# Fermions in a box

**1. The problem statement, all variables and given/known data**

a. Electrons and neutrons are fermions. Put 12 of them (6 each) in a box, and determine the

*n*value for the ones with the highest energy.

b. Do the same for 12 bosons (6 are pi zero bosons and 6 are alpha particles).

**2. Relevant equations**

E_{n} = (h^{2}n^{2})/(8mL^{2})

**3. The attempt at a solution**

I’m not even sure how to approach this problem. What is it asking? How do I know which have the highest energy? (Neutrons in general have a higher rest energy than electrons, but I don’t know if that’s at all relevant.)

My only hunch is that the Pauli Exclusion Principle is involved (like I could have 2 electrons in ground state, 2 in n=2 state, 2 in n=3 state, etc. but that doesn’t seem like what the question is asking).

http://ift.tt/P2FbCx

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