaneity, 339, 371 see SI multipliers, 23 principle of, 350 SI units proper length, 367 metric system, 16 proper time, 363 multipliers, 23 resolution, 317 prefixes, 14 rest energy, 379 simultaneity, see relativity of rest mass, 378 simultaneity right-hand rule sine waves, see waves, sinusoidal for direction of B outside a long, single-slit diffraction, 312, 325 straight, current, 207 minima, 325 for magnetic force on a moving Sklodowska, Marie charge, 202 Curie, Marie, 482 Roentgen, K. small-angle approximation, 346 discovers x-rays, 421 Soddy, Frederick, 479, 485 root mean square velocity, 114 sound waves, 324 Rutherford scattering, 498 frequencies of, 288 distance of closest approach, 501 sinusoidal equation for, 498 pure tone, 286 experimental data, 499 space and time interconnected, 339, Geiger’s and Marsden’s experiment, 361 499, 501 special theory of relativity, 339, see used to measure the charge of a relativity nucleus, 502 spectral lines, 318, 319 Rutherford, Ernest, 479, 482 produced by discharge tube, 320 discovers the nucleus, 502 spectrometers, 318 distinguishes alpha, beta and spectroscopists, 318 gamma rays, 483 spectroscopy, 318, 518 observes scattering of alpha and astronomy, 321 particles, 494 and quantum theory, 321 Rydberg atoms, 530 spectrum, see electromagnetic Rydberg formula, 520 spectrum, 319, 519 Rydberg states, 530 standard deviation, see distribution Rydberg, J. R., 519 stationary states, 517, 522 Stern, O., 467 Scattering Stokes’ law, see viscous force alpha particles, 494 STP Rutherford scattering, 498 IUPAC definition, 113 scintillation, 415, 496 NIST definition, 113 scintillation detector, 415 strong force sodium-iodide crystal, 443 nuclear force, 510 zinc sulfide, 496 subtend, 27 secondary emission, 413, 463 summation notation, 139 secondary x-rays, 538 Sun series limit, 519 1.5 × 1011 mfromEarth,34 INDEX 657

mass, 34 Ulrey,C.T.,432 volume, 34 ultrarelativistic approximations, 394 superposition rules of thumb, 395 principle of, 297 uncertainty principle, see Heisenberg uncertainty principle, 570 Temperature uniform magnetic field, see magnetic and energy, 134 field, constant SI units: kelvins (K), 101 units, 639 temperature of gases abbreviations, 639 energy of random motion of atoms, avoid looking foolish, 25, 26 116 consistency, 25 kelvin scale, 120 Tip 1: calculate efficiently with SI kinetic energy of atoms, 115 multipliers, 23 thermal energy at room temperature, Tip 2: have consistent units, 118 dimensions, 25, 26 thermal equilibrium, 94 universal gas constant, 104 thermal expansion volume coefficient of, 95 some values, 96 Vacuum, 85 Thomson, G. P., 457, 458 ultra-high, 131 verifies de Broglie wavelength, 459 valence, 77 Thomson, J. J., 229, 235, 380, 494 Van der Broek, A. charge-to-mass ratio of charges identifies nuclear charge as atomic from photoelectric effect, 402 number, 502 discovers electron, 236, 421 vectors, 56 plum-pudding model of atom, 521 addition, 57 time, 19 components, 57 units magnitude, 57 SI: second (s), 19 velocity, 56 year (y), 21 velocity filter, see Wien velocity filter time dilation, 361, 364 viscosity, 125 Torricelli, E., 85 coefficient of, 126 first vacuum, 85 how to measure, 125 Torricellian vacuum, 86 momentum transfer, 128 torsion balance, 157 of gases trajectory, 2 dependence on molecular weight, transformation, 351 135 transitions, see atoms, energy independent of density, 135 transitions in temperature dependence, 135 transmutation, 485, 509 units alpha decay, 508 poise, 126 beta decay, 508 SI: pascal seconds (Pa s), 126 transverse wave, 293, 325 viscosity of air, 252 traveling sine wave, 324 viscous force, 245 one-dimensional general form, 293 Stokes’s law, 245 Tristan particle accelerator, 398 visible light tritium, 508, 641 frequencies of, 289 two-beam polarizer, 614 658 INDEX

voltage, see electric potential work, 44 see electric potential, 173 work function, see photoelectric volume effect, 415 cylinder, 18 values for some metals, 411 formulas, 22 sphere, 22 X-ray crystal spectrometer, 446 three factors of length, 22 x-ray lines, 545 von Laue, M. x-rays, 324, 422 interference of x-rays, 423 as probe of structure, 447 von Laue, Max, 423 atomic shells, 542 characteristic, 538, 539 continuous spectrum, 432 Wang, J. L., 588 short wavelength cutoff, 433, 446 watt SI unit of power, 45 Ulrey’s data, 432 wave-particle duality, 553 detection of, 422 interference of, 423 wavelength, 288, 324 K lines, 538 size needed to determine structural L lines, 538 features, 324 line spectra, 539, 542 waves, 286, 324 and Bohr model, 542 bandwidth, 585 Kx-rays,544 energy, 325 Lx-rays,544 energy carried by, 294 photons of, 433 intensity, 294 powder diffraction, 427 interference of, see interference primary and secondary, 538 sinusoidal, 286, 324 production of, 422 amplitude of, 290 properties of, 422 displacement of, 291 short-wavelength electromagnetic frequency, 288 radiation, 422 intensity, 325 spectrometer, 429 parameters of, 286 used to identify chemical period of, 288, 289 composition, 546 periodic in space, 288 periodic in time, 288 Year phase constant, 293 3.15 × 107 s, 21 phase of, 291 Young, Thomas, 308 wavelength, 288 light is a wave, 308 superposition of, 296 velocity of, 325 Zeilinger, Anton, 477 Wien velocity filter, 209 Zou, X. Y., 588