An oscillator with frequency f = 8×1011 hz (about that of a diatomic 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)?

t =

k

b)

if t is 10% of the value you calculated in part 1), what is the ratio p1/p0?

p1 / p0 =

c)

at the temperature of part 2), what is the ratio p2/p1, where p2is the probability that the oscillator is in the second excited state (e = 2ε)?

p2/p1 =

d)

now suppose you have a large number of these oscillators (such as in a solid). at the temperature of parts 2) and 3), what is the average thermal energy per oscillator divided by kt? that is, calculate /kt. (equipartition would have this ratio be 1, but that's not the answer here.)

/ kt =