Question

This project is to determine the degree of ionization in a stellar atmosphere that is composed of pure helium. Ultimately, the class will find the temperature at the middle of the He I partial ionization zone, where half of the He I atoms have been ionized. Your task is to compute the ratios for one particular temperature.

1. Use the Saha Equation to find N_II/N_I and N_III/N_II for your temperature. The temperature is T = 13,200 K, the ionization energies of neutral helium and singly ionized helium are χ_I = 24.6 eV and χ_II = 54.4 eV, respectively. The partition functions are Z_I = 1, Z_II = 2, and Z_III =1. Use P_e = 0.2 N/m2 for the electron pressure.

2. Calculate N_II/N_tot.

Answer 1

The saha equation is given by

Here, m_e= the mass of the electron

K= the Boltzmann constant, Z= the partition function, h is the Plank’s constant, and P_e isthe pressure ofthe free electrons

xi is the ratio of ionized and neutral helium =54.4/24.6=2.2 eV

Z_i=1, Z_i+i =2

NII

Here,    Z_II =2, Z_III =1

Z_III/Z_II =1/2