Q: Calculate the ratio of molecules in the upper to those in the lower energy level when the separation between these is as follows. Assume the temperature is 300 K. Three types of energy involved are shown.

1. 11.9 J*mol^-1 (rotational)
2. 11.9 kJ*mol^-1 (vibrational)
3. 119 kJ*mol^-1 (electronic)

Solution

We apply n_upper / n_lower = exp[-DE / kT] in each case. Since E is given for 1 mol, we must use the form

n_upper / n_lower = exp[-DE / RT]

where R = 8.31 J*mol-1.

1. rotational: n_upper / n_lower = exp(-11.9/8.31*300) = 0.9952 (the two states are almost equally populated.)
   
2. vibrational: n_upper / n_lower = 8.5*10-3
3. electronic: n_upper / n_lower = 1.86*10-21