# Statistical Mechanics Occupation number

tanaygupta2000
Homework Statement:
Three bosons are to be filled in two energy states with degeneracies 3 and 4 respectively.
(1.) List all the macrostates.
(2.) How many microstates does this 3-particle system has?
(3.) Which macrostate is the most probable one?
Relevant Equations:
Partition function, Z = ∑g(j)exp(-E(j)/kT)
Upto now I've only dealt with the problems regarding non - degenerate energy states.
Since bosons do not follow Pauli's Exclusion Principle, three bosons can be filled in two energy states (say E1 and E2) as:
 E1​ E2​ 1 boson​ 2 bosons​ 2 bosons​ 1 boson​ 3 bosons​ 0 bosons​ 0 bosons​ 3 bosons​

so that there are 2 macrostates (corresponding to levels E1 and E2) and 4 microstates (corresponding to 4 possibilities).
Also the probability of occurrence of
• I Possibility = 3!/2! = 3
• II Possibility = 3!/2! = 3
• III Possibility = 3!/3! = 1
• IV Possibility = 3!/0! = 6
Is this correct way of dealing with this problem?
I do not understand the meaning behind the given degeneracies of energy states.

Mentor
so that there are 2 macrostates
Really? How do you define a macrostate?

Your calculation of microstates also appears to be wrong. So define that also.

tanaygupta2000
Really? How do you define a macrostate?

Your calculation of microstates also appears to be wrong. So define that also.
My problem has been solved. I got correct macrostates (0,3), (1,2), (2,1), (3,0), and microstates corresponding to each one of them using BE distribution function.
Thank You !

• DrClaude