[latexpage]
This appendix is broken into several tables.
Important Constants
| Symbol |
Meaning |
Best Value |
Approximate Value |
| \(c\) |
Speed of light in vacuum |
\(2\text{.}\text{99792458}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s}\) |
\(3\text{.}\text{00}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{8}\phantom{\rule{0.15em}{0ex}}\text{m}/\text{s}\) |
| \(G\) |
Gravitational constant |
\(6\text{.}\text{67408}\left(\text{31}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2}\) |
\(6\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{11}}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{kg}}^{2}\) |
| \({N}_{A}\) |
Avogadro’s number |
\(6.02214076\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}\) |
\(6\text{.}\text{02}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{\text{23}}\) |
| \(k\) |
Boltzmann’s constant |
\(1.380649\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}\) |
\(1\text{.}\text{38}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{23}}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{K}\) |
| \(R\) |
Gas constant |
\(8\text{.}\text{3144621}\left(\text{75}\right)\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K}\) |
\(8\text{.}\text{31}\phantom{\rule{0.15em}{0ex}}\text{J}/\text{mol}\cdot \text{K}=1\text{.}\text{99}\phantom{\rule{0.20em}{0ex}}\text{cal}/\text{mol}\cdot \text{K}=0\text{.}\text{0821}\text{atm}\cdot \text{L}/\text{mol}\cdot \text{K}\) |
| \(\text{σ}\) |
Stefan-Boltzmann constant |
\(5\text{.}\text{670373}\left(\text{21}\right)\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K}\) |
\(5\text{.}\text{67}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-8}\phantom{\rule{0.15em}{0ex}}\text{W}/{\text{m}}^{2}\cdot \text{K}\) |
| \(k\) |
Coulomb force constant |
\(8\text{.}\text{987551788}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}\) |
\(8.99\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{9}\phantom{\rule{0.15em}{0ex}}\text{N}\cdot {\text{m}}^{2}/{\text{C}}^{2}\) |
| \({q}_{e}\) |
Charge on electron |
\(-1.602176634\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}\) |
\(-1\text{.}\text{60}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{19}}\phantom{\rule{0.15em}{0ex}}\text{C}\) |
| \({\text{ε}}_{0}\) |
Permittivity of free space |
\(8\text{.}\text{854187817}\text{.}\text{.}\text{.}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2}\) |
\(8\text{.}\text{85}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{12}}\phantom{\rule{0.15em}{0ex}}{\text{C}}^{2}/\text{N}\cdot {\text{m}}^{2}\) |
| \({\text{μ}}_{0}\) |
Permeability of free space |
\(4\pi \phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-7}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A}\) |
\(1\text{.}\text{26}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-6}\phantom{\rule{0.15em}{0ex}}\text{T}\cdot \text{m}/\text{A}\) |
| \(h\) |
Planck’s constant |
\(6.62607015\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}\) |
\(6\text{.}\text{63}\phantom{\rule{0.15em}{0ex}}×\phantom{\rule{0.15em}{0ex}}{\text{10}}^{-\text{34}}\phantom{\rule{0.15em}{0ex}}\text{J}\cdot \text{s}\) |
Submicroscopic Masses
| Symbol |
Meaning |
Best Value |
Approximate Value |
| \({m}_{e}\) |
Electron mass |
\(9\text{.}\text{10938291}\left(\text{40}\right)×{\text{10}}^{-\text{31}}\text{kg}\) |
\(9\text{.}\text{11}×{\text{10}}^{-\text{31}}\text{kg}\) |
