Suppose that we increase an $N$-atom Einstein solid's value of $q=U / \varepsilon$ from $q$ to $q+1$. By what factor does the value of its multiplicity $\Omega$ increase? (Choose whichever result is the closest, assuming that $q1$ and $N1$.)
A) $q$
B) $3 N$
C) $q / 3 N$
D) $3 N / q$
E) $(q+3 N) / q$
F) $(q+3 N) /(q N)$

Question

Suppose that we increase an $N$-atom Einstein solid's value of $q=U / \varepsilon$ from $q$ to $q+1$. By what factor does the value of its multiplicity $\Omega$ increase? (Choose whichever result is the closest, assuming that $q>>1$ and $N>>1$.)
A) $q$
B) $3 N$
C) $q / 3 N$
D) $3 N / q$
E) $(q+3 N) / q$
F) $(q+3 N) /(q N)$

Quizplus · Accepted Answer

The multiplicity of an Einstein solid is given by $\Omega = \binom{q + N - 1}{q}$. For large $q$ and $N$, the ratio $\frac{\Omega(q+1)}{\Omega(q)}$ approximates $\frac{q+3N}{q}$.

Suppose That We Increase An NNN -Atom Einstein Solid's Value Of q=U/εq=U / \varepsilonq=U/ε

Suppose That We Increase An $N$ -Atom Einstein Solid's Value Of $q=U / \varepsilon$