1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Stat. Mech. Macrostates for four particles?

  1. Dec 5, 2015 #1
    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. jcsd
  3. Dec 10, 2015 #2
    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?
  4. Dec 10, 2015 #3
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted