Chapter 17: Useful Information

Last updated
Save as PDF

Page ID: 46261

\( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)

This appendix is broken into several tables.

Table \(\PageIndex{1}\), Important Constants
Table \(\PageIndex{2}\), Submicroscopic Masses
Table \(\PageIndex{3}\), Solar System Data
Table \(\PageIndex{4}\), Metric Prefixes for Powers of Ten and Their Symbols
Table \(\PageIndex{5}\), The Greek Alphabet
Table \(\PageIndex{6}\), SI units
Table \(\PageIndex{7}\), Selected British Units
Table \(\PageIndex{8}\), Other Units
Table \(\PageIndex{9}\), Useful Formulae

**Table** \(\PageIndex{1}\): Important Constants^¹
Symbol	Meaning	Best Value	Approximate Value
\(c\)	Speed of light in vacuum	\(2.99792458 \times 10^{8} \mathrm{~m} / \mathrm{s}\)	\(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\)
\(G\)	Gravitational constant	\(6.67430(15) \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\)	\(6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\)
\(N_{A}\)	Avogadro’s number	\(6.02214076 \times 10^{23}\)	\(6.02 \times 10^{23}\)
\(k\)	Boltzmann’s constant	\(1.380649 \times 10^{-23} \mathrm{~J} / \mathrm{K}\)	\(1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}\)
\(R\)	Gas constant	\(8.314462618 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\)	\(8.31 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\)
\(\sigma\)	Stefan-Boltzmann constant	\(5.670374419 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)	\(5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)
\(k\)	Coulomb force constant	\(8.9875517923(13) \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\)	\(8.99 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\)
\(e\)	Elementary charge	\(1.602176634 \times 10^{-19} \mathrm{C}\)	\(1.60 \times 10^{-19} \mathrm{C}\)
\(\varepsilon_{0}\)	Permittivity of free space	\(8.8541878128(13) \times 10^{-12} \mathrm{C}^{2} / \mathrm{N} \cdot \mathrm{m}^{2}\)	\(8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{N} \cdot \mathrm{m}^{2}\)
\(\mu_{0}\)	Permeability of free space	\(4 \pi \times 10^{-7} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}\)	\(1.26 \times 10^{-6} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}\)
\(h\)	Planck’s constant	\(6.62607015 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\)	\(6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\)

**Table** \(\PageIndex{2}\): Submicroscopic Masses^²
Symbol	Meaning	Best Value	Approximate Value
\(m_{e}\)	Electron mass	\(9.1093837015(28) \times 10^{-31} \mathrm{~kg}\)	\(9.11 \times 10^{-31} \mathrm{~kg}\)
\(m_{p}\)	Proton mass	\(1.67262192369(51) \times 10^{-27} \mathrm{~kg}\)	\(1.67 \times 10^{-27} \mathrm{~kg}\)
\(m_{n}\)	Neutron mass	\(1.67492749804(95) \times 10^{-27} \mathrm{~kg}\)	\(1.67 \times 10^{-27} \mathrm{~kg}\)
\(u\)	Atomic mass unit	\(1.66053906660(50) \times 10^{-27} \mathrm{~kg}\)	\(1.66 \times 10^{-27} \mathrm{~kg}\)

**Table** \(\PageIndex{3}\): Solar System Data
Sun	mass	\(1.99 \times 10^{30} \mathrm{~kg}\)
	average radius	\(6.96 \times 10^{8} \mathrm{~m}\)
	Earth-sun distance (average)	\(1.496 \times 10^{11} \mathrm{~m}\)
Earth	mass	\(5.9736 \times 10^{24} \mathrm{~kg}\)
	average radius	\(6.376 \times 10^{6} \mathrm{~m}\)
	orbital period	\(3.16 \times 10^{7} \mathrm{~s}\)
Moon	mass	\(7.35 \times 10^{22} \mathrm{~kg}\)
	average radius	\(1.74 \times 10^{6} \mathrm{~m}\)
	orbital period (average)	\(2.36 \times 10^{6} \mathrm{~s}\)
	Earth-moon distance (average)	\(3.84 \times 10^{8} \mathrm{~m}\)

