Appendix C. Useful Information



Table 1. Important Constants[3]
Symbol Meaning Best Value Approximate Value
c Speed of light in vacuum 2.99792458 × 108 m/s 3.00 × 108 m/s
G Gravitational constant 6.67384(80) × 10−11 N · m2/kg2 6.67 × 10−11 N · m2/kg2
NA Avogadro’s number 6.02214129(27) × 1023 6.02 × 1023
k Boltzmann’s constant 1.3806488(13) × 10−23 J/K 1.38 × 10−23 J/K
R Gas constant 8.3144621(75) J/mol · K 8.31 J/mol · K = 1.99 cal/mol · K = 0.0821 atm · L/mol · K
σ Stefan-Boltzmann constant 5.670373(21) × 10−8 W/m2 · K 5.67 × 10−8 W/m2 · K
k Coulomb force constant 8.987551788... × 109 N · m2/C2 8.99 × 109 N · m2/C2
qe Charge on electron −1.602176565(35) × 10−19 C −1.60 × 10−19 C
ε0 Permittivity of free space 8.854187817... × 10−12 C2/N · m2 8.85 × 10−12 C2/N · m2
µ0 Permeability of free space 4π × 10−7 T · m/A 1.26 × 10−6 T · m/A
h Planck’s constant 6.62606957(29) × 10−34 J · s 6.63 × 10−34 J · s
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Table 2. Submicroscopic Masses[4]
Symbol Meaning Best Value Approximate Value
me Electron mass 9.10938291(40) × 10−31 kg 9.11 × 10−31 kg
mp Proton mass 1.672621777(74) × 10−27 kg 1.6726 × 10−27 kg
mn 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
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Table 3. Solar System Data
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
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Table 4. Metric Prefixes for Powers of Ten and Their Symbols
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 (= 1) femto f 10−15
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Table 5. The Greek Alphabet
Alpha Α α Eta Η η Nu Ν ν
Beta Β β Tau Τ τ Theta Θ θ
Xi Ξ ξ Upsilon Υ υ Gamma Γ γ
Iota Ι ι Omicron Ο ο Phi φ ϕ
Delta Δ δ Kappa Κ κ Pi Π π
Chi Χ χ Epsilon Ε ε Lambda Λ λ
Rho Ρ ρ Psi Ψ ψ Zeta Ζ ζ
Mu Μ μ Sigma Σ σ Omega Ω ω
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Table 6. SI Units
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 = kg ⋅ m/s2 newton
Energy J = kg ⋅ m2/s2 joule
Power W = J/s watt
Pressure Pa = N/m2 pascal
Frequency Hz = 1/s hertz
Electronic potential V = J/C volt
Capacitance F = C/V farad
Charge C = s ⋅ A coulomb
Resistance Ω = V/A ohm
Magnetic field T = N/(A ⋅ m) tesla
Nuclear decay rate Bq = 1/s becquerel
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Table 7. Selected British 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
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Table 8. Other 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 m2
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
1metric 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 (°) = 1.745 × 10−2 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 ⋅ h) = 3.60 × 106 J
1 food calorie (kcal) = 4186 J
1 calorie (cal) = 4.186 J
1 electron volt (eV) = 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
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Table 9. Useful Formulae
Circumference of a circle with radius r or diameter d
C=2πr=πdC=2\pi{r}=\pi{d}\\
Area of a circle with radius r or diameter d
A=πr2=πd24A=\pi{r}^{2}=\frac{\pi{d}^{2}}{4}\\
Area of a sphere with radius r
A=4πr2A=4\pi{r}^{2}\\
Volume of a sphere with radius r
V=43(πr3)V=\frac{4}{3}\left(\pi{r}^{3}\right)\\
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  1. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
  2. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
  3. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
  4. Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (accessed May 18, 2012). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.

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