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Each allowed energy level of a system of non-interacting fermions has a degeneracy M. If there are N fermions and R is the remainder upon dividing N b
Question

Each allowed energy level of a system of non-interacting fermions has a degeneracy M. If there are N fermions and R is the remainder upon dividing N by M, then the degeneracy of the ground state is

A.

RM

B.

1

C.

M

D.

MCR

Correct option is D

Solution:

If there are N fermions and M degenerate states of each energy level for the ground state of the system (not the lowest energy level), all levels with degeneracy will be filled. The uppermost level will have R fermions to be filled in M degenerate levels, and that will be filled in "M choose R" ways, denoted as MCR. That is the degeneracy of the ground state.

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