Consider a gas of neutral hydrogen atoms, as in Example 8.1.3.
(a) 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, how many atoms are in the second excited state (n=3)? Express your answer in terms of N.
(c) As the temperature T→∞, 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? Why or why not?