# 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

### Staff: Admin

Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

3. Dec 10, 2015

### Lagraaaange

SOLVED.

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