b) (13 points) For each of the i= 1,...26 macrostates (the ones provided, plus the ones you sketched), compute the multiplicity W, of its energy microstates. Hint: the grand total energy multiplicity summed over all macrostates should add up to the number of ways (N,9) that q energy units can be divided among equally probable states of the N particles: 9 + 12 (N, ) = (**) (q + N - 1)! q!(N-1)! 9 c) (5 points) To determine the overall energy distribution, we need to compute the average number of particles in each energy state. Let N. = # of macrostates; P = # microstates in the ith macrostate (computed above) divided by the total number of microstates (computed above); and ni = # particles with energy E in the ith macrostate. Then the average number of particles n, with energy E can be computed using the following expression: N. , - ., P 1 Using this expression and your results above, show that no = 2.143 (display all steps in evaluating the sum). 2 3 4 5 6 7 00 9 10 11 12 13 ... 14 15 16 17 18 19 20 NANOOD NIL I b) (13 points) For each of the i= 1,...26 macrostates (the ones provided, plus the ones you sketched), compute the multiplicity W, of its energy microstates. Hint: the grand total energy multiplicity summed over all macrostates should add up to the number of ways (N,9) that q energy units can be divided among equally probable states of the N particles: 9 + 12 (N, ) = (**) (q + N - 1)! q!(N-1)! 9 c) (5 points) To determine the overall energy distribution, we need to compute the average number of particles in each energy state. Let N. = # of macrostates; P = # microstates in the ith macrostate (computed above) divided by the total number of microstates (computed above); and ni = # particles with energy E in the ith macrostate. Then the average number of particles n, with energy E can be computed using the following expression: N. , - ., P 1 Using this expression and your results above, show that no = 2.143 (display all steps in evaluating the sum). 2 3 4 5 6 7 00 9 10 11 12 13 ... 14 15 16 17 18 19 20 NANOOD NIL