University Physics Volume 2

# C | Fundamental Constants

University Physics Volume 2C | Fundamental Constants
Quantity Symbol Value
Atomic mass unit u $1.660 538 782(83)×10−27kg931.494 028(23)MeV/c21.660 538 782(83)×10−27kg931.494 028(23)MeV/c2$
Avogadro’s number $NANA$ $6.02214076×1023reciprocal mole(mol–1)6.02214076×1023reciprocal mole(mol–1)$
Bohr magneton $μB=eℏ2meμB=eℏ2me$ $9.274 009 15(23)×10−24J/T9.274 009 15(23)×10−24J/T$
Bohr radius $a0=ℏ2mee2kea0=ℏ2mee2ke$ $5.291 772 085 9(36)×10−11m5.291 772 085 9(36)×10−11m$
Boltzmann’s constant $kB=RNAkB=RNA$ $1.380649×10–23joule per kelvin(J⋅K–1)1.380649×10–23joule per kelvin(J⋅K–1)$
Compton wavelength $λC=hmecλC=hmec$ $2.426 310 217 5(33)×10−12m2.426 310 217 5(33)×10−12m$
Coulomb constant $ke=14πε0ke=14πε0$ $8.987 551 788...×109N·m2/C2(exact)8.987 551 788...×109N·m2/C2(exact)$
Deuteron mass $mdmd$ $3.343 583 20(17)×10−27kg2.013 553 212 724(78)u1875.612 859MeV/c23.343 583 20(17)×10−27kg2.013 553 212 724(78)u1875.612 859MeV/c2$
Electron mass $meme$ $9.109 382 15(45)×10−31kg5.485 799 094 3(23)×10−4u0.510 998 910(13)MeV/c29.109 382 15(45)×10−31kg5.485 799 094 3(23)×10−4u0.510 998 910(13)MeV/c2$
Electron volt eV $1.602 176 487(40)×10−19J1.602 176 487(40)×10−19J$
Elementary charge e $1.602176634×10−19C1.602176634×10−19C$
Gas constant R $8.314 472(15)J/mol·K8.314 472(15)J/mol·K$
Gravitational constant G $6.674 28(67)×10−11N·m2/kg26.674 28(67)×10−11N·m2/kg2$
Neutron mass $mnmn$ $1.674 927 211(84)×10−27kg1.008 664 915 97(43)u939.565 346(23)MeV/c21.674 927 211(84)×10−27kg1.008 664 915 97(43)u939.565 346(23)MeV/c2$
Nuclear magneton $μn=eℏ2mpμn=eℏ2mp$ $5.050 783 24(13)×10−27J/T5.050 783 24(13)×10−27J/T$
Permeability of free space $μ0μ0$ $4π×10−7T·m/A(exact)4π×10−7T·m/A(exact)$
Permittivity of free space $ε0=1μ0c2ε0=1μ0c2$ $8.854 187 817...×10−12C2/N·m2(exact)8.854 187 817...×10−12C2/N·m2(exact)$
Planck’s constant h
$ℏ=h2πℏ=h2π$
$6.62607015×10−34kg·m2·s–11.05457182×10−34kg·m2·s–16.62607015×10−34kg·m2·s–11.05457182×10−34kg·m2·s–1$
Proton mass $mpmp$ $1.672 621 637(83)×10−27kg1.007 276 466 77(10)u938.272 013(23)MeV/c21.672 621 637(83)×10−27kg1.007 276 466 77(10)u938.272 013(23)MeV/c2$
Rydberg constant $RHRH$ $1.097 373 156 852 7(73)×107m−11.097 373 156 852 7(73)×107m−1$
Speed of light in vacuum c $2.997 924 58×108m/s(exact)2.997 924 58×108m/s(exact)$
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.

Useful combinations of constants for calculations:

$hc=12,400eV·Å=1240eV·nm=1240MeV·fmhc=12,400eV·Å=1240eV·nm=1240MeV·fm$

$ℏc=1973eV·Å=197.3eV·nm=197.3MeV·fmℏc=1973eV·Å=197.3eV·nm=197.3MeV·fm$

$kee2=14.40eV·Å=1.440eV·nm=1.440MeV·fmkee2=14.40eV·Å=1.440eV·nm=1.440MeV·fm$

$kBT=0.02585eV atT=300KkBT=0.02585eV atT=300K$