Chapter 17: Useful Information
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This appendix is broken into several tables.
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Table
\(\PageIndex{1}\), Important Constants
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Table
\(\PageIndex{2}\), Submicroscopic Masses
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Table
\(\PageIndex{3}\), Solar System Data
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Table
\(\PageIndex{4}\), Metric Prefixes for Powers of Ten and Their Symbols
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Table
\(\PageIndex{5}\), The Greek Alphabet
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Table
\(\PageIndex{6}\), SI units
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Table
\(\PageIndex{7}\), Selected British Units
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Table
\(\PageIndex{8}\), Other Units
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Table
\(\PageIndex{9}\), Useful Formulae
Table
\(\PageIndex{1}\): Important Constants
1
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Symbol
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Meaning
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Best Value
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Approximate Value
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\(c\)
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Speed of light in vacuum
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\(2.99792458 \times 10^{8} \mathrm{~m} / \mathrm{s}\)
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\(3.00 \times 10^{8} \mathrm{~m} / \mathrm{s}\)
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\(G\)
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Gravitational constant
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\(6.67430(15) \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\)
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\(6.67 \times 10^{-11} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{kg}^{2}\)
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\(N_{A}\)
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Avogadro’s number
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\(6.02214076 \times 10^{23}\)
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\(6.02 \times 10^{23}\)
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\(k\)
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Boltzmann’s constant
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\(1.380649 \times 10^{-23} \mathrm{~J} / \mathrm{K}\)
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\(1.38 \times 10^{-23} \mathrm{~J} / \mathrm{K}\)
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\(R\)
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Gas constant
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\(8.314462618 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\)
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\(8.31 \mathrm{~J} / \mathrm{mol} \cdot \mathrm{K}\)
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\(\sigma\)
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Stefan-Boltzmann constant
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\(5.670374419 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)
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\(5.67 \times 10^{-8} \mathrm{~W} / \mathrm{m}^{2} \cdot \mathrm{K}\)
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\(k\)
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Coulomb force constant
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\(8.9875517923(13) \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\)
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\(8.99 \times 10^{9} \mathrm{~N} \cdot \mathrm{m}^{2} / \mathrm{C}^{2}\)
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\(e\)
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Elementary charge
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\(1.602176634 \times 10^{-19} \mathrm{C}\)
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\(1.60 \times 10^{-19} \mathrm{C}\)
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\(\varepsilon_{0}\)
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Permittivity of free space
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\(8.8541878128(13) \times 10^{-12} \mathrm{C}^{2} / \mathrm{N} \cdot \mathrm{m}^{2}\)
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\(8.85 \times 10^{-12} \mathrm{C}^{2} / \mathrm{N} \cdot \mathrm{m}^{2}\)
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\(\mu_{0}\)
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Permeability of free space
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\(4 \pi \times 10^{-7} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}\)
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\(1.26 \times 10^{-6} \mathrm{~T} \cdot \mathrm{m} / \mathrm{A}\)
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\(h\)
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Planck’s constant
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\(6.62607015 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\)
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\(6.63 \times 10^{-34} \mathrm{~J} \cdot \mathrm{s}\)
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Table
\(\PageIndex{2}\): Submicroscopic Masses
2
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Symbol
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Meaning
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Best Value
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Approximate Value
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\(m_{e}\)
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Electron mass
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\(9.1093837015(28) \times 10^{-31} \mathrm{~kg}\)
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\(9.11 \times 10^{-31} \mathrm{~kg}\)
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\(m_{p}\)
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Proton mass
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\(1.67262192369(51) \times 10^{-27} \mathrm{~kg}\)
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\(1.67 \times 10^{-27} \mathrm{~kg}\)
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\(m_{n}\)
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Neutron mass
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\(1.67492749804(95) \times 10^{-27} \mathrm{~kg}\)
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\(1.67 \times 10^{-27} \mathrm{~kg}\)
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\(u\)
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Atomic mass unit
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\(1.66053906660(50) \times 10^{-27} \mathrm{~kg}\)
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\(1.66 \times 10^{-27} \mathrm{~kg}\)
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Table
\(\PageIndex{3}\): Solar System Data
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Sun
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mass
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\(1.99 \times 10^{30} \mathrm{~kg}\)
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average radius
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\(6.96 \times 10^{8} \mathrm{~m}\)
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Earth-sun distance (average)
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\(1.496 \times 10^{11} \mathrm{~m}\)
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Earth
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mass
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\(5.9736 \times 10^{24} \mathrm{~kg}\)
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average radius
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\(6.376 \times 10^{6} \mathrm{~m}\)
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orbital period
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\(3.16 \times 10^{7} \mathrm{~s}\)
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Moon
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mass
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\(7.35 \times 10^{22} \mathrm{~kg}\)
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average radius
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\(1.74 \times 10^{6} \mathrm{~m}\)
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orbital period (average)
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\(2.36 \times 10^{6} \mathrm{~s}\)
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Earth-moon distance (average)
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\(3.84 \times 10^{8} \mathrm{~m}\)
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Table
\(\PageIndex{4}\): Metric Prefixes for Powers of Ten and Their Symbols
