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Fermions in a box

  1. Mar 26, 2014 #1
    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. jcsd
  3. Mar 26, 2014 #2

    Simon Bridge

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    What is special about the way Fermions fill energy levels?
     
  4. Mar 26, 2014 #3
    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).
     
  5. Mar 27, 2014 #4

    Simon Bridge

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    So you have just answered question (a).
    What is the difference with bosons?
     
  6. Mar 27, 2014 #5
    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...
     
  7. Mar 27, 2014 #6

    Simon Bridge

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