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Fermi-Dirac Distribution

  1. May 3, 2009 #1
    1. The problem statement, all variables and given/known data

    Pleas can you help me figure out what I do wrong?
    At what temperature is the probability that an energy state at 7.00 eV will be populated equal to 25 percent for copper (EF = 6.95 eV)?

    2. Relevant equations
    The formula for the fermi-Dirac Distribution is f(E) = 1/(1+e^((E-EF)/kT))

    3. The attempt at a solution
    Looking at the problem I figured that f(E) = 25%=0.25 and E-EF=7.00 - 6.95 = 0.05eV
    solving for T and found that T=3.2979e21 K, but it doesn't seem to be the right answer, why?
  2. jcsd
  3. May 3, 2009 #2
    Hmmm... That seems a bit much. What boltzmann constant are you using? And double check your work, because I get a different answer than you.
  4. May 5, 2009 #3
    That could well be the right answer (not sure of the exact answer, but you will get a big number). Metals have very high fermi temperatures - you can look at it in the following way. Fermi energy levels cannot be multiply-occupied. If that metal was made of bosons, it would have a temperature of 10^21 K because of where the highest energy electrons are.
  5. May 5, 2009 #4
    That is way too large of a temperature. Hah, that is hotter than 1 second after the big bang. Also, the temperature of the Fermi energy is not even close to that. A Fermi energy of 6.95 eV has a Fermi temperature of 80,654 K.

    viviane363 must have made a mistake somewhere in the calculation. Because I used the exact same formula and I got a completely different answer. But I think she forgot about this thread.
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