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Fermi energy in metals approximately doubling

  1. Feb 5, 2015 #1
    Between Cs and Na, the fermi energy in metal approximately doubles. why doesn't the carrier concentration also double?
  2. jcsd
  3. Feb 6, 2015 #2
    Why would you expect to double?
    The free electron concentration is not proportional to the Fermi level.
    In the free electron approximation the Fermi energy goes like n^(2/3) where n is the free electron concentration.
    n for sodium is about 2.65 and for Cs about 0.91 (from Ascroft and Mermin) . In same units, 10^22/cm^3, for example.
    If you take the ratio of the concentrations and raise it to power 2/3 you get 2 Much better that I expected to work. :)
  4. Feb 8, 2015 #3
    Thanks nasu :)
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