Problem. Consider one mole of non-interacting distinguishable hypothetical particles at a given temperature T. Assume each particle can occupy one of three energy levels with the following energies: 80 = 0; 1 = 4ɛ; 2 = 9ɛ. The degeneracy numbers for these energy levels are 1, 3, 6, respectively. Answer the following questions: 1. Write the expression for the molecular partition function q. 2. What are the values of q at T→ 0 and at T → ∞o? 3. At 300 K the level 22 and the ground level are equally populated. Determine the value of ε. 4. At this temperature, on which of the three energy levels is an arbitrarily chosen particle most likely to be found? Support your conclusion by calculating the ratio of the probabilities for a particle to be found on each of these levels. 5. Calculate the total energy of the system at this temperature. 6. Calculate the entropy of the system at this temperature. 7. At what temperature will the population of level ɛ2 be three times the population of the ground level?