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Atoms with several electrons, potential energy

  1. Nov 13, 2011 #1

    fluidistic

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    Gold Member

    1. The problem statement, all variables and given/known data
    I don't really understand the problem wording. What do they ask me exactly? Here it goes:
    Consider the potential energy V(r) of an electron in an atom whose atomic number is Z. Calculate the potential energy aproximating the distribution of charge of the others Z-1 electrons with a distribution given by the density of probability of the ground state of the hydrogen atom. Analize the behavior for the most internal electrons ([itex]r<< a_0[/itex]) and for the most external ones ([itex]r>>a_0[/itex]).


    2. Relevant equations
    [itex]V(r)=-\frac{ke^2Z}{r}[/itex] or [itex]V(r)=\frac{ke^2Z}{r}[/itex] if I consider only 2 electrons rather than proton vs electron.
    [itex]P(r)dr=\frac{4}{a_0 ^3}r^2 e^{-2r/a_0}dr[/itex].

    3. The attempt at a solution
    I'm not even sure about the word distribution. I have in mind Dirac's deltas. What has it to see with P(r)dr that I gave above?
    I must calculate the potential energy of the electrons that are close to the nucleous and the ones that are far from it?
     
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