Appendix A: Useful Information

Dr. Iftekhar Haque

Appendix A: Useful Information

This appendix is broken into several tables.

Table A1, Important Constants
Table A2, Submicroscopic Masses
Table A3, Solar System Data
Table A4, Metric Prefixes for Powers of Ten and Their Symbols
Table A5, The Greek Alphabet
Table A6, SI units
Table A7, Selected British Units
Table A8, Other Units
Table A9, Useful Formulae

Table A1 Important Constants
Symbol	Meaning	Best Value	Approximate Value
$c$ $c$	Speed of light in vacuum	$2 . 99792458 \times 10^{8} m / s$ $2 . 99792458 \times 10^{8} m / s$	$3 . 00 \times 10^{8} m / s$ $3 . 00 \times 10^{8} m / s$
$G$ $G$	Gravitational constant	$6.67408 (31) \times 10^{- 11} N \cdot m^{2} / {kg}^{2}$ $6.67408 (31) \times 10^{- 11} N \cdot m^{2} / {kg}^{2}$	$6 . 67 \times 10^{- 11} N \cdot m^{2} / {kg}^{2}$ $6 . 67 \times 10^{- 11} N \cdot m^{2} / {kg}^{2}$
$N_{A}$ $N_{A}$	Avogadro’s number	$6.02214076 \times 10^{23}$ $6.02214076 \times 10^{23}$	$6 . 02 \times 10^{23}$ $6 . 02 \times 10^{23}$
$k$ $k$	Boltzmann’s constant	$1.380649 \times 10^{- 23} J / K$ $1.380649 \times 10^{- 23} J / K$	$1 . 38 \times 10^{- 23} J / K$ $1 . 38 \times 10^{- 23} J / K$
$R$ $R$	Gas constant	$8.3144621 (75) J / mol \cdot K$ $8.3144621 (75) J / mol \cdot K$	$\begin{matrix} 8.31 J/mol \cdot K = 1.99 cal/mol \cdot K \\ = 0.0821 atm \cdot L/mol \cdot K \end{matrix}$ $\begin{matrix} 8.31 J/mol \cdot K = 1.99 cal/mol \cdot K \\ = 0.0821 atm \cdot L/mol \cdot K \end{matrix}$
$σ$ $σ$	Stefan-Boltzmann constant	$5.670373 (21) \times 10^{- 8} W / m^{2} \cdot K$ $5.670373 (21) \times 10^{- 8} W / m^{2} \cdot K$	$5 . 67 \times 10^{- 8} W / m^{2} \cdot K$ $5 . 67 \times 10^{- 8} W / m^{2} \cdot K$
$k$ $k$	Coulomb force constant	$8.987551788 . . . \times 10^{9} N \cdot m^{2} / C^{2}$ $8.987551788 . . . \times 10^{9} N \cdot m^{2} / C^{2}$	$8.99 \times 10^{9} N \cdot m^{2} / C^{2}$ $8.99 \times 10^{9} N \cdot m^{2} / C^{2}$
$q_{e}$ $q_{e}$	Charge on electron	$- 1.602176634 \times 10^{- 19} C$ $- 1.602176634 \times 10^{- 19} C$	$- 1 . 60 \times 10^{- 19} C$ $- 1 . 60 \times 10^{- 19} C$
$ε_{0}$ $ε_{0}$	Permittivity of free space	$8.854187817 . . . \times 10^{- 12} C^{2} / N \cdot m^{2}$ $8.854187817 . . . \times 10^{- 12} C^{2} / N \cdot m^{2}$	$8 . 85 \times 10^{- 12} C^{2} / N \cdot m^{2}$ $8 . 85 \times 10^{- 12} C^{2} / N \cdot m^{2}$
$μ_{0}$ $μ_{0}$	Permeability of free space	$4π \times 10^{- 7} T \cdot m / A$ $4π \times 10^{- 7} T \cdot m / A$	$1 . 26 \times 10^{- 6} T \cdot m / A$ $1 . 26 \times 10^{- 6} T \cdot m / A$
$h$ $h$	Planck’s constant	$6.62607015 \times 10^{- 34} J \cdot s$ $6.62607015 \times 10^{- 34} J \cdot s$	$6 . 63 \times 10^{- 34} J \cdot s$ $6 . 63 \times 10^{- 34} J \cdot s$

Table A2 Submicroscopic Masses
Symbol	Meaning	Best Value	Approximate Value
$m_{e}$	Electron mass	$9.10938291 (40) \times 10^{- 31} kg$	$9 . 11 \times 10^{- 31} kg$
$m_{p}$	Proton mass	$1.672621777 (74) \times 10^{- 27} kg$	$1 . 6726 \times 10^{- 27} kg$
$m_{n}$	Neutron mass	$1.674927351 (74) \times 10^{- 27} kg$	$1 . 6749 \times 10^{- 27} kg$
$u$	Atomic mass unit	$1.660538921 (73) \times 10^{- 27} kg$	$1 . 6605 \times 10^{- 27} kg$

