Chapter 17: Useful Information

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Mar 12, 2024
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- Chapter 16: Selected Radioactive Isotopes
- Chapter 18: Glossary of Key Symbols and Notation

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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.

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