Appendix C: Fundamental Constants

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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.

* c is the speed of light

Quantity	Symbol	Value
Atomic mass unit	u	1.660 538 782 (83) x 10⁻²⁷ kg 931.494 028 (23) MeV/c²*
Avogadro’s number	N_A	6.022 141 79 (30) x 10²³ particles/mol
Bohr magneton	$$\mu_{B} = \frac{e \hbar}{2 m_{e}}$$	9.274 009 15 (23) x 10⁻²⁴ J/T
Bohr radius	$$a_{0} = \frac{\hbar^{2}}{m_{e} e^{2} k_{e}}$$	5.291 772 085 9 (36) x 10⁻¹¹ m
Boltzmann’s constant	$$k_{B} = \frac{R}{N_{A}}$$	1.380 650 4 (24) x 10⁻²³ J/K
Compton wavelength	$$\lambda_{C} = \frac{h}{m_{e} c}$$	2.426 310 217 5 (33) x 10⁻¹² m
Coulomb constant	$$k_{e} = \frac{1}{4 \pi \varepsilon_{0}}$$	8.987 551 788... x 10⁹ N • m²/C² (exact)
Deuteron mass	m_d	9.109 382 15 (45) x 10⁻³¹ kg 5.485 799 094 3(23) x 10⁻⁴ u 0.510 998 910 (13) MeV/c² *
Electron mass	m_e	9.109 382 15 (45) x 10⁻³¹ kg 5.485 799 094 3(23) x 10⁻⁴ u 0.510 998 910 (13) MeV/c² *
Electron volt	eV	1.602 176 487 (40) x 10⁻¹⁹ J
Elementary charge	e	1.602 176 487 (40) x 10⁻¹⁹ C
Gas constant	R	8.314 472 (15) J/mol • K
Gravitational constant	G	6.674 28 (67) x 10⁻¹¹ N • m²/kg²
Neutron mass	m_n	1.674 927 211 (84) x 10⁻²⁷ kg 1.008 664 915 97 (43) u 939.565 346 (23) MeV/c² *
Nuclear magneton	$$\mu_{n} = \frac{e \hbar}{2 m_{p}}$$	5.050 783 24 (13) x 10⁻²⁷ J/T
Permeability of free space	$$\mu_{0}$$	4$\pi$ x 10⁻⁷T • m/A (exact)
Permittivity of free space	$$\varepsilon_{0} = \frac{1}{\mu_{0} c^{2}}$$	8.854 187 817... x 10⁻¹² C²/N • m² (exact)
Planck’s constant	h	6.626 068 96 (33) x 10⁻³⁴ J • s
Reduced Planck's constant	$$\hbar = \frac{h}{2 \pi}$$	1.054 571 628 (53) x 10⁻³⁴ J • s
Proton mass	m_p	1.672 621 637 (83) x 10⁻²⁷ kg 1.007 276 466 77 (10) u 938.272 013 (23) MeV/c² *
Rydberg constant	R_H	1.097 373 156 852 7 (73) x 10⁷ m⁻¹
Speed of light in vacuum	c	2.997 924 58 x 10⁸ m/s (exact)

Useful combinations of constants for calculations:

hc = 12,400 eV • Å = 1240 eV • nm = 1240 MeV • fm
$\hbar$c = 1973 eV • Å = 197.3 eV • nm = 197.3 MeV • fm
k_ee² = 14.40 eV • Å = 1.440 eV • nm = 1.440 MeV • fm
k_BT = 0.02585 eV at T = 300 K

Contributors and Attributions

Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a Creative Commons Attribution License (by 4.0).

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