PX282 - C4 - the boltzmann-saha equation

$\frac{N_{2}}{N_{t o t a l}}$ is needed, where, $N_{t o t a l} = N_{I} + N_{I I}$ ( $N$ in each ionization state), and $N_{I} = N_{1} + N_{2}$
the fraction of electrons in $n = 2 :$

\begin{aligned} \frac{N_{2}}{N_{t o t a l}} & = \frac{N_{I}}{N_{t o t a l}} \times \frac{N_{2}}{N_{I}} \\ = \frac{N_{I}}{N_{t o t a l}} \times \frac{N_{2}}{N_{1} + N_{2}} \\ = \frac{1}{N_{I} + N_{I I}} \times \frac{\frac{N_{2}}{N_{1}}}{1 + \frac{N_{2}}{N_{1}}} \\ ∴ \frac{N_{2}}{N_{t o t a l}} & = \frac{1}{1 + \frac{N_{I I}}{N_{I}}} \times \frac{\frac{N_{2}}{N_{1}}}{1 + \frac{N_{2}}{N_{1}}} \end{aligned}

$\frac{N_{I I}}{N_{I}}$ can be obtained from the saha equation, and $\frac{N_{2}}{N_{1}}$ from the boltzmann equation