A Reference Tables · Physics · Physics Playground

Prefix	Symbol	Value	Prefix	Symbol	Value
tera	T	10¹²	deci	d	10^–1
giga	G	10⁹	centi	c	10^–2
mega	M	10⁶	milli	m	10^–3
kilo	k	10³	micro	µ	10^–6
hecto	h	10²	nano	n	10^–9
deka	da	10¹	pico	p	10^–12
		10⁰	femto	f	10^–15

Table A1 Metric Prefixes for Powers of Ten and Their Symbols

	Entity	Abbreviation	Name
Fundamental units	Length	m	meter
	Mass	kg	kilogram
	Time	s	second
	Current	A	ampere
Supplementary unit	Angle	rad	radian
Derived units	Force	$N = k g \cdot \frac{m}{s^{2}} N = k g \cdot \frac{m}{s^{2}}$	newton
	Energy	$J = kg \cdot m^{2} / s^{2} J = kg \cdot m^{2} / s^{2}$	joule
	Power	$W = \frac{J}{s} W = \frac{J}{s}$	watt
	Pressure	$P a = \frac{N}{m^{2}} P a = \frac{N}{m^{2}}$	pascal
	Frequency	$H z = \frac{1}{s} H z = \frac{1}{s}$	hertz
	Electronic potential	$V = \frac{J}{C} V = \frac{J}{C}$	volt
	Capacitance	$F = \frac{C}{V} F = \frac{C}{V}$	farad
	Charge	$C = s \cdot A C = s \cdot A$	coulomb
	Resistance	$Ω = \frac{V}{A} Ω = \frac{V}{A}$	ohm
	Magnetic field	$T = \frac{N}{A \cdot m} T = \frac{N}{A \cdot m}$	tesla
	Nuclear decay rate	$B q = \frac{1}{s} B q = \frac{1}{s}$	becquerel

Table A2 SI Units

Length	1 inch (in.) = 2.54 cm (exactly)
	1 foot (ft) = 0.3048 m
	1 mile (mi) = 1.609 km
Force	1 pound (lb) = 4.448 N
Energy	1 British thermal unit (Btu) = 1.055 × 10³ J
Power	1 horsepower (hp) = 746 W
Pressure	1 lb/in² = 6.895 × 10³ Pa

Table A3 Selected British Units

Length	1 light year (ly) = 9.46 × 10¹⁵ m
	1 astronomical unit (au) = 1.50 × 10¹¹ m
	1 nautical mile = 1.852 km
	1 angstrom(Å) = 10^-10 m
Area	1 acre (ac) = 4.05 × 10³ m2
	1 square foot (ft²) 9.29 × 10^-2 m³
	1 barn (b) = 10^-28 m²
Volume	1 liter (L) = 10^-3 m³
	1 U.S. gallon (gal) = 3.785 × 10^-3 m³
Mass	1 solar mass = 1.99 × 10³⁰ kg
	1 metric ton = 10³ kg
	1 atomic mass unit (u) = 1.6605 × 10^-27 kg
Time	1 year (y) = 3.16 × 10⁷ s
	1 day (d) = 86,400 s
Speed	1 mile per hour (mph) = 1.609 km / h
	1 nautical mile per hour (naut) = 1.852 km / h
Angle	1 degree (°) = 1.745x10^-2 rad
	1 minute of arc (') = 1 / 60 degree
	1 second of arc ('') = 1 / 60 minute of arc
	1 grad = 1.571 × 10^-2 rad
Energy	1 kiloton TNT (kT) = 4.2 × 10¹² J
	1 kilowatt hour (kW $\cdot \cdot$ h) = 3.60 × 106 J
	1 food calorie (kcal) = 4186 J
	1 calorie (cal) = 4.186 J
	1 electron volt (cV) = 1.60 × 10^-19 J
Pressure	1 atmosphere (atm) = 1.013 × 10⁵ Pa
	1 millimeter of mercury (mm Hg) = 133.3 Pa
	1 torricelli (torr) = 1 mm Hg = 133.3 Pa
Nuclear decay rate	1 curie (Ci) = 3.70 × 10¹⁰ Bq