| \({m}_{p}\) |
Proton mass |
\(1\text{.}\text{672621777}\left(\text{74}\right)×{\text{10}}^{-\text{27}}\text{kg}\) |
\(1\text{.}\text{6726}×{\text{10}}^{-\text{27}}\text{kg}\) |
| \({m}_{n}\) |
Neutron mass |
\(1\text{.}\text{674927351}\left(\text{74}\right)×{\text{10}}^{-\text{27}}\text{kg}\) |
\(1\text{.}\text{6749}×{\text{10}}^{-\text{27}}\text{kg}\) |
| \(\text{u}\) |
Atomic mass unit |
\(1\text{.}\text{660538921}\left(\text{73}\right)×{\text{10}}^{-\text{27}}\text{kg}\) |
\(1\text{.}\text{6605}×{\text{10}}^{-\text{27}}\text{kg}\) |
Solar System Data
| Sun |
mass |
\(1\text{.}\text{99}×{\text{10}}^{\text{30}}\text{kg}\) |
|
average radius |
\(6\text{.}\text{96}×{\text{10}}^{8}\text{m}\) |
|
Earth-sun distance (average) |
\(1\text{.}\text{496}×{\text{10}}^{\text{11}}\text{m}\) |
| Earth |
mass |
\(5\text{.}\text{9736}×{\text{10}}^{\text{24}}\text{kg}\) |
|
average radius |
\(6\text{.}\text{376}×{\text{10}}^{6}\text{m}\)\(\) |
|
orbital period |
\(3\text{.}\text{16}×{\text{10}}^{7}\text{s}\) |
| Moon |
mass |
\(7\text{.}\text{35}×{\text{10}}^{\text{22}}\text{kg}\) |
|
average radius |
\(1\text{.}\text{74}×{\text{10}}^{6}\text{m}\) |
|
orbital period (average) |
\(2\text{.}\text{36}×{\text{10}}^{6}\text{s}\) |
|
Earth-moon distance (average) |
\(3\text{.}\text{84}×{\text{10}}^{8}\text{m}\) |
Metric Prefixes for Powers of Ten and Their Symbols
| Prefix |
Symbol |
Value |
Prefix |
Symbol |
Value |
| tera |
T |
\({\text{10}}^{\text{12}}\) |
deci |
d |
\({\text{10}}^{-1}\) |
| giga |
G |
\({\text{10}}^{9}\) |
centi |
c |
\({\text{10}}^{-2}\) |
| mega |
M |
\({\text{10}}^{6}\) |
milli |
m |
\({\text{10}}^{-3}\) |
| kilo |
k |
\({\text{10}}^{3}\) |
micro |
\(\mu \) |
\({\text{10}}^{-6}\) |
| hecto |
h |
\({\text{10}}^{2}\) |
nano |
n |
\({\text{10}}^{-9}\) |
| deka |
da |
\({\text{10}}^{1}\) |
pico |
p |
\({\text{10}}^{-\text{12}}\) |
| — |
— |
\({\text{10}}^{0}\left(=1\right)\) |
femto |
f |
\({\text{10}}^{-\text{15}}\) |
The Greek Alphabet
| Alpha |
\(\text{Α}\) |
\(\alpha \) |
Eta |
\(\text{Η}\) |
\(\eta \) |
Nu |
\(\text{Ν}\) |
\(\nu \) |
Tau |
\(\text{Τ}\) |
\(\tau \) |
| Beta |
\(\text{Β}\) |
\(\beta \) |
Theta |
\(\text{Θ}\) |
\(\theta \) |
Xi |
\(\text{Ξ}\) |
\(\xi \) |
Upsilon |
\(\text{Υ}\) |
\(\upsilon \) |
| Gamma |
\(\text{Γ}\) |
\(\gamma \) |
Iota |
\(\text{Ι}\) |
\(\iota \) |
Omicron |
\(\text{Ο}\) |
\(ο\) |
Phi |
\(\text{Φ}\) |
\(\varphi \) |
| Delta |
\(\text{Δ}\) |
\(\delta \) |
Kappa |
\(\text{Κ}\) |
\(\kappa \) |
Pi |
\(\text{Π}\) |
\(\pi \) |
Chi |
\(\text{Χ}\) |
\(\chi \) |
| Epsilon |
\(\text{Ε}\) |
\(\epsilon \) |
Lambda |
\(\text{Λ}\) |
\(\lambda \) |
Rho |
\(\text{Ρ}\) |
\(\rho \) |
Psi |
\(\text{Ψ}\) |
\(\psi \) |
| Zeta |
\(\text{Ζ}\) |
\(\zeta \) |
Mu |
\(\text{Μ}\) |
\(\mu \) |
Sigma |
\(\text{Σ}\) |
\(\sigma \) |
Omega |
\(\Omega \) |
\(\omega \) |
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 |
\(\text{N}=\text{kg}\cdot \text{m}/{\text{s}}^{2}\) |
newton |
|
Energy |
\(\text{J}=\text{kg}\cdot {\text{m}}^{2}/{\text{s}}^{2}\) |
joule |
|
Power |
\(\text{W}=\text{J}/\text{s}\) |
watt |
|
Pressure |
\(\text{Pa}=\text{N}/{\text{m}}^{2}\) |
pascal |
|
Frequency |
\(\text{Hz}=1/\text{s}\) |
hertz |
|
Electronic potential |
\(\text{V}=\text{J}/\text{C}\) |
volt |
|
Capacitance |
\(\text{F}=\text{C}/\text{V}\) |
farad |
|
Charge |
\(\text{C}=\text{s}\cdot \text{A}\) |
coulomb |
|
Resistance |
