Question

Suppose that a molecle has just two energy levels. The ground state is singly degenerate and the excited state is triply degerate. If the enrgy difference between the two states (on a molar basis) is 52 kJ/mol at what temperature will the two states be equally populated?

QUANTUM CHEMISTRY

Answer 1

where N_f and N_i are popualtion of excited and ground state respectively

g_f and g_i are the degeneracies of excited and ground state respectively

k_B = Boltzmann constant = 1.38 x 10^-23 J K^-1

E is the energy difference between the two states = 52 kJ/mol = 52000 J/mol

T = temperature (Kelvin)

So, for two states to be equally populated, N_f/N_i should be 1.

T = 3.43 10²⁷ K