# Statistical physics Q: macrostates

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## 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!!

Last edited:

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DrClaude
Mentor
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

Greg Bernhardt