Consider a quantum system comprising two indistinguishable particles which can occupy only three individual-particle energy levels, with energies 81 0, 82 2 and e3 38.the system is in thermal equilibrium at temperature t. (a) suppose the particles which can occupy an energy level. are spinless, and there is no limit to the number of particles (i) how many states do you expect this system to have? justify your answer (ii) make a table showing, for each state of this system, the energy of the state, the number of particles (n1, n2, n3) with each energy value and the degeneracy. (iii) write down the partition function for the system. (iv) for te/k, find the probability that the system is in its first excited state [9 marks] (b) now suppose the particles possible spin states, so there are two ways an energy level, but only one way to accommodate two particles in an energy level. are spin 2 fermions. recall that a fermion has two accommodate an individual particle in (i) make a table showing, for each state of this system, the energy of the state, the number of partieles (n, n2, n3) with each energy value and the degeneracy. (ii write down the partition function for the system [5 marks] (c) (i) the average energy of the system of particles in part (a) is given by: -2be ( 2 +3e be4e2bese 3b* _6e4bs e = + + z estimate the average energy of the system in the limit t > > e/k. hint: consider the value of exp(-be) when t > > e/k. (ii estimate the average energy of the system of particles in part (b) in the limit t > e/k. (iii) comment on your results in parts (c) (i) and (c) (ii). in particular, consider any difference from the behaviour you would expect for a realistic system