Questions

The pascale is the SI unit of pressure one nt/m$^2$. Earth's atmospheric pressure is 101325 pa, or 101.325 kpa. In cgs units, 1 pa is 10 dy/cm$^2$.

1. In the previous example at 10,080 K, what would be the electron pressure $N_e k T$ in pa, and in units of the Earth's atmospheric pressure?

2. Assume that the electron pressure $P_e = N_e k T$ is nearly the same regardless of the temperature of a star and set it equal to the value you found in Question 1. Evaluate the number of atoms in the $n=2$ state of hydrogen compared to the total number of hydrogens regardless of their state or excitation or ionization. Show that this ratio is maximum at a temperature of approximately 10,000 K. Use the Boltzmann equation and Saha ionization equilibrium starting with

$$\frac{N_2}{N_{total}} = \left(\frac{N_2}{N_1 + N_2}\right) \left(\frac{N_0}{N_{total}}\right)$$

$$\frac{N_2}{N_{total}} = \left(\frac{N_2/N_1}{1 + N_2/N_1}\right) \left(\frac{1}{1+N_{II}/N_{I}}\right)$$

where $N_{total}$ is the total number of hydrogens, $N_1$ is the number of neutral atoms in the lowest state, $N_2$ is the number of neutrals in the second lowest state, and $N_I$ and $N{_{II}}$ are the total numbers of neutrals and ions.