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Version 2.0
Updated: 19 December
2011
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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 'least-squares' 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),
633-730 (2008)
and
P. J. Mohr, B. N. Taylor, and D. B. Newell, J. Phys.
Chem. Ref. Data 37(3), 1187-1284 (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
106) |
|
|
|
|
|
|
|
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 |
me |
9.109 382 91 ×10−31 |
kg |
0.044 |
|
Avogadro constant |
NA |
6.022 141 29 ×1023 |
mol−1 |
0.044 |
|
Atomic mass constant |
mu |
1.660 538 921 ×10−27 |
kg |
0.044 |
|
Faraday constant |
F(=NAe) |
96 485.3365 |
C mol−1 |
0.022 |
|
Newtonian constant of gravitation |
G |
6.673 84 ×10−11 |
m3 kg−1s−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/me |
−1.758 820 088 ×1011 |
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/μ0c2)ħ2/mee2 |
a0 |
5.291 772 1092 ×10−11 |
m |
0.00032 |
|
Compton wavelength of electron |
λc |
2.426 310 2389 ×10−12 |
m |
0.00065 |
|
Compton wavelength of electron (λc/2π) |
ƛc |
386.159 268 00 ×10−15 |
m |
0.00065 |
|
Classical ‘radius’ of electron
(μ0c2/4π)e2/mc2 |
re |
2.817 940 3267
×10−15
|
m
|
0.00097
|
|
Thomson cross-section 8πre2/3
|
σe |
0.665 245 8734 ×10−28 |
m2 |
0.0019
|
|
Bohr magneton eħ/2me |
μB |
927.400 968 ×10−26 |
J T−1 |
0.022 |
|
Nuclear magneton eħ/2mp |
μN |
5.050 783 53 ×10−27 |
J T−1 |
0.022 |
|
Ratio of masses proton/electron |
mp/me |
1836.152 672 45 |
|
0.00041
|
|
Gyromagnetic ratio of proton |
γP |
2.675 222 005 ×108 |
s−1 T−1 |
0.024 |
|
Shielded gyromagnetic ratio of proton |
γ′P |
2.675 153 268 ×108 |
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
m3 of ideal gas at stp) |
n0
|
2.686 7805 ×1025 |
m−3
|
0.91 |
| Boltzmann constant
R/NA |
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 |
| Stefan-Boltzmann constant 2π5k4/15c2h3 |
σ |
5.670 373 ×10−8 |
W m−2K−4 |
3.6 |
| Constant in Planck formula 2π
hc2 † |
c1 |
3.74177152 ×10−16 |
W m2 |
0.044 |
| Constant in Planck formula
hc/k † |
c2 |
1.438 770 ×10−2 |
m K |
0.91 |
| |
|
|
|
|
| Electrical constants |
|
|
|
|
| Josephson constant 2e/h |
KJ |
483 597.870 |
GHz V−1 |
0.022 |
| Joesphson constant conventional value* |
KJ-90 |
483 597.9 |
GHz V−1 |
exact |
| Von Klitzing constant
h/e2 |
RK |
25 812.807 4434 |
Ω |
0.00032 |
| Von Klitzing constant conventional value* |
RK-90 |
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 ×107 |
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 ×105 |
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 ×1014 |
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 least-squares
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
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