μ_{e} + μ_{p} = μ_{H} + μ_{γ}

μ_{γ} = 0

I = (m_{e} + m_{p} - m_{H}) c^{2}

, approximately

13.6 eV

\frac{n _{e} n _{p}}{n _{H}} = \frac{g _{e} g _{p}}{g _{H}} (\frac{2 πk T}{h ^{2}} \frac{m _{e} m _{p}}{m _{H}})^{3/2} e^{- I / (k T)} .

Use

g_{e} g_{p} / g_{H} = 1

and

m_{p} / m_{H} ≃ 1

\frac{n _{e} n _{p}}{n _{H}} = (\frac{2 π m _{e} k T}{h ^{2}})^{3/2} e^{- I / (k T)} .

The assumptions are nonrelativistic, dilute, nondegenerate species at a common temperature, ground-state hydrogen with the stated degeneracy factors, negligible mass correction in the prefactor, and sufficiently rapid reactions to maintain chemical equilibrium.