PX282 - C3 - the saha equation

to get $N$ in each ionization state ( $N_{I}$ , $N_{I I}$ ), the saha equation is used:

\frac{N_{i + 1}}{N_{i}} = \frac{2}{n_{e}} \frac{U_{i + 1}}{U_{i}} {(\frac{2 π m_{e} k_{B}}{h^{2}})}^{\frac{3}{2}} \exp (- \frac{χ_{i}}{k_{B} T})

where,
$n_{e} =$ number of free electrons: the more there are, the easier it is to recombine
$\frac{2 π m_{e} k_{B}}{h^{2}} =$ a constant that involves comparing electron quantum energy to thermal energy
$- χ_{i} =$ energy needed to ionize from $i$ to $i + 1$ , eg: $χ_{1} (H) = - 13.6 e V$