# Stat. Mech. Macrostates for four particles?

1. Dec 5, 2015

### Lagraaaange

1. The problem statement, all variables and given/known data
a. Find macro states of 4 particles among two energy level one of which is twofold degenerate. SOLVED
b. Find the thermodynamic probability of each macrostate for indistinguishable particles. SOLVED
c. ------------------distinguishabled problems (need help)
d. the assembly for b and c.
Answers: a. 5. b. 5,4,3,2,1, c. 16,32,24,48,24. d. 84,15
2. Relevant equations
Concept: MBE statistics applies to classical distinguishable particles not obeying exclusion principle. FD applies to indistinguishable obeying exclusion principle. Bose Einstein applies to indistinguishable without exclusion.

Thermo. Prob. = W = (gj+Nj -1)! / (gj-1)!Nj! this is for BE stats which I used for b and obtained correcting answer
W = N! (Pi)j gj^(Nj) / Nj! (FD statistics I thought to use for c.)

where (Pi) is big pi standing for product, gj is degeneracy (2 here), Nj is particles in Energy state, N is total particle (4) FD statistics I thought to use for c.

3. The attempt at a solution
W = N! (Pi)j gj^(Nj) / Nj!
applying for macro state of 4 where one can have different arrangements of 4 particles in each level.
W4 = 16 CORRECT
W3 = 32 CORRECT
W2 = 24 CORRECT
W1 = 48 INCORRECT
W0 = 24 INCORRECT

Am I using the wrong formula? I know for d you can just sum up each macro state so I mainly need help with c please.

2. Dec 10, 2015