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Fermi Energy and Conduction Electrons

  1. Nov 3, 2016 #1
    The problem:
    A simple cubic metal has an electron density such that the Fermi energy just touches the edge of the first Brillouin zone. Calculate the number of conduction electrons per atom for this condition to be fulfilled.

    The attempt at a solution:
    I know that the electron density for a simple cubic (SC) is n=1/a3
    It says that the Fermi Energy just touches the surface of the 1st Brillouin Zone, well the 1st BZ occurs at k=+- π/a
    I know that the Fermi Energy is given by: Ef = ħ2/2m * (3π2n)2/3 where n is the electron density again.

    Now I can sub in the value of n for a simple cubic into this Fermi Energy equation, however I do not know how I can get the total number of conduction electrons from this information.

    Any pointers in the right direction would be greatly appreciated.

    Thanks,

    Tom
     
  2. jcsd
  3. Nov 8, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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