Homework Help: Macrostates in Einstein Model of a Solid

1. Sep 27, 2010

McCoy13

1. The problem statement, all variables and given/known data
Sketch all the possible microstates for an Einstein solid using dots to represents units of energy and lines to separate oscillators. In addition, identify all possible macrostates of the system. Let N=3 (oscillators) and q=3 (units of energy).

2. Relevant equations
$$\Omega (N,q) = \frac{(q+N-1)!}{q!(N-1)!}$$

3. The attempt at a solution
I got the first part just fine. I sketched out a total of ten configurations of dots distributed among three bins. What I'm not sure about is what qualifies as a macrostate for the Einstein solid. The book (Schroeder's Introduction to Thermal Physics) seems to suggest that the state N=3, q=3 is the macrostate. According to the formula given for multiplicity of a macrostate in an Einstein solid takes N and q as parameters, and for N=3, q=3 it yields 10, the number of microstates I drew. However, the lowest level of definition of state at which degeneracy occurs is a specification such as "one oscillator has 2 units and another has 1" or "one oscillator gets all 3 units of energy".

However, if we interpret the macrostate as N=3, q=3, then there is only one possible macrostate as specified by the problem. Therefore, asking for all the possible macrostates is kind of confusing (or intentionally misleading).

I emailed my professor, but he hasn't emailed me back yet, so I thought I'd ask here in the meantime.