1 Physical constants
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524 Appendices 1 Physical constants The values quoted here are those usually used in calculations and problems. Fewer significant digits are often used in the text. The constants are known with a much better precision than the number of significant digits quoted here implies. Atomic mass unit 1 u = 1.661 × 10 -27 kg = 931.5 MeV c -2 Avogadro constant N A = 6.02 × 10 23 mol -1 Boltzmann constant k = 1.38 × 10 -23 J K -1 Coulomb’s law constant 1 4πε 0 = 8.99 × 10 9 N m 2 C -2 Electric permittivity ε 0 = 8.85 × 10 -12 N -1 m -2 C 2 Gravitational constant G = 6.67 × 10 -11 N kg -2 m 2 Magnetic permeability μ 0 = 4π × 10 -7 T m A -1 Magnitude of electronic charge e = 1.60 × 10 -19 C Mass of the electron m e = 9.11 × 10 -31 kg = 5.49 × 10 -4 u = 0.511 MeV c -2 Mass of the neutron m n = 1.675 × 10 -27 kg = 1.008 665 u = 940 MeV c -2 Mass of the proton m p = 1.673 × 10 -27 kg = 1.007 276 u = 938 MeV c -2 Planck constant h = 6.63 × 10 -34 J s Speed of light in a vacuum c = 3.00 × 10 8 m s -1 Stefan–Boltzmann constant σ = 5.67 × 10 -8 W m -2 K -4 Universal gas constant R = 8.31 J mol -1 K -1 Solar constant S = 1.36 × 10 3 W m -2 Fermi radius R 0 = 1.2 × 10 -15 m A few unit conversions astronomical unit 1 AU = 1.50 × 10 11 m atmosphere 1 atm = 1.01 × 10 5 N m- 2 = 101 kPa degree 1° = π 180° rad electronvolt 1 eV = 1.60 × 10 -19 J kilowatt–hour 1 kW h = 3.60 × 10 6 J light year 1 ly = 9.46 × 10 15 m parsec 1 pc = 3.26 ly radian 1 rad = 180° π
Transcript of 1 Physical constants
524
Appendices1 Physical constantsThe values quoted here are those usually used in calculations and problems. Fewer signi� cant digits are often used in the text. The constants are known with a much better precision than the number of signi� cant digits quoted here implies.
Atomic mass unit 1 u = 1.661 × 10−27 kg = 931.5 MeV c−2
Avogadro constant NA = 6.02 × 1023 mol−1
Boltzmann constant k = 1.38 × 10−23 J K−1
Coulomb’s law constant 1
4πε0 = 8.99 × 109 N m2 C−2
Electric permittivity ε0 = 8.85 × 10−12 N−1 m−2 C2
Gravitational constant G = 6.67 × 10−11 N kg−2 m2
Magnetic permeability μ0 = 4π × 10−7 T m A−1
Magnitude of electronic charge e = 1.60 × 10−19 C
Mass of the electron me = 9.11 × 10−31 kg = 5.49 × 10−4 u = 0.511 MeV c−2
Mass of the neutron mn = 1.675 × 10−27 kg = 1.008 665 u = 940 MeV c−2
Mass of the proton mp = 1.673 × 10−27 kg = 1.007 276 u = 938 MeV c−2
Planck constant h = 6.63 × 10−34 J s
Speed of light in a vacuum c = 3.00 × 108 m s−1
Stefan–Boltzmann constant σ = 5.67 × 10−8 W m−2 K−4
Universal gas constant R = 8.31 J mol−1 K−1
Solar constant S = 1.36 × 103 W m−2
Fermi radius R0 = 1.2 × 10−15 m
A few unit conversionsastronomical unit 1 AU = 1.50 × 1011 m
atmosphere 1 atm = 1.01 × 105 N m−2 = 101 kPa
degree 1° = π
180° rad
electronvolt 1 eV = 1.60 × 10−19 J
kilowatt–hour 1 kW h = 3.60 × 106 J
light year 1 ly = 9.46 × 1015 m
parsec 1 pc = 3.26 ly
radian 1 rad = 180°
π
12 QUANTUM AND NUCLEAR PHYSICS (HL)
Appendices 2 Masses of elements and selected isotopesTable A2.1 gives atomic masses, including the masses of electrons, in the neutral atom. The masses are averaged over the isotopes of each element. In the case of unstable elements, numbers in brackets indicate the approximate mass of the most abundant isotope of the element in question. The masses are expressed in atomic mass units, u. Table A2.2 gives the atomic masses of a few selected isotopes
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Atomic number Name and symbol Atomic mass / u
1 Hydrogen, H 1.0080
2 Helium, He 4.0026
3 Lithium, Li 6.941
4 Beryllium, Be 9.012 18
5 Boron, B 10.811
6 Carbon, C 12.000 000
7 Nitrogen, N 14.007
8 Oxygen, O 15.999
9 Fluorine, F 18.998
10 Neon, Ne 20.180
11 Sodium, Na 22.999
12 Magnesium, Mg 24.31
13 Aluminium, Al 26.981
14 Silicon, Si 28.086
15 Phosphorus, P 30.974
16 Sulphur, S 32.066
17 Chlorine, Cl 35.453
18 Argon, Ar 39.948
19 Potassium, K 39.102
20 Calcium, Ca 40.078
21 Scandium, Sc 44.956
22 Titanium, Ti 47.90
23 Vanadium, V 50.942
24 Chromium, Cr 51.996
25 Manganese, Mn 54.938
26 Iron, Fe 55.847
27 Cobalt, Co 58.933
28 Nickel, Ni 58.71
29 Copper, Cu 63.54
Atomic number Name and symbol Atomic mass / u
30 Zinc, Zn 65.37
31 Gallium, Ga 69.723
32 Germanium, Ge 72.59
33 Arsenic, As 74.921
34 Selenium, Se 78.96
35 Bromine, Br 79.91
36 Krypton, Kr 83.80
37 Rubidium, Rb 85.467
38 Strontium, Sr 87.62
39 Yttrium, Y 88.906
40 Zirconium, Zr 91.224
41 Niobium, Nb 92.906
42 Molybdenum, Mo 95.94
43 Technetium, Tc (99)
44 Ruthenium, Ru 101.07
45 Rhodium, Rh 102.906
46 Palladium, Pd 106.42
47 Silver, Ag 107.868
48 Cadmium, Cd 112.40
49 Indium, In 114.82
50 Tin, Sn 118.69
51 Antimony, Sb 121.75
52 Tellurium, Te 127.60
53 Iodine, I 126.904
54 Xenon, Xe 131.30
55 Caesium, Cs 132.91
56 Barium, Ba 137.34
57 Lanthanum, La 138.91
58 Cerium, Ce 140.12
Table A2.1 Atomic numbers and atomic masses of the elements.