Table A4 Other Units

Circumference of a circle with radius r or diameter d	$C = 2 π r = π d C = 2 π r = π d$
Area of a circle with radius r or diameter d	$A = π r^{2} = π d^{2} / 4 A = π r^{2} = π d^{2} / 4$
Area of a sphere with radius r	$A = 4 π r^{2} A = 4 π r^{2}$
Volume of a sphere with radius r	$V = (4 / 3) (π r^{3}) V = (4 / 3) (π r^{3})$

Table A5 Useful formulae

Symbol	Meaning	Best Value	Approximate Value
c	Speed of light in vacuum	$2.99792458 \times 10^{8} m / s 2.99792458$	$3.00 \times 10^{8} m / s 3.00$
G	Gravitational constant	$6.67384 (80) \times 10^{–11} N \cdot m^{2} / {kg}^{2} 6.67384 (80) \times 10^{–11} N \cdot m^{2} / {kg}^{2}$	$6.67 \times 10^{–11} N \cdot m^{2} / {kg}^{2} 6.67$
^NA	Avogadro’s number	$6.02214129 (27) \times 10^{23} J / K 6.02214129 (27) \times 10^{23} J / K$	$6.02 \times 10^{23} 6.02$
k	Boltzmann’s constant	$1.3806488 (13) \times 10^{–23} J / K 1.3806488 (13) \times 10^{–23} J / K$	$1.38 \times 10^{–23} J / K 1.38$
R	Gas constant	$8.3144621 (75) J / mol \cdot K 8.3144621 (75) J / mol \cdot K$	$8.31 J / mol \cdot K = 1.99 cal / mol \cdot K 8.31 J / mol \cdot K = 1.99 cal / mol \cdot K$ $= 0.0821 atm \cdot L / mol \cdot K = 0.0821 atm \cdot L / mol \cdot K$
σ	Stefan-Boltzmann Constant	$5.670373 (21) \times 10^{–8} W / m^{2} \cdot K 5.670373 (21) \times 10^{–8} W / m^{2} \cdot K$	$5.67 \times 10^{–8} W / m^{2} \cdot K 5.67$
k	Coulomb force constant	$8.987551788... \times 10^{9} N \cdot m^{2} / C^{2} 8.987551788...$	$8.99 \times 10^{9} N \cdot m^{2} / C^{2} 8.99$
^qe	Charge on electron	$–1.602176565 (35) \times 10^{–19} C –1.602176565 (35) \times 10^{–19} C$	$–1.60 \times 10^{–19} C –1.60$
^ε0	Permittivity of free space	$8.854187817... \times 10^{–12} C^{2} / N \cdot m^{2} 8.854187817...$	$8.85 \times 10^{–12} C^{2} / N \cdot m^{2} 8.85$
^µ0	Permeability of free space	$4 π \times 10^{–7} T \cdot m / A 4 π \times 10^{–7} T \cdot m / A$	$1.26 \times 10^{–6} T \cdot m / A 1.26$
h	Planck’s constant	$6.62606957 (29) \times 10^{- 34} J \cdot s 6.62606957 (29) \times 10^{- 34} J \cdot s$	$6.63 \times 10^{- 34} J \cdot s 6.63$

Table A6 Important Constants

Alpha	$Α Α$	$α α$
Beta	$Β Β$	$β β$
Gamma	$Γ Γ$	$γ γ$
Delta	$Δ Δ$	$δ δ$
Epsilon	$Ε Ε$	$ε ε$
Zeta	$Ζ Ζ$	$ζ ζ$
Eta	$Η Η$	$η η$
Theta	$Θ Θ$	$θ θ$
Iota	$Ι Ι$	$ι ι$
Kappa	$Κ Κ$	$κ κ$
Lambda	$Λ Λ$	$λ λ$
Mu	$Μ Μ$	$μ μ$
Nu	$Ν Ν$	$ν ν$
Xi	$Ξ Ξ$	$ξ ξ$
Omicron	$Ο Ο$	$ο ο$
Pi	$Π Π$	$π π$
Rho	$Ρ Ρ$	$ρ ρ$
Sigma	$Σ Σ$	$σ σ$
Tau	$Τ Τ$	$τ τ$
Upsilon	$ϒ ϒ$	$υ υ$
Phi	$Φ Φ$	$ϕ ϕ$
Chi	$Χ Χ$	$χ χ$
Psi	$Ψ Ψ$	$ψ ψ$
Omega	$Ω Ω$	$ω ω$

