1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Question: # of particles within an energy range below Fermi Energy.

  1. Dec 5, 2011 #1
    1. The problem statement, all variables and given/known data
    Here's what the question says.

    "Consider a cube of gold 1 mm on an edge. calculate the approximate number of conduction electrons in this cube whose energies lie in the range from 4.000 to 4.025 at 300k. Assume Ef(300K) = Ef(0)."



    2. Relevant equations

    Well, I know that n(E)dE = g(E)Ffd(E)dE, where g(E) is the density of states, and Ffd is the Fermi-Dirac probability.

    Also, N/V = 0-inf∫ n(E)dE

    and the Fermi Energy for gold is 5.53 ev


    3. The attempt at a solution

    Finding the Volume is easy, which is just V = (1e-3)^3

    Then, I try to find g(E), which is g(E)dE = DE^(1/2)dE, where D =[itex]\frac{8*sqrt(2)*pi*Me^(3/2)}{h^3}[/itex]

    Using 4.00eV for E^(1/2) (and consequently converting it to Joules) I get g(E) = 6.79^37 Energy States/m^3.

    Here's what I did in wolfram alpha language:

    here's D: http://www.wolframalpha.com/input/?i=(8*sqrt(2)*pi*(9.109e-31)^(3/2))/(6.626e-34)^3)

    Now here's D*E^(1/2): http://www.wolframalpha.com/input/?i=1.06e56*(4*1.602e-19)




    Pretty much my question is "What do I do next?" Due to N/V equaling an integral, I'm a little iffy on what to do.

    Thanks :)
     
  2. jcsd
  3. Dec 6, 2011 #2
    Hmm sorry, I actually only multiplied by E, not E^1/2.....


    Here's E^1/2: 1.06e56*((4*1.602e-19)^(1/2))
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Question: # of particles within an energy range below Fermi Energy.
  1. Fermi Energy (Replies: 1)

  2. Fermi Energy (Replies: 1)

  3. Fermi energy (Replies: 0)

  4. Fermi Energy (Replies: 6)

Loading...