Statistical physics Q: macrostates

[Irishdoug]

Homework Statement

There are 5 Bosonic particles N = 5 populating 2 degenerate energy levels E1 and E2 such that:

E1 < E2, N2 ≤ N1

and the respective statistical weights are

g1 = 3 and g2 = 2.
.

What are the possible macrostates of this system?

The Attempt at a Solution

I'm not sure if the answer is: for E1 either 5 or 4 or 3 macrostates (as N1>N2)

and for E2 either 2 or 1 macrostates.

or

13 macrostates:

E1 , g = 3

E1 N1 = 5 --> (5,0,0) (410) (320) (311)
E1 N1 = 4 --> (400) (310) (220)
E1 N1 = 3 --> (300) (210) (111)

E2 , g = 2

E2 N2 = 2 --> (2,0) (1,1)
E2 N2 = 1 --> (1,0)

so 13 macrostates overall.

Any idea which is correct or are they both wrong!

 

[DrClaude]

In the attempt, I don't understand why you are considering separately E₁ and E₂.

A macrostate is characterized by its total energy. Therefore, I count 3 macrostates:
E = 5 E₁
E = 4 E₁ + E₂
E = 3 E₁ + 2 E₂