Table A3 Solar System Data
Sun	mass	$1 . 99 \times 10^{30} kg$
	average radius	$6 . 96 \times 10^{8} m$
	Earth-sun distance (average)	$1 . 496 \times 10^{11} m$
Earth	mass	$5 . 9736 \times 10^{24} kg$
	average radius	$6 . 376 \times 10^{6} m$
	orbital period	$3 . 16 \times 10^{7} s$
Moon	mass	$7 . 35 \times 10^{22} kg$
	average radius	$1 . 74 \times 10^{6} m$
	orbital period (average)	$2 . 36 \times 10^{6} s$
	Earth-moon distance (average)	$3 . 84 \times 10^{8} m$

Table A4 Metric Prefixes for Powers of Ten and Their Symbols
Prefix	Symbol	Value	Prefix	Symbol	Value
tera	T	$10^{12}$ $10^{12}$	deci	d	$10^{- 1}$ $10^{- 1}$
giga	G	$10^{9}$ $10^{9}$	centi	c	$10^{- 2}$ $10^{- 2}$
mega	M	$10^{6}$ $10^{6}$	milli	m	$10^{- 3}$ $10^{- 3}$
kilo	k	$10^{3}$ $10^{3}$	micro	$μ$	$10^{- 6}$ $10^{- 6}$
hecto	h	$10^{2}$ $10^{2}$	nano	n	$10^{- 9}$ $10^{- 9}$
deka	da	$10^{1}$ $10^{1}$	pico	p	$10^{- 12}$ $10^{- 12}$
—	—	$10^{0} (= 1)$ $10^{0} (= 1)$	femto	f	$10^{- 15}$ $10^{- 15}$

Table A5 The Greek Alphabet
Alpha	$Α$ $Α$	$α$ $α$	Eta	$Η$ $Η$	$η$ $η$	Nu	$Ν$ $Ν$	$ν$ $ν$	Tau	$Τ$ $Τ$	$τ$ $τ$
Beta	$Β$ $Β$	$β$ $β$	Theta	$Θ$ $Θ$	$θ$ $θ$	Xi	$Ξ$ $Ξ$	$ξ$ $ξ$	Upsilon	$Υ$ $Υ$	$υ$ $υ$
Gamma	$Γ$ $Γ$	$γ$ $γ$	Iota	$Ι$ $Ι$	$ι$ $ι$	Omicron	$Ο$ $Ο$	$ο$ $ο$	Phi	$Φ$ $Φ$	$ϕ$ $ϕ$
Delta	$Δ$ $Δ$	$δ$ $δ$	Kappa	$Κ$ $Κ$	$κ$ $κ$	Pi	$Π$ $Π$	$π$ $π$	Chi	$Χ$ $Χ$	$χ$ $χ$
Epsilon	$Ε$ $Ε$	$ε$ $ε$	Lambda	$Λ$ $Λ$	$λ$ $λ$	Rho	$Ρ$ $Ρ$	$ρ$ $ρ$	Psi	$Ψ$ $Ψ$	$ψ$ $ψ$
Zeta	$Ζ$ $Ζ$	$ζ$ $ζ$	Mu	$Μ$ $Μ$	$μ$ $μ$	Sigma	$Σ$ $Σ$	$σ$ $σ$	Omega	$Ω$ $Ω$	$ω$ $ω$

Table A6 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	$N = kg \cdot m / s^{2}$	newton
	Energy	$J = kg \cdot m^{2} / s^{2}$	joule
	Power	$W = J / s$	watt
	Pressure	$Pa = N / m^{2}$	pascal
	Frequency	$Hz = 1 / s$	hertz
	Electronic potential	$V = J / C$	volt
	Capacitance	$F = C / V$	farad
	Charge	$C = s \cdot A$	coulomb
	Resistance	$Ω = V / A$	ohm
	Magnetic field	$T = N / (A \cdot m)$	tesla
	Nuclear decay rate	$Bq = 1 / s$	becquerel

Table A7 Selected British Units
Length	$1 inch (in .) = 2 . 54 cm (exactly)$ $1 inch (in .) = 2 . 54 cm (exactly)$
	$1 foot (ft) = 0 . 3048 m$ $1 foot (ft) = 0 . 3048 m$
	$1 mile (mi) = 1 . 609 km$ $1 mile (mi) = 1 . 609 km$
Force	$1 pound (lb) = 4 . 448 N$ $1 pound (lb) = 4 . 448 N$
Energy	$1 British thermal unit (Btu) = 1 . 055 \times 10^{3} J$ $1 British thermal unit (Btu) = 1 . 055 \times 10^{3} J$
Power	$1 horsepower (hp) = 746 W$ $1 horsepower (hp) = 746 W$
Pressure	$1 lb / {in}^{2} = 6 . 895 \times 10^{3} Pa$ $1 lb / {in}^{2} = 6 . 895 \times 10^{3} Pa$

