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Unless otherwise stated this page contains Version 1.0 content (Read more about versions)

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

γP

  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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