APPENDICES
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Atomic number Name and symbol Atomic mass / u
59 Praseodymium, Pr 140.907
60 Neodymium, Nd 144.24
61 Promethium, Pm (144)
62 Samarium, Sm 150.4
63 Europium, Eu 152.0
64 Gadolinium, Gd 157.25
65 Terbium, Tb 158.92
66 Dysprosium, Dy 162.50
67 Holmium, Ho 164.93
68 Erbium, Er 167.26
69 Thulium, Tm 168.93
70 Ytterbium, Yb 173.04
71 Lutetium, Lu 174.97
72 Hafnium, Hf 178.49
73 Tantalum, Ta 180.95
74 Tungsten, W 183.85
75 Rhenium, Re 186.2
76 Osmium, Os 190.2
77 Iridium, I 192.2
78 Platinum, Pt 195.09
79 Gold, Au 196.97
80 Mercury, Hg 200.59
81 Thallium, Tl 204.37
Atomic number Name Atomic mass / u
1 Hydrogen, H 1.007 825
1 Deuterium, D 2.014 102
1 Tritium, T 3.016 049
2 Helium-3 3.016 029
2 Helium-4 4.002 603
3 Lithium-6 6.015 121
3 Lithium-7 7.016 003
4 Beryllium-9 9.012 182
5 Boron-10 10.012 937
5 Boron-11 11.009 305
6 Carbon-12 12.000 000
6 Carbon-13 13.003 355
6 Carbon-14 14.003 242
Atomic number Name and symbol Atomic mass / u
82 Lead, Pb 207.2
83 Bismuth, Bi 208.980
84 Polonium, Po (210)
85 Astatine, At (218)
86 Radon, Rn (222)
87 Francium, Fr (223)
88 Radium, Ra (226)
89 Actinium, Ac (227)
90 Thorium, Th (232)
91 Protactinium, Pa (231)
92 Uranium, U (238)
93 Neptunium, Np (239)
94 Plutonium, Pu (239)
95 Americium, Am (243)
96 Curium, Cm (245)
97 Berkelium, Bk (247)
98 Californium, Cf (249)
99 Einsteinium, Es (254)
100 Fermium, Fm (253)
101 Mendelevium, Md (255)
102 Nobelium, No (255)
103 Lawrencium, Lr (257)
Atomic number Name Atomic mass / u
7 Nitrogen-14 14.003 074
7 Nitrogen-15 15.000 109
8 Oxygen-16 15.994 915
8 Oxygen-17 16.999 131
8 Oxygen-18 17.999 160
19 Potassium-39 38.963 708
19 Potassium-40 39.964 000
92 Uranium-232 232.037 14
92 Uranium-235 235.043 925
92 Uranium-236 236.045 563
92 Uranium-238 238.050 786
92 Uranium-239 239.054 291
Table A2.2 Atomic masses of a few selected isotopes.
Table A2.1 contd.
APPENDICES
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3 Some important mathematical resultsIn physics problems, the following are useful.
a−x = 1ax axay = ax+y
ax
ay = ax−y
log a = x ⇒ 10x = a ln a = x ⇒ ex = a
ln(ab) = ln a + ln b ln ab = ln a − ln b
ln(ax ) = x ln a ln(1) = 0 e0 = 1
sin 2x = 2 sin x cos x
cos 2x = 2 cos2 x − 1 = 1 − 2 sin2 x = cos2 x − sin2 x
The quadratic equation ax2 + bx + c = 0 has two roots given by
x = −b ± b2 − 4ac
2a
The following approximations are useful:
sin x ≈ x − x3
6 + …
and
cos x ≈ 1 − x2
2 + …
valid when x in radians is small.From geometry, we must know the following expressions for lengths, areas and volumes.
Property Formula
Circumference of a circle of radius R 2π R
Area of a circle of radius R π R2
Surface area of a sphere of radius R 4π R2
Volume of a sphere of radius R 4π R3
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Volume of a cylinder of base radius R and height h π R2h
The length of an arc of a circle of radius R that subtends an angle θ at the centre of the circle is s = Rθ. In this formula the angle must be expressed in radians. An angle of 2π radians is equivalent to an angle of 360°, so
1 radian = 360°2π = 57.3°
APPENDICES