Table A8 Other Units
Length	$1 light year (ly) = 9 . 46 \times 10^{15} m$ $1 light year (ly) = 9 . 46 \times 10^{15} m$
	$1 astronomical unit (au) = 1 . 50 \times 10^{11} m$ $1 astronomical unit (au) = 1 . 50 \times 10^{11} m$
	$1 nautical mile = 1 . 852 km$ $1 nautical mile = 1 . 852 km$
	$1 angstrom (Å) = 10^{- 10} m$ $1 angstrom (Å) = 10^{- 10} m$
Area	$1 acre (ac) = 4 . 05 \times 10^{3} m^{2}$ $1 acre (ac) = 4 . 05 \times 10^{3} m^{2}$
	$1 square foot ({ft}^{2}) = 9 . 29 \times 10^{- 2} m^{2}$ $1 square foot ({ft}^{2}) = 9 . 29 \times 10^{- 2} m^{2}$
	$1 barn (b) = 10^{- 28} m^{2}$ $1 barn (b) = 10^{- 28} m^{2}$
Volume	$1 liter (L) = 10^{- 3} m^{3}$ $1 liter (L) = 10^{- 3} m^{3}$
Volume	$1 U.S. gallon (gal) = 3 . 785 \times 10^{- 3} m^{3}$ $1 U.S. gallon (gal) = 3 . 785 \times 10^{- 3} m^{3}$
Mass	$1 solar mass = 1 . 99 \times 10^{30} kg$ $1 solar mass = 1 . 99 \times 10^{30} kg$
	$1 metric ton = 10^{3} kg$ $1 metric ton = 10^{3} kg$
	$1 atomic mass unit (u) = 1 . 6605 \times 10^{- 27} kg$ $1 atomic mass unit (u) = 1 . 6605 \times 10^{- 27} kg$
Time	$1 year (y) = 3 . 16 \times 10^{7} s$ $1 year (y) = 3 . 16 \times 10^{7} s$
Time	$1 day (d) = 86, 400 s$ $1 day (d) = 86, 400 s$
Speed	$1 mile per hour (mph) = 1 . 609 km / h$ $1 mile per hour (mph) = 1 . 609 km / h$
Speed	$1 nautical mile per hour (naut) = 1 . 852 km / h$ $1 nautical mile per hour (naut) = 1 . 852 km / h$
Angle	$1 degree (°) = 1 . 745 \times 10^{- 2} rad$ $1 degree (°) = 1 . 745 \times 10^{- 2} rad$
	$1 minute of arc (^{'}) = 1 / 60 degree$ $1 minute of arc (^{‘}) = 1 / 60 degree$
	$1 second of arc (^{''}) = 1 / 60 minute of arc$ $1 second of arc (^{”}) = 1 / 60 minute of arc$
	$1 grad = 1 . 571 \times 10^{- 2} rad$ $1 grad = 1 . 571 \times 10^{- 2} rad$
Energy	$1 kiloton TNT (kT) = 4 . 2 \times 10^{12} J$ $1 kiloton TNT (kT) = 4 . 2 \times 10^{12} J$
	$1 kilowatt hour (kW \cdot h) = 3 . 60 \times 10^{6} J$ $1 kilowatt hour (kW \cdot h) = 3 . 60 \times 10^{6} J$
	$1 food calorie (kcal) = 4186 J$ $1 food calorie (kcal) = 4186 J$
	$1 calorie (cal) = 4 . 186 J$ $1 calorie (cal) = 4 . 186 J$
	$1 electron volt (eV) = 1 . 60 \times 10^{- 19} J$ $1 electron volt (eV) = 1 . 60 \times 10^{- 19} J$
Pressure	$1 atmosphere (atm) = 1 . 013 \times 10^{5} Pa$ $1 atmosphere (atm) = 1 . 013 \times 10^{5} Pa$
	$1 millimeter of mercury (mm Hg) = 133 . 3 Pa$ $1 millimeter of mercury (mm Hg) = 133 . 3 Pa$
	$1 torricelli (torr) = 1 mm Hg = 133 . 3 Pa$ $1 torricelli (torr) = 1 mm Hg = 133 . 3 Pa$
Nuclear decay rate	$1 curie (Ci) = 3 . 70 \times 10^{10} Bq$ $1 curie (Ci) = 3 . 70 \times 10^{10} Bq$

Table A9 Useful Formulae
Circumference of a circle with radius $r$ $r$ or diameter $d$ $d$	$C = 2 πr = πd$ $C = 2 πr = πd$
Area of a circle with radius $r$ $r$ or diameter $d$ $d$	$A = {πr}^{2} = {πd}^{2} / 4$ $A = {πr}^{2} = {πd}^{2} / 4$
Area of a sphere with radius $r$ $r$	$A = 4 {πr}^{2}$ $A = 4 {πr}^{2}$
Volume of a sphere with radius $r$ $r$	$V = (4 / 3) ({πr}^{3})$ $V = (4 / 3) ({πr}^{3})$

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