= Solution
<Chemical equilibrium> imposes $\mu_e+\mu_p=\mu_H+\mu_\gamma$. For blackbody <photons>, $\mu_\gamma=0$. Define the positive <Hydrogen binding energy> by $I=(m_e+m_p-m_H)c^2$, approximately $13.6\,\mathrm{eV}$. Multiplying the two <Maxwell-Boltzmann distribution> number densities and dividing by the neutral-hydrogen density gives
$$
\frac{n_en_p}{n_H}=\frac{g_eg_p}{g_H}
\left(\frac{2\pi kT}{h^2}\frac{m_em_p}{m_H}\right)^{3/2}e^{-I/(kT)}.
$$
Use $g_eg_p/g_H=1$ and $m_p/m_H\simeq1$ to obtain the <Saha ionization equation>
$$
\boxed{\frac{n_en_p}{n_H}=\left(\frac{2\pi m_e kT}{h^2}\right)^{3/2}e^{-I/(kT)}.}
$$
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>.
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