Table A7 The Greek Alphabet

Sun	mass	1.99 × 10³⁰ kg
	average radius	6.96 × 10⁸ m
	Earth-sun distance (average)	1.496 × 10¹¹ m
Earth	mass	5.9736 × 10²⁴ kg
	average radius	6.376 × 10⁶ m
	orbital period	3.16 × 10⁷ s
Moon	mass	7.35 × 10²² kg
	average radius	1.74 × 10⁶ m
	orbital period (average)	2.36 × 10⁶ s
	Earth-moon distance (average)	3.84 × 10⁸ m

Table A8 Solar System Data

Atomic number, Z	Name	Atomic Mass Number, A	Symbol	Atomic Mass (u)	Percent Abundance or Decay Mode	Half-life, ^t1/2
0	neutron	1	n	1.008 665	β^–	10.37 min
1	Hydrogen	1	¹H	1.007 825	99.985%
	Deuterium	2	²H or D	2.014 102	0.015%
	Tritium	3	³H or T	3.016 050	β^–	12.33 y
2	Helium	3	³He	3.016 030	1.38 × 10⁻⁴ %
		4	⁴He	4.002 603	≈100%
3	Lithium	6	⁶Li	6.015 121	7.5%
		7	⁷Li	7.016 003	92.5%
4	Beryllium	7	⁷Be	7.016 928	EC	53.29 d
		9	⁹Be	9.012 182	100%
5	Boron	10	¹⁰B	10.012 937	19.9%
		11	¹¹B	11.009 305	80.1%
6	Carbon	11	¹¹C	11.011 432	EC, β⁺
		12	¹²C	12.000 000	98.90%
		13	¹³C	13.003 355	1.10%
		14	¹⁴C	14.003 241	β^–	5730 y
7	Nitrogen	13	¹²N	13.005 738	β⁺	9.96 min
		14	¹³N	14.003 074	99.63%
		15	¹⁴N	15.000 108	0.37%
8	Oxygen	15	¹⁵O	15.003 065	EC, β⁺	122 s
		16	¹⁶O	15.994 915	99.76%
		18	¹⁸O	17.999 160	0.200%
9	Fluorine	18	¹⁸F	18.000 937	EC, β⁺	1.83 h
		19	¹⁹F	18.998 403	100%
10	Neon	20	²⁰Ne	19.992 435	90.51%
		22	²²Ne	21.991 383	9.22%
11	Sodium	22	²²Na	21.994 434	β⁺	2.602 y
		23	²³Na	22.989 767	100%
		24	²⁴Na	23.990 961	β^–	14.96 h
12	Magnesium	24	²⁴Mg	23.985 042	78.99%
13	Aluminum	27	²⁷Al	26.981 539	100%
14	Silicon	28	²⁸Si	27.976 927	92.23%	2.62h
		31	³¹Si	30.975 362	β^–
15	Phosphorus	31	³¹P	30.973 762	100%
		32	³²P	31.973 907	β^–	14.28 d
16	Sulfur	32	³²S	31.972 070	95.02%
		35	³⁵S	34.969 031	β^–	87.4 d
17	Chlorine	35	³⁵Cl	34.968 852	75.77%
		37	³⁷Cl	36.965 903	24.23%
18	Argon	40	⁴⁰Ar	39.962 384	99.60%
19	Potassium	39	³⁹K	38.963 707	93.26%
		40	⁴⁰K	39.963 999	0.0117%, EC, β^–	1.28 × 10⁹ y
20	Calcium	40	⁴⁰Ca	39.962 591	96.94%
21	Scandium	45	⁴⁵Sc	44.955 910	100%
22	Titanium	48	⁴⁸Ti	47.947 947	73.8%
23	Vanadium	51	⁵¹V	50.943 962	99.75%
24	Chromium	52	⁵²Cr	51.940 509	83.79%
25	Manganese	55	⁵⁵Mn	54.938 047	100%
26	Iron	56	⁵⁶Fe	55.934 939	91.72%
27	Cobalt	59	⁵⁹Co	58.933 198	100%
		60	⁶⁰Co	59.933 819	β^–	5.271 y
