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# Physical constant

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

There are many such constants used in science, some of the most famous of which being: Planck's constant, the gravitational constant and Avogadro's constant (better known as Avogadro's number). Constants can take many forms; some, such as the Planck length represents a fundamental physical distance, others such as the speed of light signifies the maximun speed limit of the universe, yet others are dimensionless quantities such as the fine-structure constant which embodies the interaction between electrons and photons.

Below is a list of physical constants:

Quantity Symbol Value Ref.
speed of light in vacuum c 299 792 458 m·s-1 (defined) a
permeability of vacuum μ0 4π × 10-7 N A-2 (defined) a
12.566 370 614... × 10-7 N A-2 a
permittivity of vacuum ε0 = 1/(μ0c2) 8.854 187 817 ... × 10-12 F·m-1 a
characteristic impedance of vacuum Z0 = μ0c 376.730 313 461... Ω (defined) a
gravitational constant G 6.672 59(85) × 10-11 m3·kg-1·s-2 ?
Planck's constant h 6.626 068 76(52) × 10-34 J·s a
Dirac's constant h = h / (2π) 1.054 571 596(82) × 10-34 J·s a
Planck mass mp = (hc / G) kg a
Planck length lp= (hG / c3) m a
Planck time tp = (hG / c5) s a
elementary charge e 1.602 176 462(63) × 10-19 C a
electron rest mass me 9.109 381 88(72) × 10-31 kg a
proton rest mass mp 1.672 621 58(13) × 10-27 kg a
neutron rest mass mn 1.674 927 16(13) × 10-27 kg a
atomic mass constant, (unified atomic mass unit) mu = 1 u 1.660 538 73(13) × 10-27 kg a
Avogadro's number L, NA 6.022 141 99(47) × 1023 a
Boltzmann constant k 1.380 6503(24) × 10-23 J·K-1 a
Faraday constant F 9.648 534 15(39) × 104 C·mol-1 a
gas constant R 8.314 472(15) J·K-1·mol-1 a
zero of the Celsius scale   273.15 K (defined) ?
molar volume, ideal gas, p = 1 bar, θ = 00C   22.710 981(40) L·mol-1 a
standard atmosphere atm 101 325 Pa (defined) a
fine structure constant α = μ0e2c / (2h) 7.297 352 533(27) × 10-3 a
α-1 137.035 999 76(50) a
Bohr radius a0 5.291 772 083(19) × 10-11 m a
Hartree energy Eh 4.359 743 81(34) × 10-18 J a
Rydberg constant R 1.097 373 156 8549(83) × 107 m-1 a
Bohr magneton μB 9.274 008 99(37) × 10-24 J·T-1 a
electron magnetic moment μe -9.284 763 62(37) × 10-24 J·T-1 a
nuclear magneton μN 5.050 786 6(17) × 10-27 J·T-1 ?
proton magnetic moment μp 1.410 607 61(47) × 10-26 J·T-1 ?
proton magnetogyric ratio γp 2.675 221 28(81) × 108 s-1·T-1 ?
magnetic moment of protons in H20, μ'p μ'p / μB 1.520 993 129(17) × 10-3 ?
proton resonance frequency per field in H20 γ'p / (2π) 42.576 375 (13) M·Hz·T-1 ?
Stefan-Boltzmann constant σ 5.670 400(40) × 10-8 W·m-2·K-4 a
first radiation constant c1 3.741 774 9(22) × 10-16 W·m2 ?
second radiation constant c2 1.438 769 (12) × 10-2 m·K ?
standard acceleration of free fall gn 9.80665 m·s-2 (defined) ?

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

## References

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