# Multiplicity of a Large einstein solid

1. Mar 1, 2009

### pentazoid

1. The problem statement, all variables and given/known data

Use the equation ln(q+N) to derived an equation similar to the equation, omega(N,q)=e^(N*ln(q/N))*e^(N)=(eq/N)^N only when q >> N, for a multiplicity of an einstein solid in the "low temperature" limit , q<<N

2. Relevant equations

ln(q+N)

ln (omega)=ln((q+N)!/(q!N!))=(q+N)ln(q+N)-q*ln(q)-N*ln(N)
3. The attempt at a solution

now that N>>q, I should factor out a N rather than a q.

ln(q+N)=ln(N*(q/N+1))=ln(N)+ln(q/N+1)
=ln(N)+q/N, since ln(x+1)=x and 1>>abs(x)

ln(N)+q/N=ln(N) since q/N approximates to zero since N>>q, right?

2. Mar 5, 2009

### pentazoid

Anybody not understand the question ?