Appendix C: Fundamental Constants

Table C1 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	$\begin{matrix} 1.660 538 782 (83) \times 10^{−27} kg \\ 931.494 028 (23) MeV/ c^{2} \end{matrix}$
Avogadro’s number	$N_{A}$	$6.02214076 \times 10^{23} reciprocal mole ({mol}^{–1})$
Bohr magneton	$μ_{B} = \frac{e ℏ}{2 m_{e}}$	$9.274 009 15 (23) \times 10^{−24} J/T$
Bohr radius	$a_{0} = \frac{ℏ^{2}}{m_{e} e^{2} k_{e}}$	$5.291 772 085 9 (36) \times 10^{−11} m$
Boltzmann’s constant	$k_{B} = \frac{R}{N_{A}}$	$1.380649 \times 10^{–23} joule per kelvin (J \cdot K^{–1})$
Compton wavelength	$λ_{C} = \frac{h}{m_{e} c}$	$2.426 310 217 5 (33) \times 10^{−12} m$
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	$m_{d}$	$\begin{matrix} 3.343 583 20 (17) \times 10^{−27} kg \\ 2.013 553 212 724 (78) u \\ 1875.612 859 MeV/ c^{2} \end{matrix}$
Electron mass	$m_{e}$	$\begin{matrix} 9.109 382 15 (45) \times 10^{−31} kg \\ 5.485 799 094 3 (23) \times 10^{−4} u \\ 0.510 998 910 (13) MeV/ c^{2} \end{matrix}$
Electron volt	eV	$1.602 176 487 (40) \times 10^{−19} J$
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	$m_{n}$	$\begin{matrix} 1.674 927 211 (84) \times 10^{−27} kg \\ 1.008 664 915 97 (43) u \\ 939.565 346 (23) MeV/ c^{2} \end{matrix}$
Nuclear magneton	$μ_{n} = \frac{e ℏ}{2 m_{p}}$	$5.050 783 24 (13) \times 10^{−27} J/T$
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	$m_{p}$	$\begin{matrix} 1.672 621 637 (83) \times 10^{−27} kg \\ 1.007 276 466 77 (10) u \\ 938.272 013 (23) MeV/ c^{2} \end{matrix}$
Rydberg constant	$R_{H}$	$1.097 373 156 852 7 (73) \times 10^{7} m^{−1}$
Speed of light in vacuum	c	$2.997 924 58 \times 10^{8} m/s (exact)$

This table has 3 columns labeled quantity, symbol and value. Each row describes 1 quantity as follows: Atomic mass unit, u, 1.660538782 in parentheses 83 into 10 to the power minus 27 kg or 9.31494028 in parentheses 23 MeV by c squared; Avogadro’s number, N subscript A, 6.02214179 in parentheses 30 into 10 to the power 23 particles per mole; Bohr magneton, mu subscript b equal to e h bar upon 2 m subscript e, 9.27400915 in parentheses 23 into 10 to the power minus 24 J by T; Bohr radius, a subscript 0 equal to h bar squared upon m subscript e e squared k subscript e, 5.2917720859 in parentheses 36 into 10 to the power minus 11 m; Boltzmann’s constant, k subscript B equal to R by N subscript A, 1.3806504 in parentheses 24 into 10 to the power 23 J by K; Compton wavelength, lambda subscript C equal to h upon m subscript e c, 2.4263102175 in parentheses 33 into 10 to the power minus 12 m; Coulomb constant, k subscript e equal to 1 upon 4 pi epsilon subscript 0, 8.987551788 into 10 to the power 9 N m squared by C squared exact; Deuteron mass, m subscript d, 3.34358320 in parentheses 17 into 10 to the power minus 27 kg or 2.013553212724 in parentheses 78 u or 1875.612859 MeV by c squared; Electron mass, m subscript e, 9.10938215 in parentheses 45 into 10 to the power minus 31 kg or 5.4857990943 in parentheses 23 into 10 to the power minus 4 u or 0.510998910 in parentheses 13 MeV by c squared; Electron volt, eV, 1.602176487 in parentheses 40 into 10 to the power minus 19 J; Elementary charge, e, 1.602176487 in parentheses 40 into 10 to the power minus 19 C; Gas constant, R, 8.314472 in parentheses 15 J by mol K; Gravitational constant, G, 6.67428 in parentheses 67 into 10 to the power minus 11 N m squared by kg squared; Neutron mass, m subscript n, 1.674927211 in parentheses 84 into 10 to the power minus 27 kg or 1.00866491597 in parentheses 43 u or 939.565346 in parentheses 23 MeV by c squared; Nuclear magneton, mu subscript n equal to e h bar upon 2 m subscript p, 5.05078324 in parentheses 13 into 10 to the power minus 27 J by T; Permeability of free space, mu subscript 0, 4 pi into 10 to the power minus 7 T m by A exact; Permittivity of free space; epsilon 0 equal to 1 upon mu 0 c squared, 8,854187817 into 10 to the power minus 12 C squared by N m squared exact; Planck’s constant, h or h bar equal to h by 2 pi, 6.62606896 in parentheses 33 into 10 to the power minus 34 J s or 1.054571628, in parentheses 53 into 10 to the power minus 34 J s; Proton mass m subscript p, 1.672621637 in parentheses 83 into 10 to the power minus 27 kg or 1.00727646677 in parentheses 10 u or 938.272013 in parentheses 23 MeV by c squared; Rydberg constant, R subscript H, 1.0973731568527 in parentheses 73 into 10 to the power 7 m to the power minus 1; Speed of light in vacuum, c, 2.99792458 into 10 to the power 8 m by s exact.

Useful combinations of constants for calculations:

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

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

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

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