Given the energy levels in the two-level system shown in the diagram below.

1. Write an expression for the molecular partition function of a two level system

2. What is the magnitude of the partition function at T = 0 K? 

3. What is the magnitude of the partition function at T = ¥ K?

4. If e = 1000 cm^-1, at what temperature is the probability of the upper level equal to 0.25?