View Single Post
 P: 115 1. The problem statement, all variables and given/known data Show that the multiplicity of an Einstein solid with large N and q is $$\frac{\left(\frac{q+N}{q}\right)^q\left(\frac{q+N}{N}\right)^N}{\sqrt{2 \pi q\left(q+N\right)/N}}$$ 2. Relevant equations $$N! \approx N^N e^{-N} \sqrt{2 \pi N}$$ 3. The attempt at a solution Well, I've done thus so far: $$\Omega(N,q) = \frac{(q+N-1)!}{q!(N-1)!} \approx \frac{(q+N)!}{q!N!} ln(\Omega) = ln(q+N)! - lnq! - lnN \par \approx (q+N)ln(q+N) - (q+N) - qlnq+q - NlnN + N = (q+N)ln(q+N) - qlnq - NlnN$$ I feel like I'm close, but I've no idea where to go from here.