Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 310 / 2 / a / Solution

Chemical equilibrium for $e^{-}+p\leftrightarrow H+\gamma$ gives ${\mu }_e+{\mu }_p={\mu }_H$, since ${\mu }_{\gamma }=0$. Insert the supplied nonrelativistic equilibrium densities. Neglecting $m_e/m_p$ in the translational reduced mass and using the stated degeneracy convention givesCharge neutrality gives $n_p=n_e$, soThis is the hydrogen Saha ionization equation.