28	Nickel	58	⁵⁸Ni	57.935 346	68.27%
		60	⁶⁰Ni	59.930 788	26.10%
29	Copper	63	⁶³Cu	62.939 598	69.17%
			⁶⁵Cu	64.927 793	30.83%
30	Zinc	64	⁶⁴Zn	63.929 145	48.6%
		66	⁶⁶Zn	65.926 034	27.9%
31	Gallium	69	⁶⁹Ga	68.925 580	60.1%
32	Germanium	72	⁷²Ge	71.922 079	27.4%
		74	⁷⁴Ge	73.921 177	36.5%
33	Arsenic	75	⁷⁵As	74.921 594	100%
34	Selenium	80	⁸⁰Se	79.916 520	49.7%
35	Bromine	79	⁷⁹Br	78.918 336	50.69%
36	Krypton	84	⁸⁴Kr	83.911 507	57.0%
37	Rubidium	85	⁸⁵Rb	84.911 794	72.17%
38	Strontium	86	⁸⁶Sr	85.909 267	9.86%
		88	⁸⁸Sr	87.905 619	82.58%
		90	⁹⁰Sr	89.907 738	β^–	28.8 y
39	Yttrium	89	⁸⁹Y	88.905 849	100%
		90	⁹⁰Y	89.907 152	β^–	64.1 h
40	Zirconium	90	⁹⁰Zr	89.904 703	51.45%
41	Niobium	93	⁹³Nb	92.906 377	100%
42	Molybdenum	98	⁹⁸Mo	97.905 406	24.13%
43	Technetium	98	⁹⁸Tc	97.907 215	β^–	4.2 × 10⁶ y
44	Ruthenium	102	¹⁰²Ru	101.904 348	31.6%
45	Rhodium	103	¹⁰³Rh	102.905 500	100%
46	Palladium	106	¹⁰⁶Pd	105.903 478	27.33%
47	Silver	107	¹⁰⁷Ag	106.905 092	51.84%
		109	¹⁰⁹Ag	108.904 757	48.16%
48	Cadmium	114	¹¹⁴Cd	113.903 357	28.73%
49	Indium	115	¹¹⁵In	114.903 880	95.7%, β^–	4.4 × 10¹⁴ y
50	Tin	120	¹²⁰Sn	119.902 200	32.59%
51	Antimony	121	¹²¹Sb	120.903 821	57.3%
52	Tellurium	130	¹³⁰Te	129.906 229	33.8%, β^–	2.5 × 10²¹ y
53	Iodine	127	¹²⁷I	126.904 473	100%
		131	¹³¹I	130.906 114	β^–	8.040 d
54	Xenon	132	¹³²Xe	131.904 144	26.9%
		136	¹³⁶Xe	135.907 214	8.9%
55	Cesium	133	¹³³Cs	132.905 429	100%
		134	¹³⁴Cs	133.906 696	EC, β^–	2.06 y
56	Barium	137	¹³⁷Ba	136.905 812	11.23%
		138	¹³⁸Ba	137.905 232	71.70%
57	Lanthanum	139	¹³⁹La	138.906 346	99.91%
58	Cerium	140	¹⁴⁰Ce	139.905 433	88.48%
59	Praseodymium	141	¹⁴¹Pr	140.907 647	100%
60	Neodymium	142	¹⁴²Nd	141.907 719	27.13%
61	Promethium	145	¹⁴⁵Pm	144.912 743	EC, α	17.7 y
62	Samarium	152	¹⁵²Sm	151.919 729	26.7%
63	Europium	153	¹⁵³Eu	152.921 225	52.2%
64	Gadolinium	158	¹⁵⁸Gd	157.924 099	24.84%
65	Terbium	159	¹⁵⁹Tb	158.925 342	100%
66	Dysprosium	164	¹⁶⁴Dy	163.929 171	28.2%
67	Holmium	165	¹⁶⁵Ho	164.930 319	100%
68	Erbium	166	¹⁶⁶Ho	165.930 290	33.6%
69	Thulium	169	¹⁶⁹Tm	168.934 212	100%
70	Ytterbium	174	¹⁷⁴Yb	173.938 859	31.8%
71	Lutecium	175	¹⁷⁵Lu	174.940 770	97.41%
72	Hafnium	180	¹⁸⁰Hf	179.946 545	35.10%
73	Tantalum	181	¹⁸¹Ta	180.947 992	99.98%
