An oscillator with frequency f = 2.1×10^(12) Hz (about typical for a greenhouse gas molecule) is in equilibrium with a thermal reservoir at temperature T. The spacing between the energy levels of the oscillator is given by ε = hf, where h = 6.626×10^(-34) J*sec.
(a) For what temperature does P1/P0 = 1/2, where P1 is the probability that the oscillator has E = ε (the first excited state) and P0 is the probability that it has E = 0 (the lowest energy state)?
(b) If T is 10% of the value you calculated in part 1), what is the ratio P1/P0?
(c) At the temperature of part (b), what is the ratio P2/P1, where P2is the probability that the oscillator is in the second excited state (E = 2ε)?