**Table** \(\PageIndex{4}\): Metric Prefixes for Powers of Ten and Their Symbols
Prefix	Symbol	Value	Prefix	Symbol	Value
tera	T	\(10^{12}\)	deci	d	\(10^{-1}\)
giga	G	\(10^{9}\)	centi	c	\(10^{-2}\)
mega	M	\(10^{6}\)	milli	m	\(10^{-3}\)
kilo	k	\(10^{3}\)	micro	\(\mu\)	\(10^{-6}\)
hecto	h	\(10^{2}\)	nano	n	\(10^{-9}\)
deka	da	\(10^{1}\)	pico	p	\(10^{-12}\)
—	—	\(10^{\circ}(=1)\)	femto	f	\(10^{-15}\)

**Table** \(\PageIndex{5}\): The Greek Alphabet
Alpha	\(\text { A }\)	\(\alpha\)	Eta	\(\mathrm{H}\)	\(\eta\)	Nu	\(N\)	\(\nu\)	Tau	\(\mathrm{T}\)	\(\tau\)
Beta	\(\text { B }\)	\(\beta\)	Theta	\(\Theta\)	\(\theta\)	Xi	\(\Xi\)	\(\xi\)	Upsilon	\(\Upsilon\)	\(v\)
Gamma	\(\Gamma\)	\(\gamma\)	Iota	\(\mathrm{I}\)	\(\iota\)	Omicron	\(\mathrm{O}\)	\(o\)	Phi	\(\Phi\)	\(\phi\)
Delta	\(\Delta\)	\(\delta\)	Kappa	\(\mathrm{K}\)	\(\kappa\)	Pi	\(\Pi\)	\(\pi\)	Chi	\(\mathrm{X}\)	\(\chi\)
Epsilon	\(\mathrm{E}\)	\(\varepsilon\)	Lambda	\(\Lambda\)	\(\lambda\)	Rho	\(\mathrm{P}\)	\(\rho\)	Psi	\(\Psi\)	\(\psi\)
Zeta	\(\text { Z }\)	\(\zeta\)	Mu	\(\mathrm{M}\)	\(\mu\)	Sigma	\(\Sigma\)	\(\sigma\)	Omega	\(\Omega\)	\(\omega\)

**Table** \(\PageIndex{6}\): 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	\(\mathrm{N}=\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}\)	newton
	Energy	\(\mathrm{J}=\mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\)	joule
	Power	\(\mathrm{W}=\mathrm{J} / \mathrm{s}\)	watt
	Pressure	\(\mathrm{Pa}=\mathrm{N} / \mathrm{m}^{2}\)	pascal
	Frequency	\(\mathrm{Hz}=1 / \mathrm{s}\)	hertz
	Electronic potential	\(\mathrm{V}=\mathrm{J} / \mathrm{C}\)	volt
	Capacitance	\(\mathrm{F}=\mathrm{C} / \mathrm{V}\)	farad
	Charge	\(\mathrm{C}=\mathrm{s} \cdot \mathrm{A}\)	coulomb
	Resistance	\(\Omega=\mathrm{V} / \mathrm{A}\)	ohm
	Magnetic field	\(\mathrm{T}=\mathrm{N} /(\mathrm{A} \cdot \mathrm{m})\)	tesla
	Nuclear decay rate	\(\mathrm{Bq}=1 / \mathrm{s}\)	becquerel

**Table** \(\PageIndex{7}\): Selected British Units
Length	\(1 \text { inch }(\text { in })=2.54 \mathrm{~cm} \text { (exactly) }\)
	\(1 \text { foot }(\mathrm{ft})=12 \text { in }=0.3048 \mathrm{~m}\)
	\(1 \operatorname{yard}(\mathrm{y d})=3 \mathrm{ft}=0.9144 \mathrm{~m}\)
	\(1 \text { mile }(\mathrm{mi})=1760 \mathrm{yd}=1.609 \mathrm{~km}\)
Force	\(1 \text { pound }(\mathrm{lb})=4.448 \mathrm{~N}\)
Energy	\(1 \text { British thermal unit }(\mathrm{Btu})=1.055 \times 10^{3} \mathrm{~J}\)
Power	\(1 \text { horsepower }(\mathrm{hp})=746 \mathrm{~W}\)
Pressure	\(1 \mathrm{lb} / \mathrm{in}^{2}=6.895 \times 10^{3} \mathrm{~Pa}\)

