Fundamental Constants

Samuel J. Ling; William Moebs; Jeff Sanny

Fundamental Constants

Fundamental Constants *Note:* These constants are the values recommended in 2006 by CODATA, based on a least-squares adjustment of data from different measurements. The numbers in parentheses for the values represent the uncertainties of the last two digits.
Quantity	Symbol	Value
Atomic mass unit	u	$\begin{matrix} 1.660 538782 (83) \times 10^{- 27} kg \\ 931.494 028 (23) MeV/ c^{2} \end{matrix}$
Avogadro’s number	$N_{A}$	$6.02214076 \times 10^{23} reciprocal mole ({mol}^{- 1})$
Bohr magneton	$μ_{B} = \frac{e ℏ}{2 m_{e}}$	$9.274 00915 (23) \times 10^{- 24} J/T$
Bohr radius	$a_{0} = \frac{ℏ^{2}}{m_{e} e^{2} k_{e}}$	$5.291 7720859 (36) \times 10^{- 11} m$
Boltzmann’s constant	$k_{B} = \frac{R}{N_{A}}$	$1.380649 \times 10^{- 23} joule per kelvin (J \cdot K^{- 1})$
Compton wavelength	$λ_{C} = \frac{h}{m_{e} c}$	$2.426 3102175 (33) \times 10^{- 12} m$
Coulomb constant	$k_{e} = \frac{1}{4 π ε_{0}}$	$8.987 551 788. . . \times 10^{9} N \cdot m^{2} {/C}^{2} (exact)$
Deuteron mass	$m_{d}$	$\begin{matrix} 3.343 58320 (17) \times 10^{- 27} kg \\ 2.013 553212724 (78) u \\ 1875.612 859 MeV/ c^{2} \end{matrix}$
Electron mass	$m_{e}$	$\begin{matrix} 9.109 38215 (45) \times 10^{- 31} kg \\ 5.485 7990943 (23) \times 10^{- 4} u \\ 0.510 998910 (13) MeV/ c^{2} \end{matrix}$
Electron volt	eV	$1.602 176487 (40) \times 10^{- 19} J$
Elementary charge	e	$1.602176634 \times 10^{- 19} C$
Gas constant	R	$8.314 472 (15) J/mol \cdot K$
Gravitational constant	G	$6.674 28 (67) \times 10^{- 11} N \cdot m^{2} {/kg}^{2}$
Neutron mass	$m_{n}$	$\begin{matrix} 1.674 927211 (84) \times 10^{- 27} kg \\ 1.008 66491597 (43) u \\ 939.565 346 (23) MeV/ c^{2} \end{matrix}$
Nuclear magneton	$μ_{n} = \frac{e ℏ}{2 m_{p}}$	$5.050 78324 (13) \times 10^{- 27} J/T$
Permeability of free space	$μ_{0}$	$4 π \times 10^{- 7} T \cdot m/A (exact)$
Permittivity of free space	$ε_{0} = \frac{1}{μ_{0} c^{2}}$	$8.854 187 817. . . \times 10^{- 12} C^{2} / N \cdot m^{2} (exact)$
Planck’s constant	h $ℏ = \frac{h}{2 π}$	$\begin{matrix} 6.62607015 \times 10^{- 34} kg \cdot m^{2} \cdot s^{- 1} \\ 1.05457182 \times 10^{- 34} kg \cdot m^{2} \cdot s^{- 1} \end{matrix}$
Proton mass	$m_{p}$	$\begin{matrix} 1.672 621637 (83) \times 10^{- 27} kg \\ 1.007 27646677 (10) u \\ 938.272 013 (23) MeV/ c^{2} \end{matrix}$
Rydberg constant	$R_{H}$	$1.097 3731568527 (73) \times 10^{7} m^{- 1}$
Speed of light in vacuum	c	$2.997 92458 \times 10^{8} m/s (exact)$

Useful combinations of constants for calculations:

$h c = 12, 400 eV \cdot Å = 1240 eV \cdot nm = 1240 MeV \cdot fm$

$ℏ c = 1973 eV \cdot Å = 197.3 eV \cdot nm = 197.3 MeV \cdot fm$

$k_{e} e^{2} = 14.40 eV \cdot Å = 1.440 eV \cdot nm = 1.440 MeV \cdot fm$

$k_{B} T = 0.02585 eV at T = 300 K$

Licenses and Attributions

Appendix C Fundamental Constants. Authored by: OpenStax College. Located at: https://openstax.org/books/university-physics-volume-2/pages/c-fundamental-constants. License: CC BY: Attribution. License Terms: Download for free at https://openstax.org/books/university-physics-volume-2/pages/1-introduction

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