Please help with the stat-mech question below:

The question is COMPLETE! Nothing is missing.

This problem set is all about changing particle numbers! In this rst problem we will explore the ionization of hydrogen. Lets rst consider the thermal excitation of a hydrogen atom. The energy levels of an electron bound to hydrogen are given by E E O E02136BV, n6{112133'\"}7 n _;3 where n is the quantum number for energy and E0 is the Rydberg unit of energy/the ionization energy of ground state atomic hydrogen. Also recall that the degeneracy of the energy levels in hydrogen are given by g(En) : 2712. (a) Using canonical methods (rather than micro-canonical or grand canonical), determine the relative fraction of hydrogen atoms that are in the n = 2 first excited state vs. the n = 1 ground state as a function of the temperature T. At what temperature does this fraction reach 1 part in 106? How about 1 part in 1000? If we consider the energy levels of an electron in hydrogen as an \"internal structure\" (in contrast to the \"external structure" where we treat the atomic hydrogen as an ideal gas). That is, we can use the states of hydrogen described earlier as the one-particle microstates for calculating an internal one-particle canonical partition function, Zim. You can see from part (a) that if T