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.

 

[DrClaude]

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 !