
Unless otherwise stated this page contains Version 1.0 content (Read more about versions)
Version 2.0 Updated: 19 December
2011 Previous
versions
1.2.3 Atomic constants
The values of the constants given in this section are the 2010 CODATA
values published on the NIST website (http://physics.nist.gov/cuu/Constants/index.html), where
the values of other constants and information about the relationships between
constants are also available. The CODATA values were obtained, not from
individual experiments, but using a weighted 'leastsquares' statistical
treatment of selected experimental data. The general procedures used were the
same as those in earlier adjustments, described in detail in a paper reporting
the 2006 adjustment and published in:
P. J. Mohr, B. N. Taylor, and D. B. Newell, Rev. Mod. Phys 80(2),
633730 (2008) and P. J. Mohr, B. N. Taylor, and D. B. Newell, J. Phys.
Chem. Ref. Data 37(3), 11871284 (2008).
A detailed description of the 2010 adjustment will be available on the
NIST website in late 2011 or early 2012. Meanwhile, a brief overview of the
2010 adjustment is available at
http://physics.nist.gov/cuu/Constants/briefOverview2010.pdf.
Some details of earlier procedures were included in the 16th (1995) edition of
Kaye & Laby and these can be viewed in the archived
Version 1.0 of this section.
Table of fundamental constants

Symbol 
2010 CODATA value 
SI unit 
Relative Standard Uncertainty (parts in
10^{6}) 





Principal constants 




Speed of light in vacuum 
c 
299 792 458 
m s^{−1} 
exact 
Planck constant 
h 
6.626 069 57 ×10^{−34} 
J s 
0.044 
Planck constant (h/2π) 
ħ 
1.054 571 726 ×10^{−34} 
J s 
0.044 
Elementary charge 
e 
1.602 176 565 ×10^{−19} 
C 
0.022 
Mass of electron 
m_{e} 
9.109 382 91 ×10^{−31} 
kg 
0.044 
Avogadro constant 
N_{A} 
6.022 141 29 ×10^{23} 
mol^{−1} 
0.044 
Atomic mass constant 
m_{u} 
1.660 538 921 ×10^{−27} 
kg 
0.044 
Faraday constant 
F(=N_{A}e) 
96 485.3365 
C mol^{−1} 
0.022 
Newtonian constant of gravitation 
G 
6.673 84 ×10^{−11} 
m^{3} kg^{−1}s^{−2} 
120 
Spectroscopy and atoms 




Planck constant 
h 
4.135 667 516 ×10^{−15} 
eV s 
0.022 
Planck constant (h/2π) 
ħ

6.582 119 28 ×10^{−16} 
eV s 
0.022 
Charge/mass ratio of electron 
−e/m_{e} 
−1.758 820 088 ×10^{11} 
C kg^{−1} 
0.022 
Fine structure constant 
α

7.297 352 5698 ×10^{−3} 

0.00032

Fine structure constant, reciprocal 
α^{−1} 
137.035 999 074 

0.00032

Rydberg constant (fixed nucleus) 
R_{∞} 
10 973 731.568 539 
m^{−1} 
0.000005

Bohr radius (4π/μ_{0}c^{2})ħ^{2}/m_{e}e^{2} 
a_{0} 
5.291 772 1092 ×10^{−11} 
m 
0.00032 
Compton wavelength of electron 
λ_{c} 
2.426 310 2389 ×10^{−12} 
m 
0.00065 
Compton wavelength of electron (λ_{c}/2π) 
ƛ_{c} 
386.159 268 00 ×10^{−15} 
m 
0.00065 
Classical ‘radius’ of electron
(μ_{0}c^{2}/4π)e^{2}/mc^{2} 
r_{e} 
2.817 940 3267
×10^{−15}

m 
0.00097 
Thomson crosssection 8πr_{e}^{2}/3

σ_{e} 
0.665 245 8734 ×10^{−28} 
m^{2 } 
0.0019

Bohr magneton eħ/2m_{e} 
μ_{B} 
927.400 968 ×10^{−26} 
J T^{−1} 
0.022 
Nuclear magneton eħ/2m_{p} 
μ_{N} 
5.050 783 53 ×10^{−27} 
J T^{−1} 
0.022 
Ratio of masses proton/electron 
m_{p}/m_{e} 
1836.152 672 45 