74	Tungsten	184	¹⁸⁴W	183.950 928	30.67%
75	Rhenium	187	¹⁸⁷Re	186.955 744	62.6%, β^–	4.6 × 10¹⁰y
76	Osmium	191	¹⁹¹Os	190.960 920	β^–	15.4 d
		192	¹⁹²Os	191.961 467	41.0%
77	Iridium	191	¹⁹¹Ir	190.960 584	37.3%
		193	¹⁹³Ir	192.962 917	62.7%
78	Platinum	195	¹⁹⁵Pt	194.964 766	33.8%
79	Gold	197	¹⁹⁷Au	196.966 543	100%
		198	¹⁹⁸Au	197.968 217	β^–	2.696 d
80	Mercury	199	¹⁹⁹Hg	198.968 253	16.87%
		202	²⁰²Hg	201.970 617	29.86%
81	Thallium	205	²⁰⁵Tl	204.974 401	70.48%
82	Lead	206	²⁰⁶Pb	205.974 440	24.1%
		207	²⁰⁷Pb	206.975 872	22.1%
		208	²⁰⁸Pb	207.976 627	52.4%
		210	²¹⁰Pb	209.984 163	α, β^–	22.3 y
		211	²¹¹Pb	210.988 735	β^–	36.1 min
		212	²¹²Pb	211.991 871	β^–	10.64 h
83	Bismuth	209	²⁰⁹Bi	208.980 374	100%
		211	²¹¹Bi	210.987 255	α, β^–	2.14 min
84	Polonium	210	²¹⁰Po	209.982 848	α	138.38 d
85	Astatine	218	²¹⁸At	218.008 684	α, β^–	1.6 s
86	Radon	222	²²²Rn	222.017 570	α	3.82 d
87	Francium 2	223	²²³Fr	223.019 733	α, β^–	21.8 min
88	Radium	226	²²⁶Ra	226.025 402	α	1.60 × 10³ y
89	Actinium	227	²²⁷Ac	227.027 750	α, β^–	21.8 y
90	Thorium	228	²²⁸Th	228.028 715	α	1.91 y
		232	²³²Th	232.038 054	100%, α	1.41 × 10¹⁰ y
91	Protactinium	231	²³¹Pa	231.035 880	α	3.28 × 10⁴ y
92	Uranium	233	²³³U	233.039 628	α	1.59 × 10³ y
		235	²³⁵U	235.043 924	0.720%, α	7.04 × 10⁸ y
		236	²³⁶U	236.045 562	α	2.34 × 10⁷ y
		238	²³⁸U	238.050 784	99.2745%, α	4.47 × 10⁹ y
		239	²³⁹U	239.054 289	β^–	23.5 min
93	Neptunium	239	²³⁹Np	239.052 933	β^–	2.355 d
94	Plutonium	239	²³⁹Pu	239.052 157	α	2.41 × 10⁴ y
95	Americium	243	²⁴³Am	243.061 375	α, fission	7.37 × 10³ y
96	Curium	245	²⁴⁵Cm	245.065 483	α	8.50 × 10³ y
97	Berkelium	245	²⁴⁷Bk	247.070 300	α	1.38 × 10³ y
98	Californium	249	²⁴⁹Cf	249.074 844	α	351 y
99	Einsteinium	254	²⁵⁴Es	254.088 019	α, β^–	276 d
100	Fermium	253	²⁵³Fm	253.085 173	EC, α	3.00 d
101	Mendelevium	255	²⁵⁵Md	255.091 081	EC, α	27 min
102	Nobelium	255	²⁵⁵No	255.093 260	EC, α	3.1 min
103	Lawrencium	257	²⁵⁷Lr	257.099 480	EC, α	0.646 s
104	Rutherfordium	261	²⁶¹Rf	261.108 690	α	1.08 mim
105	Dubnium	262	²⁶²Db	262.113 760	α, fission	34 s
106	Seaborgium	263	²⁶³Sg	263.11 86	α, fission	0.8 s
107	Bohrium	262	²⁶²Bh	262.123 1	α	0.102 s
108	Hassium	264	²⁶⁴Hs	264.128 5	α	0.08 ms
108	Meitnerium	266	²⁶⁶Mt	266.137 8	α	3.4 ms