\(\Omega =\text{V}/\text{A}\) |
ohm |
|
Magnetic field |
\(\text{T}=\text{N}/\left(\text{A}\cdot \text{m}\right)\) |
tesla |
|
Nuclear decay rate |
\(\text{Bq}=1/\text{s}\) |
becquerel |
Selected British Units
| Length |
\(1\phantom{\rule{0.20em}{0ex}}\text{inch}\phantom{\rule{0.20em}{0ex}}\left(\text{in}\text{.}\right)=2\text{.}\text{54}\phantom{\rule{0.20em}{0ex}}\text{cm}\phantom{\rule{0.20em}{0ex}}\left(\text{exactly}\right)\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{foot}\phantom{\rule{0.20em}{0ex}}\left(\text{ft}\right)=0\text{.}\text{3048}\phantom{\rule{0.20em}{0ex}}\text{m}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{mile}\phantom{\rule{0.20em}{0ex}}\left(\text{mi}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}\) |
| Force |
\(1\phantom{\rule{0.20em}{0ex}}\text{pound}\phantom{\rule{0.20em}{0ex}}\left(\text{lb}\right)=4\text{.}\text{448}\phantom{\rule{0.20em}{0ex}}\text{N}\) |
| Energy |
\(1\phantom{\rule{0.20em}{0ex}}\text{British thermal unit}\phantom{\rule{0.20em}{0ex}}\left(\text{Btu}\right)=1\text{.}\text{055}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{J}\) |
| Power |
\(1\phantom{\rule{0.20em}{0ex}}\text{horsepower}\phantom{\rule{0.20em}{0ex}}\left(\text{hp}\right)=\text{746}\phantom{\rule{0.20em}{0ex}}\text{W}\) |
| Pressure |
\(1\phantom{\rule{0.20em}{0ex}}\text{lb}/{\text{in}}^{2}=6\text{.}\text{895}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{Pa}\) |
Other Units
| Length |
\(1\phantom{\rule{0.20em}{0ex}}\text{light year}\phantom{\rule{0.20em}{0ex}}\left(\text{ly}\right)=9\text{.}\text{46}×{\text{10}}^{\text{15}}\phantom{\rule{0.20em}{0ex}}\text{m}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{astronomical unit}\phantom{\rule{0.20em}{0ex}}\left(\text{au}\right)=1\text{.}\text{50}×{\text{10}}^{\text{11}}\phantom{\rule{0.20em}{0ex}}\text{m}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{nautical mile}=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{angstrom}\left(\text{Å}\right)\phantom{\rule{0.20em}{0ex}}={\text{10}}^{-\text{10}}\phantom{\rule{0.20em}{0ex}}\text{m}\) |
| Area |
\(1\phantom{\rule{0.20em}{0ex}}\text{acre}\phantom{\rule{0.20em}{0ex}}\left(\text{ac}\right)=4\text{.}\text{05}×{\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{square foot}\phantom{\rule{0.20em}{0ex}}\left({\text{ft}}^{2}\right)=9\text{.}\text{29}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{barn}\phantom{\rule{0.20em}{0ex}}\left(b\right)={\text{10}}^{-\text{28}}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{2}\) |
| Volume |
\(1\phantom{\rule{0.20em}{0ex}}\text{liter}\phantom{\rule{0.20em}{0ex}}\left(L\right)={\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{U.S. gallon}\phantom{\rule{0.20em}{0ex}}\left(\text{gal}\right)=3\text{.}\text{785}×{\text{10}}^{-3}\phantom{\rule{0.20em}{0ex}}{\text{m}}^{3}\) |
| Mass |
\(1\phantom{\rule{0.20em}{0ex}}\text{solar mass}\phantom{\rule{0.20em}{0ex}}=1\text{.}\text{99}×{\text{10}}^{\text{30}}\phantom{\rule{0.20em}{0ex}}\text{kg}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{metric ton}={\text{10}}^{3}\phantom{\rule{0.20em}{0ex}}\text{kg}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{atomic mass unit}\phantom{\rule{0.20em}{0ex}}\left(u\right)=1\text{.}\text{6605}×{\text{10}}^{-\text{27}}\phantom{\rule{0.20em}{0ex}}\text{kg}\) |
| Time |