**Table** \(\PageIndex{8}\): Other Units
Length	\(1 \text { light year }(\text {ly})=9.46 \times 10^{15} \mathrm{~m}\)
	\(1 \text { astronomical unit }(\mathrm{au})=1.50 \times 10^{11} \mathrm{~m}\)
	\(1 \text { nautical mile }=1.852 \mathrm{~km}\)
	\(1 \text { angstrom }(Å)=10^{-10} \mathrm{~m}\)
Area	\(1 \text { acre }(\mathrm{ac})=4.05 \times 10^{3} \mathrm{~m}^{2}\)
	\(1 \text { square foot }\left(\mathrm{ft}^{2}\right)=9.29 \times 10^{-2} \mathrm{~m}^{2}\)
	\(1 \operatorname{barn}(b)=10^{-28} \mathrm{~m}^{2}\)
Volume	\(1 \text { liter }(L)=10^{-3} \mathrm{~m}^{3}\)
Volume	\(1 \text { U.S. gallon (gal) }=3.785 \times 10^{-3} \mathrm{~m}^{3}\)
Mass	\(1 \text { solar mass }=1.99 \times 10^{30} \mathrm{~kg}\)
	\(1 \text { metric ton }=10^{3} \mathrm{~kg}\)
	\(1 \text { atomic mass unit }(u)=1.6605 \times 10^{-27} \mathrm{~kg}\)
Time	\(1 \operatorname{year} \ (y)=3.16 \times 10^{7} \mathrm{~s}\)
Time	\(1 \text { day }(d)=86,400 \mathrm{~s}\)
Speed	\(1 \text { mile per hour }(\mathrm{mph})=1.609 \mathrm{~km} / \mathrm{h}\)
Speed	\(1 \text { nautical mile per hour (naut) }=1.852 \mathrm{~km} / \mathrm{h}\)
Angle	\(1 \text { degree }\left(^{\circ}\right)=1.745 \times 10^{-2} \mathrm{~rad}\)
	\(1 \text { minute of arc }\left(^{\prime}\right)=1 / 60 \text { degree }\)
	\(1 \text { second of arc }(")=1 / 60 \text { minute of arc }\)
	\(1 \mathrm{~grad~}=1.571 \times 10^{-2} \mathrm{~rad}\)
Energy	\(1 \text { kiloton TNT }(\mathrm{kT})=4.2 \times 10^{12} \mathrm{~J}\)
	\(1 \text { kilowatt hour }(\mathrm{kW} \cdot h)=3.60 \times 10^{6} \mathrm{~J}\)
	\(1 \text { food calorie }(\mathrm{kcal})=4186 \mathrm{~J}\)
	\(1 \text { calorie }(\mathrm{cal})=4.186 \mathrm{~J}\)
	\(1 \text { electron volt }(\mathrm{eV})=1.60 \times 10^{-19} \mathrm{~J}\)
Pressure	\(1 \text { atmosphere }(\text {atm})=1.013 \times 10^{5} \mathrm{~Pa}\)
	\(1 \text { millimeter of mercury }(\mathrm{mm} \mathrm{Hg})=133.3 \mathrm{~Pa}\)
	\(1 \text { torricelli (torr) }=1 \mathrm{~mm} \mathrm{Hg}=133.3 \mathrm{~Pa}\)
Nuclear decay rate	\(1 \text { curie }(\mathrm{Ci})=3.70 \times 10^{10} \mathrm{~Bq}\)

**Table** \(\PageIndex{9}\): Useful Formulae
Circumference of a circle with radius \(r\) or diameter \(d\)	\(C=2 \pi r=\pi d\)
Area of a circle with radius \(r\) or diameter \(d\)	\(A=\pi r^{2}=\pi d^{2} / 4\)
Area of a sphere with radius \(r\)	\(A=4 \pi r^{2}\)
Volume of a sphere with radius \(r\)	\(V=(4 / 3)\left(\pi r^{3}\right)\)

Footnotes

1 Stated values are according to the National Institute of Standards and Technology Reference on Constants, Units, and Uncertainty, www.physics.nist.gov/cuu (2018 values). 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 (2018 values). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.