Formulas n in n. n! r(v)=(- 1)! = e-"x-da, where v > 0. sin(k)ek dk 0. yk2 -yk2 consider n impurity atoms. each impurity can be in one of two states, with respectively. the microstates are specified by the set of occupations energies 0 and e, numbers n; }, where n; = 0 or 1 and i= . the total energy of the system is e en1 where n1 is the total number of the excited impurities. (a) in the micro-canonical ensemble: i. find the number of distinct microstates (e en1, n) ii. find the entropy s(e, n) iii. find the internal energy e(t, n) in the limit of n1, n> 1. as a function of t and n. (b) in the canonical ensemble: i. find the canonical partition function. ii. find the internal energy e (t, n).