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# Physical constant

In science, a physical constant is a physical quantity whose numerical value does not change. It can be contrasted with a mathematical constant, which is a fixed value that does not directly involve a physical measurement.

There are many physical constants in science, some of the most famous being Planck's constant, the gravitational constant, and Avogadro's number. Constants can take many forms: the Planck length represents a fundamental physical distance; the speed of light in a vacuum signifies a maximum speed limit of the universe; and the fine-structure constant, which characterizes the interaction between electrons and photons, is dimensionless.

Beginning with Paul Dirac in 1937, some scientists have speculated that physical constants may actually decrease in proportion to the age of the universe. Scientific experiments have not yet pinpointed any definite evidence that this is the case, although they have placed upper bounds on the maximum possible relative change per year at very small amounts (roughly 10-5 per year for the fine structure constant $\alpha \,\!$ and 10-11 for the gravitational constant $G \,\!$).

Some "constants" are really artifacts of the unit system used, such as SI or cgs. In natural units, some of these supposedly physical constants turn out to be conversion factors.

Constants that are independent of systems of units are typically dimensionless numbers, and are known as fundamental physical constants.

Some believe that if the physical constants had slightly different values, our universe would be so different that intelligent life would probably not have emerged, and that our universe seems to be fine-tuned for intelligent life.