Table A9 Atomic Masses and Decay

Isotope	^t1/2	Decay Mode	Energy(MeV)	Percent		T-Ray Energy(MeV)	Percent
³H	12.33 y	β^–	0.0186	100%
¹⁴C	5730 y	β^–	0.156	100%
¹³N	9.96 min	β⁺	1.20	100%
²²Na	2.602 y	β⁺	1.20	90%	γ	1.27	100%
³²P	14.28 d	β^–	1.71	100%
³⁵S	87.4 d	β^–	0.167	100%
³⁶Ci	3.00 × 105 y	β^–	0.710	100%
⁴⁰K	1.28 × 109 y	β^–	1.31	89%
⁴³K	22.3 h	β^–	0.827	87%	γs	0.373	87%
						0.618	87%
⁴⁵Ca	165 d	β^–	0.257	100%
⁵¹Cr	27.70 d	EC			γ	0.320	10%
⁵²Mn	5.59d	β⁺	3.69	28%	γ s	1.33	28%
						1.43	28%
⁵²Fe	8.27 h	β⁺	1.80	43%		0.169	43%
						0.378	43%
⁵⁹Fe	44.6 d	β^– s	0.273	45%	γ s	1.10	57%
			0.466	55%		1.29	43%
⁶⁰Co	5.271 y	β^–	0.318	100%	γ s	1.17	100%
						1.33	100%
⁶⁵Zn	244.1 d	EC			γ	1.12	51%
⁶⁷Ga	78.3 h	EC			γ s	0.0933	70%
						0.185	35%
						0.300	19%
						others
⁷⁵Se	118.5 d	EC			γ s	0.121	20%
						0.136	65%
						0.265	68%
						0.280	20%
						others
⁸⁶Rb	18.8 d	β^– s	0.69	9%	γ	1.08	9%
			1.77	91%
⁸⁵Sr	64.8 d	EC			γ	0.514 1	100%
⁹⁰Sr	28.8 y	β^–	0.546	100%
⁹⁰Y	64.1 h	β^–	2.28	100%
⁹⁹^mTc	6.02 h	IT			γ	0.142	100%
¹¹³mIn	99.5 ^min	IT			γ	0.392	100%
¹²³I	13.0 h	EC			γ	0.159	≈100%
¹³¹I	8.040 d	β^– s	0.248	7%	γ s	0.364	85%
			0.607	93%		others
			others
¹²⁹Cs	32.3 h	EC			γ s	0.0400	35%
						0.372	32%
						0.411	25%
						others
¹³⁷Cs	30.17 y	β^– s	0.511	95%	γ	0.662	95%
			1.17	5%
¹⁴⁰Ba	12.79 d	β^–	1.035	≈100%	γ s	0.030	25%
						0.044	65%
						0.537	24%
						others
¹⁹⁸Au	2.696 d	β^–	1.161	≈100%	γ	0.412	≈100%
¹⁹⁷Hg	64.1 h	EC			γ	0.0733	100%
²¹⁰Po	138.38 d	α	5.41	100%
²²⁶Ra	1.60 × 103 y	αs	4.68	5%	γ	0.186 1	100%
			4.87	95%
²³⁵U	7.038 × 108 y	α	4.68	≈100%	γ s	Numerous	<0.400%
²³⁸U	4.468 × 109 y	αs	4.22	23%	γ	0.050	23%
			4.27	77%
²³⁷Np	2.14 × 106 y	αs	numerous		γ s	numerous	<0.250%
			4.96 (max.)
²³⁹Pu	2.41 × 104 y	αs	5.19	11%	γ s	7.5 × 10-5	73%
			5.23	15%		0.013	15%
			5.24	73%		0.052	15%
						others
²⁴³Am	7.37 × 103 y	αs	Max. 5.44		γ s	0.075
			5.37	88%		others
			5.32	11%
			others

Table A10 Selected Radioactive Isotopes

Symbol	Meaning	Best Value	Approximate Value
m_e	Electron mass	9.10938291(40) × 10^–31 kg	9.11 × 10^–31 kg
m_p	Proton mass	1.672621777(74) × 10^–27 kg	1.6726 × 10^–27 kg
m_n	Neutron mass	1.674927351(74) × 10^–27 kg	1.6749 × 10^–27 kg
u	Atomic mass unit	1.660538921(73) × 10^–27 kg	1.6605 × 10^–27 kg