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Prefix
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Symbol
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Value
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Prefix
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Symbol
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Value
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tera
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T
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\(10^{12}\)
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deci
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d
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\(10^{-1}\)
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giga
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G
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\(10^{9}\)
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centi
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c
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\(10^{-2}\)
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mega
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M
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\(10^{6}\)
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milli
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m
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\(10^{-3}\)
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kilo
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k
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\(10^{3}\)
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micro
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\(\mu\)
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\(10^{-6}\)
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hecto
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h
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\(10^{2}\)
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nano
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n
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\(10^{-9}\)
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deka
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da
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\(10^{1}\)
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pico
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p
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\(10^{-12}\)
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—
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—
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\(10^{\circ}(=1)\)
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femto
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f
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\(10^{-15}\)
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Table
\(\PageIndex{5}\): The Greek Alphabet
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Alpha
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\(\text { A }\)
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\(\alpha\)
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Eta
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\(\mathrm{H}\)
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\(\eta\)
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Nu
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\(N\)
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\(\nu\)
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Tau
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\(\mathrm{T}\)
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\(\tau\)
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Beta
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\(\text { B }\)
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\(\beta\)
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Theta
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\(\Theta\)
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\(\theta\)
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Xi
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\(\Xi\)
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\(\xi\)
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Upsilon
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\(\Upsilon\)
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\(v\)
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Gamma
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\(\Gamma\)
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\(\gamma\)
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Iota
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\(\mathrm{I}\)
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\(\iota\)
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Omicron
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\(\mathrm{O}\)
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\(o\)
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Phi
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\(\Phi\)
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\(\phi\)
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Delta
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\(\Delta\)
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\(\delta\)
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Kappa
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\(\mathrm{K}\)
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\(\kappa\)
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Pi
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\(\Pi\)
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\(\pi\)
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Chi
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\(\mathrm{X}\)
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\(\chi\)
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Epsilon
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\(\mathrm{E}\)
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\(\varepsilon\)
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Lambda
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\(\Lambda\)
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\(\lambda\)
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Rho
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\(\mathrm{P}\)
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\(\rho\)
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Psi
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\(\Psi\)
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\(\psi\)
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Zeta
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\(\text { Z }\)
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\(\zeta\)
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Mu
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\(\mathrm{M}\)
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\(\mu\)
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Sigma
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\(\Sigma\)
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\(\sigma\)
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Omega
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\(\Omega\)
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\(\omega\)
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Table
\(\PageIndex{6}\): SI Units
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Entity
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Abbreviation
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Name
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Fundamental units
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Length
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m
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meter
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Mass
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kg
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kilogram
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Time
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s
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second
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Current
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A
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ampere
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Supplementary unit
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Angle
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rad
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radian
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Derived units
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Force
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\(\mathrm{N}=\mathrm{kg} \cdot \mathrm{m} / \mathrm{s}^{2}\)
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newton
