# Boltzmann distribution

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${\displaystyle {\frac {n_{2}}{n_{1}}}={\frac {g_{2}}{g_{1}}}e^{-{\frac {\Delta E}{kT}}}\,\!}$
where ${\displaystyle n_{1},n_{2}}$ are the number (or number density) of atoms in energy states 1 and 2, respectively, ${\displaystyle g_{1},g_{2}}$ are the respective degeneracies of those energy states (i.e., how many distinct configurations of the atom have that same energy state), ${\displaystyle \Delta E=E_{2}-E_{1}}$ is the energy difference between the two states, ${\displaystyle k}$ is Boltzmann’s constant, and ${\displaystyle T}$ is the temperature describing the distribution of states in the system