 Saha half-ionization temperature

With the rounded hydrogen Saha equation coefficient, the condition $X_e=1/2$ gives the displayed equation for $y=\mathcal{B}/T$. Its low-temperature root is about $42$, hence $T\simeq 0.32$ eV for hydrogen binding energy $13.6$ eV. Dropping the slowly varying logarithm gives the rough leading-log estimate $T\sim 0.4$ eV. This equilibrium convention is distinct from photon decoupling and from a full kinetic recombination calculation.