# List of Physical Constants Digits shown within parentheses indicate the standard uncertainty of the constant. > [!Speed of light in a vacuum] In the *special theory of relativity*, the speed of light in a vacuum is the *upper limit* for the speed at which matter, energy, or information can travel. >$c=299\;792\;458\text{ m s}^{-1}$ ^7456b7 > [!Planck constant] The Planck constant is the constant of proportionality that relates the *energy* and *wavelength* of a *photon*. >$h=6.626\;070\;15\times10^{-34}\text{ J s}$ > [!Reduced Planck constant] The reduced Planck constant is the Planck constant divided by $2\pi$ and is used in the presence of [[angular frequency]]. >$\hbar=1.054\;571\;817\ldots\times10^{-34}\text { J s}$ > [!Newtonian constant of gravitation] The *empirical* constant of proportionality in Newton's *law of universal gravitation*. >$G=6.674\;30(15)\ldots\times10^{-11}\text{ N m}^{2}\text{ kg}^{-2}$ > [!Vacuum permittivity] Vacuum permittivity is the *absolute dielectric permittivity* of a *classical vacuum*. It is also known as the *electric constant*. It is the capability of an electric field to permeate a vacuum. >$\varepsilon_{0}=8.854\;187\;8128(13)\ldots\times10^{-12}\text{ F m}^{-1}$ ^c1570b > [!Vacuum permeability] Vacuum permeability is the *magnetic permeability* of a *classical vacuum*. It is also known as the *magnetic constant*. It is the capability of a magnetic field to permeate a vacuum. >$\mu_{0}=1.256\;637\;062\;12(19)\ldots\times10^{-6}\text{ H m}^{-1}$ ^45bd61 > [!Impedance of free space] The impedance of free space relates the *magnitudes* of the electric and magnetic fields of *electromagnetic radiation* travelling through *free space*. >$Z_{0}=376.730\;313\;668(57)\ldots\;\Omega$ > [!Avogadro constant] The constant of proportionality that relates the *number* of *constituent particles* of a sample with the *amount of substance* in that sample. >$N_{A}=6.022\;140\;76\times10^{23}\;\text{mol}^{-1}$ > [!Elementary charge] The *magnitude* of *[[electric charge]]* carried by a *single* proton or electron. >$e=1.602\;176\;634\times10^{-19}\text{ C}$ ^a35416 > [!Coulomb constant] The constant of proportionality in several *electrostatics* equations. >$k_{e}=8.987\;551\;7923(14)\times10^{9}\text{ N m}^{2}\text{ C}^{2}$ > [!Electron mass] >$m_{e}=9.109\;383\;7015(28)\ldots\times10^{-31}\text{ kg}$ > [!Proton mass] >$m_{p}=1.672\;621\;923\;69(51)\ldots\times10^{-27}\text{ kg}$ > [!Neutron mass] >$m_{n}=1.674\;927\;498\;04(95)\ldots\times10^{-27}\text{ kg}$ > [!Bohr radius] The *approximate* most probable distance between the nucleus and the electron in a *hydrogen* atom in its *ground state*. >$a_{0}=5.291\;772\;109\;03(80)\ldots\times10^{-11}\text{ m}$ > [!Rydberg constant] The constant used for *heavy atoms* in the *Rydberg formula* for calculating wavelengths of *spectral lines*. >$R_{\infty}=10\;973\;731.568\;160(21)\ldots\text{ m}^{-1}$ > [!Unified atomic mass unit] The unified atomic mass unit or dalton is defined as $\frac{1}{12}$ the mass of an *unbound neutral* atom of *carbon-12* in its *ground state* and *at rest*. >$u,m_{u}=1.660\;539\;066\;60(50)\ldots\times10^{-27}\text{ kg}$ > [!Boltzmann constant] The constant of proportionality that relates the *average relative kinetic energy* of particles in a gas with the *thermodynamic temperature* of the gas. >$k_{B}=1.380\;649\times10^{-23}\text{ J K}^{-1}$ > [!Molar gas constant] The *molar equivalent* to the *Boltzmann constant*. >$R=8.314\;462\;618\ldots\text{ J K}^{-1}\text{ mol}^{-1}$ > [!NOTE] Stefan-Boltzmann constant The constant of proportionality in the *Stefan-Boltzmann law* relating the power radiated by a *black body* to its *thermodynamic temperature*. >$\sigma=5.670\;374\;419\ldots\times10^{-8}\text{ W m}^{-2}\text{ K}^{-2}$ > [!Wien's displacement constant] The constant of proportionality used in *Wien's displacement law* when used with wavelengths. >$b=2.897\;771\;955\ldots\times10^{-3}\text{ m K}$ > [!Electronvolt] An electronvolt is the amount of *kinetic energy* gained by a *single electron* accelerating *from rest* through an electric potential difference of *one volt*. Its magnitude in joules is equal to the value of *elementary charge*. >$\text{eV}=1.602\;176\;634\times10^{-19}\text{ J}$ > [!Atomic mass energy equivalent] The *equivalent* energy within one *unified atomic mass unit* at rest. >$m_{u}c^{2}=931.494\;102\;42(28)\text{ MeV}$ > [!Standard acceleration due to gravity] The *nominal* gravitational acceleration of an object in a *vacuum* near the surface of Earth. >$g_{n}=9.806\;65\text{ m s}^{-2}$ > [!Standard atmosphere] The unit of pressure *approximately* equal to the *average* atmospheric pressure of Earth at *sea level*. > $\text{atm}=101\;325\text{ Pa}$