## Table of physical constants

Table of physical constants
Universal constants
Quantity Symbol Value1 (SI units) Relative Standard Uncertainty Reference
characteristic impedance of vacuum $Z_0 = \mu_0 c \,$ 376.730 313 461... Ω defined a
permittivity of vacuum (electric constant) $\epsilon_0 = 1 / ( \mu_0 c^2 )\,$ 8.854 187 817... × 10-12F·m-1 defined a
permeability of vacuum (magnetic constant) $\mu_0 \,$ 4π × 10-7 N·A-2 = 1.2566 370 614... × 10-6 N·A-2 defined a
Newtonian constant of gravitation $G \,$ 6.6742(10) × 10-11m3·kg-1·s-2 1.5 × 10-4 a
Planck's constant $h \,$ 6.626 0693(11) × 10-34 J·s 1.7 × 10-7 a
Dirac's constant $\hbar = h / (2 \pi)$ 1.054 571 68(18) × 10-34 J·s 1.7 × 10-7 a
Planck length $l_p = (\hbar G / c^3)^ \frac{1}{2} \,$ 1.616 24(12) × 10-35 m 7.5 × 10-5 a
Planck mass $m_p = ( \hbar c / G )^ \frac{1}{2} \,$ 2.176 45(16) × 10-8 kg 7.5 × 10-5 a
Planck temperature $T_p = ( \hbar c^5 / G )^ \frac{1}{2} / k$ 1.416 79(11) × 1032 K 7.5 × 10-5 a
Planck time $t_p = (\hbar G / c^5)^ \frac{1}{2}$ 5.391 21(40) × 10-44 s 7.5 × 10-5 a
speed of light in vacuum $c \,$ 299 792 458 m·s-1 defined a
Electromagnetic constants
Quantity Symbol Value1 (SI units) Relative Standard Uncertainty Reference
Bohr magneton $\mu_B = e \hbar / 2 m_e$ 927.400 949(80) × 10-26 J·T-1 8.6 × 10-8 a
conductance quantum $G_0 = 2 e^2 / h \,$ 7.748 091 733(26) × 10-5 S 3.3 × 10-9 a
elementary charge (electron charge) $e \,\!$ 1.602 176 53(14) × 10-19 C 8.5 × 10-8 a
Josephson constant $K_J = 2 e / h \,$ 483 597.879(41) × 109 Hz· V-1 8.5 × 10-8 a
magnetic flux quantum $\phi_0 = h / 2 e \,$ 2.067 833 72(18) × 10-15 Wb 8.5 × 10-8 a
nuclear magneton $\mu_N = e \hbar / 2 m_p$ 5.050 783 43(43) × 10-27 J·T-1 8.6 × 10-8 a
resistance quantum $R_0 = h / 2 e^2 \,$ 12 906.403 725(43) Ω 3.3 × 10-9 a
von Klitzing constant $R_K = h / e^2 \,$ 25 812.807 449(86) Ω 3.3 × 10-9 a
Atomic and nuclear constants
Quantity Symbol Value1 (SI units) Relative Standard Uncertainty Reference
alpha particle mass2 $m_\alpha \,$ 6.644 6565(11) × 10-27 kg 1.7 × 10-7 a
Bohr radius $a_0 = \alpha / 4 \pi R_\infin \,$ 0.529 177 2108(18) × 10-10 m 3.3 × 10-9 a
deuteron magnetic moment $\mu_d \,$ 0.433 073 482(38) × 10-26 J · T-1 8.7 × 10-8 a
mass2 $m_d \,$ 3.343 583 35(57) × 10-27 kg 1.7 × 10-7 a
rms charge radius $R_d \,$ 2.1394 × 10-15 m 1.3 × 10-3 a
electron classical radius $r_e = \alpha^2 a_0 \,$ 2.817 940 325(28) × 10-15 m 1.0 × 10-8 a
Compton wavelength $\lambda_C = h / m_e c \,$ 2.426 310 238(16) × 10-12 m 6.7 × 10-9 a
g factor (Lande g factor) $g_e = 2 \mu_e / \mu_B \,$ -2.002 319 304 3718(75) 3.8 × 10-12 a
gyromagnetic ratio $\gamma_e = 2 |\mu_e| / \hbar$ 1.760 859 74(15) × 1011 s-1 T-1 8.6 × 10-8 a
magnetic moment $\mu_e \,$ -928.476 412(80) × 10-26 J·T-1 8.6 × 10-8 a
mass2 $m_e \,$ 9.109 3826(16) × 10-31 kg 1.7 × 10-7 a
Fermi coupling constant $G_F / (\hbar c)^3$ 1.166 39(1) × 10-5 GeV-2 8.6 × 10-6 a
fine-structure constant $\alpha = \mu_0 e^2 c / (2 h) \,$ 7.297 352 568(24) × 10-3 3.3 × 10-9 a
$\alpha^{-1} \,$ 137.035 999 11(46) 3.3 × 10-9 a
Hartree energy $E_h = 2 R_\infin h c \,$ 4.359 744 17(75) × 10-18 J 1.7 × 10-7 a
helion mass2 $m_h \,$ 5.006 412 14(86) × 10-27 kg 1.7 × 10-7 a
shielded gyromagnetic ratio $\gamma_h^'(\,^3\mbox{He}) = 2 |\mu_h^'(\,^3\mbox{He})| / \hbar$ 2.037 894 70(18) × 108 s-1 T-1 8.7 × 10-8 a
shielded magnetic moment $\mu_h^'(\,^3\mbox{He})$ -1.074 553 024(93) × 10-26 J · T-1 8.7 × 10-8 a
muon Compton wavelength $\lambda_{C,\mu} = h / m_\mu c \,$ 11.734 441 05(30) × 10-15 m 2.5 × 10-8 a
g factor $g_\mu \,$ -2.002 331 8396(12) 6.2 × 10-10 a
magnetic moment $\mu_\mu \,$ -4.490 447 99(40) × 10-26 J · T-1 8.9 × 10-8 a
magnetic moment anomaly $a_\mu = |\mu_\mu| / (e \hbar / 2 m_\mu) - 1$ 1.165 919 81(62) × 10-3 5.3 × 10-7 a
mass2 $m_\mu \,$ 1.883 531 40(33) × 10-28 kg 1.7 × 10-7 a
neutron Compton wavelength $\lambda_{C,n} = h / m_n c \,$ 1.319 590 9067(88) × 10-15 m 6.7 × 10-9 a
