Hey there! Sign in to join this conversationNew here? Join for free
    • Thread Starter
    Offline

    3
    ReputationRep:
    Here's the question -

    What is the chemical potential, mu (in units of hbar.w), at T = 0 K of 46 6Li atoms with spin ½ contained in a 3D harmonic potential well with energy levels, Ei = (i + 3/2)hbar.w and degeneracies gi = 1/2(i +1)(i + 2).

    Basically, I know that the chemical potential should be equal to the fermi energy at T=0K but I really don't know how to use Ei and gi to get there. Literally no idea. Plus, we haven't discussed calculating the fermi energy in class much yet (we did last year but not everyone took that course). Help please!!?

    So far in the question I have derived the f(E) distribution (the occupation probabilities) for fermions, and we are given the statistical weight of a fermi gas.

    Thanks! I will rep! x
    • Thread Starter
    Offline

    3
    ReputationRep:
    BUMP
    Offline

    0
    ReputationRep:
    I'm not sure if this is the neatest way to do it, but if you know the energy and degeneracy of each level you can find the partition function, and hence the average energy, and then you can use the relation between the average energy and the Fermi energy for a 3D case.

    more hints
    Spoiler:
    Show

    Partition function Z = sum over i (gi x exp(-beta * Ei))
    Average energy = - partial derivative of ln Z w.r.t beta
    and you should be able to derive the average energy in terms of the Fermi energy by considering the Fermi sphere in k-space.
 
 
 
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • Poll
    Did TEF Bronze Award affect your UCAS choices?
  • See more of what you like on The Student Room

    You can personalise what you see on TSR. Tell us a little about yourself to get started.

  • The Student Room, Get Revising and Marked by Teachers are trading names of The Student Room Group Ltd.

    Register Number: 04666380 (England and Wales), VAT No. 806 8067 22 Registered Office: International House, Queens Road, Brighton, BN1 3XE

    Quick reply
    Reputation gems: You get these gems as you gain rep from other members for making good contributions and giving helpful advice.