# Fermions in a box

## Homework Statement

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).

## Homework Equations

En = (h2n2)/(8mL2)

## 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).

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Simon Bridge
Homework Helper
What is special about the way Fermions fill energy levels?

Two fermions can't occupy the same quantum state. So if there are 6 electrons the highest energy level would be n=3 (same for the neutrons).

Simon Bridge
Homework Helper
So you have just answered question (a).
What is the difference with bosons?

Bosons aren't subject to the Pauli Exclusion Principle so they can all occupy the ground state.

I wasn't sure if I was over- or under-thinking the problem, it seemed too easy...

Simon Bridge