Determine the equilibrium ionization fraction for the reaction

\[
\mathrm{Na} ightleftarrows \mathrm{Na}^{+}+e^{-}
\]

in a sodium vapor. Treat all three species as ideal classical monatomic gases. The ionization energy of sodium is \(5.139 \mathrm{eV}, \mathrm{Na}^{+}\)ions are spin-zero, and neutral \(\mathrm{Na}\) and free \(e^{-}\)are both spin- \(\frac{1}{2}\). Derive the Saha equation for the ionized fraction \(\left[\mathrm{Na}^{+}ight] /\left([\mathrm{Na}]+\left[\mathrm{Na}^{+}ight]ight)\)for a neutral plasma as a function of temperature at a fixed total density. Plot the ionized fraction as a function of temperature for some chosen total density.