g factor $g_n = 2 \mu_n / \mu_N \,$ -3.826 085 46(90) 2.4 × 10-7 a
gyromagnetic ratio $\gamma_n = 2 |\mu_n| / \hbar$ 1.832 471 83(46) × 108 s-1 T-1 2.5 × 10-7 a
magnetic moment $\mu_n \,$ -0.966 236 45(24) × 10-26 J · T-1 2.5 × 10-7 a
mass2 $m_n \,$ 1.674 927 28(29) × 10-27 kg 1.7 × 10-7 a
proton Compton wavelength $\lambda_{C,p} = h /m_p c \,$ 1.321 409 8555(88) × 10-15 m 6.7 × 10-9 a
g factor $g_p = 2 \mu_p / \mu_N \,$ 5.585 694 701(56) 1.0 × 10-8 a
gyromagnetic ratio $\gamma_p = 2 \mu_P / \hbar$ 2.675 222 05(23) × 108 s-1·T-1 8.6 × 10-8 a
magnetic moment $\mu_p \,$ 1.410 606 71(12) × 10-26 J·T-1 8.7 × 10-8 a
mass2 $m_p \,$ 1.672 621 71(29) × 10-27 kg 1.7 × 10-7 a
shielded gyromagnetic ratio $\gamma_p^' = 2 \mu_p^' / \hbar$ 2.675 153 33(23) × 108 s-1 T-1 8.6 × 10-8 a
shielded magnetic moment $\mu_p^'$ 1.410 570 47(12) × 10-26 J · T-1 8.7 × 10-8 a
quantum of circulation $h / 2 m_e \,$ 3.636 947 550(24) × 10-4 m2 s-1 6.7 × 10-9 a
Rydberg constant $R_\infin = \alpha^2 m_e c / 2 h \,$ 10 973 731.568 525(73) m-1 6.6 × 10-12 a
tauon Compton wavelength $\lambda_{C,\tau} = h / m_\tau c \,$ 0.697 72(11) × 10-15 m 1.6 × 10-4 a
mass2 $m_\tau \,$ 3.167 77(52) × 10-27 kg 1.6 × 10-4 a
Thomson cross section $(8 \pi / 3)r_e^2$ 0.665 245 873(13) × 10-28 m2 2.0 × 10-8 a
weak mixing angle $\sin^2 \theta_W = 1 - (m_W / m_Z)^2 \,$ 0.222 15(76) 3.4 × 10-3 a
Physico-chemical constants
Quantity Symbol Value1 (SI units) Relative Standard Uncertainty Reference
atomic mass constant (unified atomic mass unit) $m_u = 1 u \,$ 1.660 538 86(28) × 10-27 kg 1.7 × 10-7 a
Avogadro's number $N_A, L \,$ 6.022 1415(10) × 1023 1.7 × 10-7 a
Boltzmann constant $k = R / N_A \,$ 1.380 6505(24) × 10-23 J·K-1 1.8 × 10-6 a
Faraday constant $F = N_A e \,$ 96 485.3383(83)C·mol-1 8.6 × 10-8 a
first radiation constant $c_1 = 2 \pi h c^2 \,$ 3.741 771 38(64) × 10-16 W·m2 1.7 × 10-7 a
for spectral radiance $c_{1L} \,$ 1.191 042 82(20) × 10-16 W · m2 sr-1 1.7 × 10-7 a
Loschmidt constant at T=273.15 K and p=101.325 kPa $n_0 = N_A / V_m \,$ 2.686 7773(47) × 1025 m-3 1.8 × 10-6 a
molar gas constant $R \,$ 8.314 472(15) J·K-1·mol-1 1.7 × 10-6 a
molar Planck constant $N_A h \,$ 3.990 312 716(27) × 10-10 J · s · mol-1 6.7 × 10-9 a
molar volume of an ideal gas at T=273.15 K and p=100 kPa $V_m = R T / p \,$ 22.710 981(40) × 10-3 m3 ·mol-1 1.7 × 10-6 a
at T=273.15 K and p=101.325 kPa 22.413 996(39) × 10-3 m3 ·mol-1 1.7 × 10-6 a
Sackur-Tetrode constant at T=1 K and p=100 kPa $S_0 / R = \frac{5}{2}$
$+ \ln\left[ (2\pi m_u k T / h^2)^{3/2} k T / p \right]$
-1.151 7047(44) 3.8 × 10-6 a
at T=1 K and p=101.325 kPa -1.164 8677(44) 3.8 × 10-6 a
second radiation constant $c_2 = h c / k \,$ 1.438 7752(25) × 10-2 m·K 1.7 × 10-6 a
Stefan-Boltzmann constant $\sigma = (\pi^2 / 60) k^4 / \hbar^3 c^2$ 5.670 400(40) × 10-8 W·m-2·K-4 7.0 × 10-6 a
Wien displacement law constant $b = (h c / k) / \,$ 4.965 114 231... 2.897 7685(51) × 10-3 m · K 1.7 × 10-6 a
Quantity Symbol Value (SI units) Relative Standard Uncertainty Reference
conventional value of Josephson constant3 $K_{J-90} \,$ 483 597.9 × 109 Hz · V-1 defined a
conventional value of von Klitzing constant4 $R_{K-90} \,$ 25 812.807 Ω defined a
molar mass constant $M_u = M(\,^{12}\mbox{C}) / 12$ 1 × 10-3 kg · mol-1 defined a
of carbon-12 $M(\,^{12}\mbox{C}) = N_A m(\,^{12}\mbox{C})$ 12 × 10-3 kg · mol−1 defined a
standard acceleration of gravity (gee, free fall on Earth) $g_n \,\!$ 9.806 65 m·s-2 defined a
standard atmosphere $atm \,\!$ 101 325 Pa defined a

Notes:
1the values are given in the so-called concise form; the number in brackets is the standard uncertainty which is the value multiplied by the relative standard uncertainty.
2the given value is for rest mass.
3This is the value adopted internationally for realizing representations of the volt using the Josephson effect.
4This is the value adopted internationally for realizing representations of the ohm using the quantum Hall effect.

03-10-2013 05:06:04