0.00041

Gyromagnetic ratio of proton 
γ_{P} 
2.675 222 005 ×10^{8} 
s^{−1} T^{−1} 
0.024 
Shielded gyromagnetic ratio of proton 
γ′_{P} 
2.675 153 268 ×10^{8} 
s^{−1} T^{−1} 
0.025 





Thermal Constants 




Molar gas constant 
R 
8.314 4621 
J mol^{−1} K^{−1} 
0.91 
Loschmidt constant (number of molecules in 1
m^{3} of ideal gas at stp) 
n_{0}

2.686 7805 ×10^{25} 
m^{−3}

0.91 
Boltzmann constant
R/N_{A} 
k 
1.380 6488 ×10^{−23} 
J K^{−1} 
0.91 
Boltzmann constant 
k 
8.617 3324 ×10^{−5} 
eV K^{−1} 
0.91 
Energy kT for T=273.15 K 

0.023 538 243 
eV 
0.91 
StefanBoltzmann constant 2π^{5}k^{4}/15c^{2}h^{3} 
σ 
5.670 373 ×10^{−8} 
W m^{−2}K^{−4} 
3.6 
Constant in Planck formula 2π
hc^{2} ^{†} 
c_{1} 
3.74177152 ×10^{−16} 
W m^{2} 
0.044 
Constant in Planck formula
hc/k ^{†} 
c_{2} 
1.438 770 ×10^{−2} 
m K 
0.91 





Electrical constants 




Josephson constant 2e/h 
K_{J} 
483 597.870 
GHz V^{−1} 
0.022 
Joesphson constant conventional value* 
K_{J90} 
483 597.9 
GHz V^{−1} 
exact 
Von Klitzing constant
h/e^{2} 
R_{K} 
25 812.807 4434 
Ω 
0.00032 
Von Klitzing constant conventional value* 
R_{K90} 
25 812.807 
Ω 
exact 





Conversion factors for mass, energy, wavelength and
frequency 




Electron volt 

1.602 176 565 ×10^{−19} 
J 
0.022 
Atomic mass unit 

931.494 061 
MeV 
0.022 
1 MeV 

1.073 544 150 ×10^{−3} 
u 
0.022 
Rest mass of electron 

0.510 998 928 
MeV 
0.022 
1 eV per molecule 

9.648 533 65 ×10^{7} 
J kmol^{−1} 
0.022 
Quantum energy ÷ wave number 

1.986 445 68 ×10^{−25} 
J m 
0.044 
Energy × wavelength 

1.239 841 93 ×10^{−6} 
eV m 
0.022 
Wave number ÷ energy 

8.065 544 29 ×10^{5} 
eV^{−1} m^{−1} 
0.022 
Quantum energy ÷ frequency 

4.135 667 513 ×10^{−15} 
eV Hz^{−1} 
0.022 
Frequency ÷ energy 

2.417 989 350 ×10^{14} 
Hz eV^{−1} 
0.022 
† See also
section
2.5.2
* the conventional values of the Josephson constant and the von Klitzing
constant were agreed by the International Committee for Weights and Measures
(CIPM) in
1988 and came into international use on 1 January 1990. They are distinguished
from the corresponding SI units by adding "90" to the subscript. The values of
these units are very similar to their corresponding SI units, but are not
identical because the SI values are calculated within the CODATA leastsquares
fitting exercise, while the conventional values have been fixed to provide
continuity in the measurement of electrical quantities based on the Josephson
and von Klitzing effects. Such measurements are not, therefore, strictly
expressed in SI units.
S. Bennett

