Question

In the inner solar system, (inside of Mars' orbit) a reasonable characteristic temperature for planetary atmospheres is 200K. suppose a certain molecule has two levels energies differ by amount corresponding to the maximum frequency at this temperature. a.) what is this maximum frequency and the corresponding energy of this transition? b) By what factor does the rate of transitions between the levels of our molecule differ from the rate of spontaneous transition from the upper to lower level?

Answer 1

(a)

According to Wien's displacement law, the maximum frequency at a temperature T is

So, the maximum frequency at temperature T = 200 K is

Corresponding energy to this transition is

(b)

The rate of stimulated emission transitions and the rate of spontaneous emission transitions are related by the Einstein's A and B coefficients and relations between them as

where k = Boltzman constant and other symbols have usual meanings.

So, for present temperature T= 200 K and the frequency , we have