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Four distinguishable particles fill up energy levels 0,ϵ,2ϵ. The number of available microstates for the total energy 4ϵ is
Question

Four distinguishable particles fill up energy levels 0,ϵ,2ϵ. The number of available microstates for the total energy 4ϵ is

A.

20

B.

24

C.

11

D.

19

Correct option is D

Solution:

​Let us consider those microstates where the total energy is 4ϵ4 \epsilon4ϵ. Three cases that may occur where energy is 4ϵ4 \epsilon4ϵ have been categorized in the following table. We must see in how many ways these cases may occur.

​Therefore, the total number of microstates is 1 + 12 + 6 = 19.

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