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Boltzmann Distribution

Relates the average kinetic energy of particles to temperature, influencing vibrational population distributions and spectral intensities.
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The statement of the theorem

The population ratio Ni/NjN_i / N_j of two energy states EiE_i and EjE_j at thermal equilibrium temperature TT is determined by the Boltzmann factor: NiNj=e−(Ei−Ej)kBT\frac{N_i}{N_j} = e^{-\frac{(E_i - E_j)}{k_B T}}. For a general energy level EiE_i, the population NiN_i is given by the Boltzmann distribution: Ni=Ntotale−Ei/kBTN_i = N_{total} e^{-E_i / k_B T}, where kBk_B is the Boltzmann constant and NtotalN_{total} is the total number of particles.