Consider a gas of neutral hydrogen atoms.
(a) Determine at what temperature will equal numbers of atoms have electrons in the ground state and in the second excited state (n=3).
(b) At a temperature of 85,400 K, when equal numbers N of atoms are in the ground state and in the first excited state, determine how many atoms are in the second excited state (n=3). Write your answer in terms of N.
(c) As the temperature T → [infinity], determine how will the electrons in the hydrogen atoms be distributed, according to the Boltzmann equation. That is, what will be the relative numbers of electrons in the n=1,2,3, ... orbitals? Will this, in fact, be the distribution that actually occurs? Justify.
