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Particle number density

  • 12-01-2012 4:13pm
    #1
    thecatspjs
    Closed Accounts Posts: 519 ✭✭✭


    Could someone help me here. I am getting 2 answers for the particle number density of aluminium. 60x10^28 and 180x10^28. I must have lost a factor of 3 somewhere because i'm pretty sure 60 is right, but I can't find where it is.

    I've been using

    Fermi Energy = [(h^2)/8m] x [3n/Pi]^1.5

    I know the Fermi energy is 11.66eV and I've to figure out n.

    Can anyone tell where I might have gone wrong.

    Cheers


Comments

  • #2
    ApeXaviour
    Registered Users, Registered Users 2 Posts: 5,523 ✭✭✭ApeXaviour


    I tried it and I got 60.22E(28) also. How are you doing it? Please give your attempted answer/method if you can.

    Density of Al = 2700 kg/m^3
    Molar weight of Al = 0.027kg
    Avogadro's constant. 6.022E(23)

    Nice round cancelling numbers there, you should be pretty much able to see straight away from them why it's 60 (as opposed to 180.)

    .


  • #3
    thecatspjs
    Closed Accounts Posts: 519 ✭✭✭thecatspjs


    Thanks for the response. I'm using the equation I mentioned above. I see the way you have done it there, but for the purpose of this class I have to calculate it by using the Fermi energy.

    Edit; I think I figured it out, it's actually the free electron density I'm looking for and since Al has 3 valence electrons 180 makes sense. Silly oversight on my part, but thanks you for your help.


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