Table A11 Submicroscopic masses

Substance	p(kg/m³)	Substance	p(kg/m³)
Air	1.29	Iron	7.86 × 10³
Air (at 20°C and Atmospheric pressure)	1.20	Lead	11.3 × 10³
Aluminum	2.70 × 10³	Mercury	13.6 × 10³
Benzene	0.879 × 10³	Nitrogen gas	1.25
Brass	8.4 × 10³	Oak	0.710 × 10³
Copper	8.92 × 10³	Osmium	22.6 × 10³
Ethyl alcohol	0.806 × 10³	Oxygen gas	1.43
Fresh water	1.00 × 10³	Pine	0.373 × 10³
Glycerin	1.26 × 10³	Platinum	21.4 × 10³
Gold	1.93 × 10³	Seawater	1.03 × 10³
Helium gas	1.79 × 10^–1	Silver	10.5 × 10³
Hydrogen gas	8.99 × 10^–2	Tin	7.30 × 10³
Ice	0.917 × 10³	Uranium	18.7 × 10³

Table A12 Densities of common substances (including water at various temperatures)

Substance	Specific Heat (J/kg $\cdot \cdot$ °C)	Substance	Specific Heat (J/kg $\cdot \cdot$ °C)
Elemental solids		Other solids
Aluminum	900	Brass	380
Beryllium	1830	Glass	837
Cadmium	230	Ice (–5 °C)	2090
Copper	387	Marble	860
Germanium	322	Wood	1700
Gold	129	Liquids
Iron	448	Alcohol (ethyl)	2400
Lead	128	Mercury	140
Silicon	703	Water (15 °C)	4186
Silver	234	Gas
		Steam (100 °C)	2010
Note: To convert values to units of cal/g $\cdot \cdot$ °C, divide by 4186

Table A13 Specific heats of common substances

Substance	Melting Point (°C)	Latent Heat of Fusion (J/kg)	Boiling Point (°C)	Latent Heat of Vaporization (J/kg)
Helium	–272.2	5.23 × 10³	–268.93	2.09 × 10⁴
Oxygen	–218.79	1.38 × 10⁴	–182.97	2.13 × 10⁵
Nitrogen	–209.97	2.55 × 10⁴	–195.81	2.01 × 10⁵
Ethyl Alcohol	–114	1.04 × 10⁵	78	8.54 × 10⁵
Water	0.00	3.33 × 10⁵	100.00	2.26 × 10⁶
Sulfur	119	3.81 × 10⁴	444.60	2.90 × 10⁵
Lead	327.3	3.97 × 10⁵	1750	8.70 × 10⁵
Aluminum	660	3.97 × 10⁵	2516	1.05 × 10⁷
Silver	960.80	8.82 × 10⁴	2162	2.33 × 10⁶
Gold	1063.00	6.44 × 10⁴	2856	1.58 × 10⁶
Copper	1083	1.34 × 10⁵	2562	5.06 × 10⁶

Table A14 Heats of fusion and vaporization for common substances

Materials (Solids)	Average Linear Expansion Coefficient (a)(°C)^–1	Material (Liquids and Gases)	Average Volume Expansion Coefficient (B)(°C)^–1
Aluminum	24 × 10^–6	Acetone	1.5 × 10^–4
Brass and Bronze	19 × 10^–6	Alcohol, ethyl	1.12 × 10^–4
Concrete	12 × 10^–6	Benzene	1.24 × 10^–4
Copper	17 × 10^–6	Gasoline	9.6 × 10^–4
Glass (ordinary)	9 × 10^–6	Glycerin	4.85 × 10^–4
Glass (Pyrex)	3.2 × 10^–6	Mercury	1.82 × 10^–4
Invar (Ni-Fe alloy)	1.3 × 10^–6	Turpentine	9.0 × 10^–4
Lead	29 × 10^–6	Air* at 0°C	3.67 × 10^–3
Steel	13 × 10^–6	Helium*	3.665 × 10^–3
* The values given here assume the gases undergo expansion at constant pressure. However, the expansion of gases depends on the pressure applied to the gas. Therefore, gases do not have a specific value for the volume expansion coefficient.

Table A15 Coefficients of thermal expansion for common substances

Medium	v(m/s)	Medium	v(m/s)	Medium	v(m/s)
Gases		Liquids at 25°C		Solids*
Hydrogen	1286	Glycerol	1904	Pyrex glass	5640
Helium	972	Seawater	1533	Iron	5950
Air (20 °C)	343	Water	1493	Aluminum	5100
Air (0 °C)	331	Mercury	1450	Brass	4700
Oxygen	317	Kerosene	1324	Copper	3560
		Methyl Alcohol	1143	Gold	3240
		Carbon tetrachloride	926	Lucite	2680
				Lead	1322
				Rubber	1600
*Values given here are for propagation of longitudinal waves in bulk media. However, speeds for longitudinal waves in thin rods are slower, and speeds of transverse waves in bulk are even slower.

Table A16 Speed of sound in various substances

Source of Sound	B(dB)
Nearby jet airplane	150
Jackhammer machine gun	130
Siren; rock concert	120
Subway; power lawn mower	100
Busy traffic	80
Vacuum cleaner	70
Normal Conversation	60
Mosquito buzzing	40
whisper	30
Rustling leaves	10
Threshold of hearing	0

Table A17 Conversion of sound intensity to decibel level

Wavelength Range (nm)	Color Description
400-430	Violet
430-485	Blue
485-560	Green
560-590	Yellow
590-625	Orange
625-700	Red

Table A18 Wavelengths of visible light

Substance	Index of Refraction	Substance	Index of Refraction
Solids at 20°C		Liquids at 20°C
Cubic zirconia	2.15	Benzene	1.501
Diamond (C)	2.419	Carbon disulfide	1.628
Flourite (CaF₂)	1.434	Carbon tetrachloride	1.461
Fused quartz (SiO₂)	1.458	Ethyl alcohol	1.361
Gallium phosphide	3.50	Glycerin	1.473
Glass, crown	1.52	Water	1.333
Glass, flint	1.66
Ice (H₂O)	1.309	Gases at 0°C, 1 atm
Polystyrene	1.49	Air	1.000 293
Sodium chloride (NaCl)	1.544	Carbon dioxide	1.000 45
Note: These values assume that light has a wavelength of 589 nm in vacuum.

Table A19 Indices of refraction

Hoop or thin cylindrical shell	$I_{C M} = M R^{2} I_{C M} = M R^{2}$
Hollow cylinder	$I_{C M} = \frac{1}{2} M (R_{1}^{2} + R_{2}^{2}) I_{C M} = \frac{1}{2} M (R_{1}^{2} + R_{2}^{2})$
Solid cylinder or disk	$I_{C M} = \frac{1}{2} M R^{2} I_{C M} = \frac{1}{2} M R^{2}$
Rectangular plane	$I_{C M} = \frac{1}{12} M (a^{2} + b^{2}) I_{C M} = \frac{1}{12} M (a^{2} + b^{2})$
Long, thin rod with rotation axis through center	$I_{C M} = \frac{1}{12} M L^{2} I_{C M} = \frac{1}{12} M L^{2}$
Long, thin rod with rotation axis through end	$I_{C M} = \frac{1}{3} M L^{2} I_{C M} = \frac{1}{3} M L^{2}$
Solid sphere	$I_{C M} = \frac{2}{5} M R^{2} I_{C M} = \frac{2}{5} M R^{2}$
Thin spherical shell	$I_{C M} = \frac{2}{3} M R^{2} I_{C M} = \frac{2}{3} M R^{2}$

Table A20 Moments of inertia for different shapes

	μ_s	μ_k
Rubber on dry concrete	1.0	0.8
Steel on steel	0.74	0.57
Aluminum on steel	0.61	0.47
Glass on glass	0.94	0.4
Copper on steel	0.53	0.36
Wood on wood	0.25-0.5	0.2
Waxed wood on wet snow	0.14	0.1
Waxed wood on dry snow	0.1	0.04
Metal on metal (lubricated)	0.15	0.06
Teflon on Teflon	0.04	0.04
Ice on ice	0.1	0.03
Synovial joints in humans	0.01	0.003
Note: All values are approximate. In some cases, the coefficient of friction can exceed 1.0.

Table A21 Coefficients of friction for common objects on other objects

Material	Dielectric Constant ĸ	Dielectric Strength* (10⁶V/m)
Air (dry)	1.000 59	3
Bakelite	4.9	24
Fused quartz	4.3	8
Mylar	3.2	7
Neoprene rubber	6.7	12
Nylon	3.4	14
Paper	3.7	16
Paraffin-impregnated paper	3.5	11
Polystyrene	2.56	24
Polyvinyl chloride	3.4	40
Porcelain	6	8
Pyrex glass	5.6	14
Silicone oil	2.5	15
Strontium titanate	233	8
Teflon	2.1	60
Vacuum	1.000 00	∞
Water	80	3

Table A22 Dielectric constants