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Total charge density of all electrons in the closed subshell n=3, l=2

  1. Dec 4, 2013 #1
    1. The problem statement, all variables and given/known data
    Hey guys,

    So the title pretty much says it. I have to find the total charge density produced by all the electrons in a closed subshell where n = 3 and l = 2. The charge density produced by a single electron is [itex](-e)|R_{32}(r)Y_{2,m}(\theta , \phi)|^{2}[/itex]


    2. Relevant equations
    So he gave an example in lectures, but that was for something that had n=2, l=1 subshell. This is what I've got written down:

    [itex]|P_{21}|^{2}=2(-e)\sum_{m=-1}^{+1}|Y_{lm}|^{2}=2(-e)|R_{21}|^{2}\frac{3}{4\pi}[/itex]


    3. The attempt at a solution
    I'm not sure that equation above is right for my situation...does it change when the quantum numbers change? of course the sum will now range from m = -2 -> +2 but is that all that changes? I cant even find any material on this, in my book or elsewhere...

    thanks guys!
     
  2. jcsd
  3. Dec 5, 2013 #2
    The charge distribution is just [tex] \rho = -e \sum |\Psi_{nlm}|^2 [/tex] where the sum is over all the electrons you're interested in. In this case, they are the electrons with n=3, l=2 so you should sum is over m and ms, for all values possible for this shell.
     
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