Example 9.2 obtains a ratio of the number of particles expected in the n = 2 state to that...

Example 9.2 obtains a ratio of the number of particles expected in the n = 2 state to that in the ground slate. Rather than the n = 2 state, consider arbitrary n

(a) Show that the ratio is

Note that hydrogen atom energies are En = -13.6eV/n2.

(b) What is the limit of this ratio as n becomes very large? Can it exceed 1 ? If so, under what condition(s)?

(c) In Example 9.2, we found that even at the temperature of the Sun's surface (~6000 K), the ratio for n = 2 is only 10-8. For what value of n would the ratio be 0.01?

(d) Is it realistic that the number of atoms with high n could be greater than the number with low n?