\(1\phantom{\rule{0.20em}{0ex}}\text{year}\phantom{\rule{0.20em}{0ex}}\left(y\right)=3\text{.}\text{16}×{\text{10}}^{7}\phantom{\rule{0.20em}{0ex}}\text{s}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{day}\phantom{\rule{0.20em}{0ex}}\left(d\right)=\text{86},\text{400}\phantom{\rule{0.20em}{0ex}}\text{s}\) |
| Speed |
\(1\phantom{\rule{0.20em}{0ex}}\text{mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{mph}\right)=1\text{.}\text{609}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{nautical mile per hour}\phantom{\rule{0.20em}{0ex}}\left(\text{naut}\right)=1\text{.}\text{852}\phantom{\rule{0.20em}{0ex}}\text{km}/\text{h}\) |
| Angle |
\(1\phantom{\rule{0.20em}{0ex}}\text{degree}\phantom{\rule{0.20em}{0ex}}\left(°\right)=1\text{.}\text{745}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{minute of arc}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{‘}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{degree}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{second of arc}\text{}\phantom{\rule{0.20em}{0ex}}{\left(}^{\text{”}}\right)=1/\text{60}\phantom{\rule{0.20em}{0ex}}\text{minute of arc}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{grad}=1\text{.}\text{571}×{\text{10}}^{-2}\phantom{\rule{0.20em}{0ex}}\text{rad}\) |
| Energy |
\(1\phantom{\rule{0.20em}{0ex}}\text{kiloton TNT}\phantom{\rule{0.20em}{0ex}}\left(\text{kT}\right)=4\text{.}2×{\text{10}}^{\text{12}}\phantom{\rule{0.20em}{0ex}}\text{J}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{kilowatt hour}\phantom{\rule{0.20em}{0ex}}\left(\text{kW}\cdot h\right)=3\text{.}\text{60}×{\text{10}}^{6}\phantom{\rule{0.20em}{0ex}}\text{J}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{food calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{kcal}\right)=\text{4186}\phantom{\rule{0.20em}{0ex}}\text{J}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{calorie}\phantom{\rule{0.20em}{0ex}}\left(\text{cal}\right)=4\text{.}\text{186}\phantom{\rule{0.20em}{0ex}}\text{J}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{electron volt}\phantom{\rule{0.20em}{0ex}}\left(\text{eV}\right)=1\text{.}\text{60}×{\text{10}}^{-\text{19}}\phantom{\rule{0.20em}{0ex}}\text{J}\) |
| Pressure |
\(1\phantom{\rule{0.20em}{0ex}}\text{atmosphere}\phantom{\rule{0.20em}{0ex}}\left(\text{atm}\right)=1\text{.}\text{013}×{\text{10}}^{5}\phantom{\rule{0.20em}{0ex}}\text{Pa}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{millimeter of mercury}\phantom{\rule{0.20em}{0ex}}\left(\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}\right)=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}\) |
|
\(1\phantom{\rule{0.20em}{0ex}}\text{torricelli}\phantom{\rule{0.20em}{0ex}}\left(\text{torr}\right)=1\phantom{\rule{0.20em}{0ex}}\text{mm}\phantom{\rule{0.20em}{0ex}}\text{Hg}=\text{133}\text{.}3\phantom{\rule{0.20em}{0ex}}\text{Pa}\) |
| Nuclear decay rate |
\(1\phantom{\rule{0.20em}{0ex}}\text{curie}\phantom{\rule{0.20em}{0ex}}\left(\text{Ci}\right)=3\text{.}\text{70}×{\text{10}}^{\text{10}}\phantom{\rule{0.20em}{0ex}}\text{Bq}\) |
Useful Formulae
| Circumference of a circle with radius \(r\) or diameter \(d\) |
\(C=2\pi r=\mathrm{\pi d}\) |
| Area of a circle with radius \(r\) or diameter \(d\) |
\(A={\mathrm{\pi r}}^{2}={\mathrm{\pi d}}^{2}/4\) |
| Area of a sphere with radius \(r\) |
\(A=4{\pi r}^{2}\) |
| Volume of a sphere with radius \(r\) |
\(V=\left(4/3\right)\left({\mathrm{\pi r}}^{3}\right)\) |