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Energy
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\(\mathrm{J}=\mathrm{kg} \cdot \mathrm{m}^{2} / \mathrm{s}^{2}\)
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joule
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Power
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\(\mathrm{W}=\mathrm{J} / \mathrm{s}\)
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watt
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Pressure
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\(\mathrm{Pa}=\mathrm{N} / \mathrm{m}^{2}\)
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pascal
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Frequency
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\(\mathrm{Hz}=1 / \mathrm{s}\)
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hertz
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Electronic potential
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\(\mathrm{V}=\mathrm{J} / \mathrm{C}\)
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volt
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Capacitance
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\(\mathrm{F}=\mathrm{C} / \mathrm{V}\)
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farad
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Charge
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\(\mathrm{C}=\mathrm{s} \cdot \mathrm{A}\)
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coulomb
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Resistance
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\(\Omega=\mathrm{V} / \mathrm{A}\)
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ohm
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Magnetic field
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\(\mathrm{T}=\mathrm{N} /(\mathrm{A} \cdot \mathrm{m})\)
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tesla
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Nuclear decay rate
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\(\mathrm{Bq}=1 / \mathrm{s}\)
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becquerel
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Table
\(\PageIndex{7}\): Selected British Units
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Length
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\(1 \text { inch }(\text { in })=2.54 \mathrm{~cm} \text { (exactly) }\)
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\(1 \text { foot }(\mathrm{ft})=12 \text { in }=0.3048 \mathrm{~m}\)
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\(1 \operatorname{yard}(\mathrm{y d})=3 \mathrm{ft}=0.9144 \mathrm{~m}\)
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\(1 \text { mile }(\mathrm{mi})=1760 \mathrm{yd}=1.609 \mathrm{~km}\)
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Force
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\(1 \text { pound }(\mathrm{lb})=4.448 \mathrm{~N}\)
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Energy
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\(1 \text { British thermal unit }(\mathrm{Btu})=1.055 \times 10^{3} \mathrm{~J}\)
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Power
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\(1 \text { horsepower }(\mathrm{hp})=746 \mathrm{~W}\)
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Pressure
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\(1 \mathrm{lb} / \mathrm{in}^{2}=6.895 \times 10^{3} \mathrm{~Pa}\)
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Table
\(\PageIndex{8}\): Other Units
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Length
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\(1 \text { light year }(\text {ly})=9.46 \times 10^{15} \mathrm{~m}\)
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\(1 \text { astronomical unit }(\mathrm{au})=1.50 \times 10^{11} \mathrm{~m}\)
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\(1 \text { nautical mile }=1.852 \mathrm{~km}\)
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\(1 \text { angstrom }(Å)=10^{-10} \mathrm{~m}\)
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Area
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\(1 \text { acre }(\mathrm{ac})=4.05 \times 10^{3} \mathrm{~m}^{2}\)
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\(1 \text { square foot }\left(\mathrm{ft}^{2}\right)=9.29 \times 10^{-2} \mathrm{~m}^{2}\)
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\(1 \operatorname{barn}(b)=10^{-28} \mathrm{~m}^{2}\)
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Volume
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\(1 \text { liter }(L)=10^{-3} \mathrm{~m}^{3}\)
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\(1 \text { U.S. gallon (gal) }=3.785 \times 10^{-3} \mathrm{~m}^{3}\)
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Mass
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\(1 \text { solar mass }=1.99 \times 10^{30} \mathrm{~kg}\)
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\(1 \text { metric ton }=10^{3} \mathrm{~kg}\)
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\(1 \text { atomic mass unit }(u)=1.6605 \times 10^{-27} \mathrm{~kg}\)
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Time
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\(1 \operatorname{year} \ (y)=3.16 \times 10^{7} \mathrm{~s}\)
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\(1 \text { day }(d)=86,400 \mathrm{~s}\)
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Speed
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\(1 \text { mile per hour }(\mathrm{mph})=1.609 \mathrm{~km} / \mathrm{h}\)
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\(1 \text { nautical mile per hour (naut) }=1.852 \mathrm{~km} / \mathrm{h}\)
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Angle
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\(1 \text { degree }\left(^{\circ}\right)=1.745 \times 10^{-2} \mathrm{~rad}\)
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\(1 \text { minute of arc }\left(^{\prime}\right)=1 / 60 \text { degree }\)
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\(1 \text { second of arc }(")=1 / 60 \text { minute of arc }\)
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\(1 \mathrm{~grad~}=1.571 \times 10^{-2} \mathrm{~rad}\)
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Energy
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\(1 \text { kiloton TNT }(\mathrm{kT})=4.2 \times 10^{12} \mathrm{~J}\)
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\(1 \text { kilowatt hour }(\mathrm{kW} \cdot h)=3.60 \times 10^{6} \mathrm{~J}\)
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\(1 \text { food calorie }(\mathrm{kcal})=4186 \mathrm{~J}\)
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\(1 \text { calorie }(\mathrm{cal})=4.186 \mathrm{~J}\)
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\(1 \text { electron volt }(\mathrm{eV})=1.60 \times 10^{-19} \mathrm{~J}\)
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Pressure
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\(1 \text { atmosphere }(\text {atm})=1.013 \times 10^{5} \mathrm{~Pa}\)
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\(1 \text { millimeter of mercury }(\mathrm{mm} \mathrm{Hg})=133.3 \mathrm{~Pa}\)
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\(1 \text { torricelli (torr) }=1 \mathrm{~mm} \mathrm{Hg}=133.3 \mathrm{~Pa}\)
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Nuclear decay rate
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\(1 \text { curie }(\mathrm{Ci})=3.70 \times 10^{10} \mathrm{~Bq}\)
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Table
\(\PageIndex{9}\): Useful Formulae
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Circumference of a circle with radius \(r\) or diameter \(d\)
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\(C=2 \pi r=\pi d\)
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Area of a circle with radius \(r\) or diameter \(d\)
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\(A=\pi r^{2}=\pi d^{2} / 4\)
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Area of a sphere with radius \(r\)
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\(A=4 \pi r^{2}\)
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Volume of a sphere with radius \(r\)
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\(V=(4 / 3)\left(\pi r^{3}\right)\)
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Footnotes
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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
(2018 values). Values in parentheses are the uncertainties in the last digits. Numbers without uncertainties are exact as defined.
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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.