Problem 4 (of 5): [Total: 12 pts)Consider an atom in thermal equilibrium with a heat bath at temperature T. The atom has aground state with zero energy and a 4-fold degenerate excited state with energy ɛ, as shown in the energy level diagram below. Show your work clearly for all parts. a) Write down the partition function for this system. b) Find an expression for the probability of finding the atom in the ground state. c) Assume now that the atom has a second excited state that's 9-fold degenerate and has energy 2ɛ. At what temperature would it be equally likely that you would find the atom with either energy ɛ or 2ɛ?