# Fermions in a box

1. Mar 26, 2014

### baubletop

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
En = (h2n2)/(8mL2)

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).

2. Mar 26, 2014

### Simon Bridge

What is special about the way Fermions fill energy levels?

3. Mar 26, 2014

### baubletop

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).

4. Mar 27, 2014

### Simon Bridge

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

5. Mar 27, 2014

### baubletop

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...

6. Mar 27, 2014

### Simon Bridge

I know - it throws you out when it's not something subtle or tricky.
But it's good practice.