66.12: Physical Constants
- Page ID
- 91942
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Table \(\PageIndex{1}\). Fundamental physical constants (CODATA 2018).
| Description | Symbol | Value |
|---|---|---|
| Speed of light (vacuum) | \(\mathrm{c }\) | \(2.99792458 \times 10^8 \mathrm{m} / \mathrm{s} \) |
| Gravitational constant | \(\mathrm{G }\) | \(6.67430 \times 10^{-11} \mathrm{~m}^3 \mathrm{~kg}^{-1} \mathrm{s}^{-2} \) |
| Elementary charge\( | \(\mathrm{e }\) | \(1.602176634 \times 10^{-19} \mathrm{C} \) |
| Permittivity of free space | \( \varepsilon_0 \) | \(8.8541878128 \times 10^{-12} \mathrm{F} / \mathrm{m} \) |
| Permeability of free space | \( \mu_{0 }\) | \(1.2566370621210^{-6} \mathrm{N} / \mathrm{A}^2 \) |
| Coulomb constant \left(1 /\left(4 \pi \varepsilon_0\right)\right) | \(\mathrm{k_c }\) | \(8.9875517923 \times 10^9 \mathrm{m} / \mathrm{F} \) |
| Electron mass | \(\mathrm{m_e }\) | \(9.1093837015 \times 10^{-31} \mathrm{kg} \) |
| Proton mass | \(\mathrm{m_p }\) | \(1.67262192369 \times 10^{-27} \mathrm{kg} \) |
| Neutron mass | \(\mathrm{m_n }\) | \(1.67492749804 \times 10^{-27} \mathrm{kg} \) |
| Atomic mass unit (\mathrm{amu}) | \(\mathrm{u }\) | \(1.66053906660 \times 10^{-27} \mathrm{kg} \) |
| Planck constant | \(\mathrm{h }\) | \(6.62607015 \times 10^{-34} \mathrm{J} \) \mathrm{s} |
| Planck constant \div 2 \pi | \(\hbar \) | \(1.0545718176461564 \times 10^{-34} \mathrm{~J} \mathrm{s} \) |
| Boltzmann constant | \(\mathrm{k_B }\) | \(1.380649 \times 10^{-23} \mathrm{J} / \mathrm{K} \) |
| Avogadro constant | \(\mathrm{N_A }\) | \(6.02214076 \times 10^{23} \mathrm{mol}^{-1} \) |
Table \(\PageIndex{2}\). Other physical constants.
| Description | Symbol | Value |
|---|---|---|
| Acceleration due to gravity at Earth surface | \(\mathrm{g }\) | \(9.80 \mathrm{~m} / \mathrm{s}^2\) |
| Radius of the Earth (eq.) | \(R_{\oplus}\) | \(6378.140 \mathrm{~km}\) |
| Mass of the Earth | \(R_{\oplus}\) | \(5.97320 \times 10^{24} \mathrm{~kg}\) |
| Earth gravity constant | \(G \; M_{\oplus}\) | \(3.986005 \times 10^{14} \mathrm{~m}^3 \mathrm{~s}^{-2}\) |
| Speed of sound in air \left(20^{\circ} \mathrm{C}\right) | \(v_{\text {snd }}\) | \(343 \mathrm{~m} / \mathrm{s}\) |
| Density of air (sea level) | \(\rho_{\text {air }}\) | \(1.29 \mathrm{~kg} / \mathrm{m}^3\) |
| Density of water | \(\rho_{\mathrm{w}}\) | \(1 \mathrm{~g} / \mathrm{cm}^3=1000 \mathrm{~kg} / \mathrm{m}^3\) |
| Index of refraction of water | \(n_{\mathrm{W}}\) | \(1.33\) |
| Resistivity of copper \(\left(20^{\circ} \mathrm{C}\right)\) | \(\rho_{\mathrm{Cu}}\) | \(1.68 \times 10^{-8} \Omega \mathrm{m}\) |