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!

Archived CMP. Probability of finding electron with E > fermi energy.

  1. Apr 6, 2013 #1
    1. The problem statement, all variables and given/known data
    what is the probability of finding an electron with energy between 5eV and 5.5eV at T=300k, given that the fermi energy of the metal is 4.2 eV.


    2. Relevant equations

    ##P(E,T)dE= \frac{3}{2} E_F^\frac {-3}{2} \frac{E^\frac{1}{2}}{e^\frac{E-E_F}{K_B T}+1}dE##


    3. The attempt at a solution

    I have got an answer and just wanted check and see if it is correct. I have used the eV value for ##K_B##

    ##P(5,300)0.5= \frac{3}{2}4.2^\frac {-3}{2} \frac{5^\frac{1}{2}}{e^\frac{5-4.2}{K_B 300}+1}0.5##


    ##P(5,300)0.5≈ 7.07*10^-13 % ##

    Have I used the right method for solving this? the answer kind of makes sense as it suggests there is a very low probability of having **loose** electrons at 300K
     
  2. jcsd
  3. Feb 5, 2016 #2

    DrClaude

    User Avatar

    Staff: Mentor

    Probability distributions are made to be integrated:
    $$
    \frac{3}{2} E_F^{-3/2} \int_{5\ \mathrm{eV}}^{5.5\ \mathrm{eV}} \frac{E^{1/2}}{\exp[(E -E_F)/k_B T]} dE \approx 3.67 \times 10^{-16}
    $$
    for ##E_F = 4.2\ \mathrm{eV}## and ##T = 300\ \mathrm{K}##.

    While this number may be small, the total number of conduction electrons can be huge (~Avogadro number).
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted