Question

2) Consider a stellar atmosphere composed of pure helium. You will find the temperature at the middle of the He I partial ionization zone, where half of the He I atoms have been ionized. (Such an atmosphere would be found on a white dwarf of spectral type DB.) The ionization energies of neutral helium and singly ionized helium are Eion-24.6 ev and Eion-54.4 ev, respectively. The partition functions are Zi: 1,211-2, and Zill=1 (as expected for any completely ionized atom). Use Pe-20 N m 2 for the electron pressure. (a) Use the Saha equation to find Nu/Ni and NIl/Nu for temperatures of 5000 K, 15,000 K, and 25,000 K. How do they compare? (b) Show that Nu/Ntot N/(Nr+N+NIm) can be expressed in terms of the ratios Nu/Ni and Nl/NI. (c) Make a graph of Nu/Neot for a range of temperatures from 5000 K to 25,000 K. What is the temperature at the middle of the He I partial ionization zone, where half of the atoms have been ionized? Because the temperatures of the middle of the hydrogen and He I partial ionization zones are so similar, they are sometimes considered to be a single partial ionization zone with a characteristic temperature of 1-1.5x104 K 3) Follow the procedure of the previous problem to find the temperature at the middle of the He II partial ionization zone, where half of the He II atoms have been ionized. This ionization zone is found at a greater depth in the star, and so the electron pressure is larger - use a value of Pe 1000 N m2. Let your temp range from 10,000 K to 60,000 K. This particular ionization zone plays a crucial role in pulsating stars. eratures

Need help with 3. Have to follow number 2 in regards to using saha equation

Answer 1

Given that (saha equation) N_i + 1/N_i = 2KTZ_i + 1/P_e + i(2 pi me^kT/h^2)^3/2 e^-xi/kT Now for i = 1 N_II/N_I = 2 KT_z/PeZ_1(2 pi me^kT/h^2)^3/2 e^-x_1/kT N_II/N_I = 2kT times 2/20 times 1(2 pi me^k/h^2)^3/2 T^3/2 e^= 24.6/kT N_II/N_I = 1.6 times 10^-10 times 7/5(2pi me^k/h^2)^3/2 T^3/2 e^= 24.6/kT N_II/N_I = 1.6 times 10^-19 T/5 (1.48) T^3/2 e^-(24.6/kT 1/7 N_II/N_I = 3.2 times 10^-18 T(1.48)T^3/2 e^-(24.6/1.6 times 10^-19)1/7 N_II/N_I = 4.75 times 10^-18 T^3/2 exe(-15.376/7) Now T = 5000 N_II/N_I = 4.75 times 10^-18(5000)^3/2 exp(-15.396/5000) = 1.679 times 10^-12 xex (-0.003075) \r\n = 1.679 times 10^-12(0.99) times 5000 N_II/N_I = 5000 times 1.67 times 10^-12 N_II/N_I = 8.35 times 10^-9 similarly for 15,000 25,000 k i = 2 Now W_II/N_II = 2kT/20 times 2(2 pi Me^k/h^2)^3/2 T^3/2 e^-54.4/kT = 1.6 times 10^-19/20 T(1.48)T^3/2 e^-(54.4/1.6)^1/7 = (0.1189) times 10^-19 T^5/2 exp(-34/7) for T = 5000 N_III/N_II = (0.1184) times 10^-19(0.9) = 2 - 09 times 10^-11 as we can see N_I/Ntotal =