P=(2J+1)exp(-(BJ(J+1))/kT) where B, k and T are constants

Question

a. Show that dP/dJ=(2-(B(2J+1)^2)/kT)exp(-BJ(J+1)/kT)

b. Show that P exhibits a maximum and determine the expression for Jmax

c. Find the value of P when J=0 and the limiting value of P when J becomes large(infinity).

Answer 1

I would skip a) and do b) by differentiating Log(P). For positive P, Log(P) has a maximum at a point if and only if P is maximal there.