Imagine a particle in thermal contact with a reservoir at temperature T. The particle can be in any one of only three energy levels at energies 0, +, and +2. The degeneracies of the levels are g(0) = 1, g(e) = 2, g(2) = 4. g(E) 4 2 1 E 2 W + 3 4 i=0 a) Calculate the partition function for the particle. b) Calculate the probability that the particle is found with each of the 3 energies. That is, compute 3 probabilities: P(E = 0), P(E = ), and P(E = 2). c) In Mathematica, plot the 3 probabilities vs. dimensionless temperature kT/. Show all 3 probabilities on the same graph. d) Calculate the average energy E of the particle. What is the high-temperature limitte of the average energy? Go to Settin