# Atoms with several electrons, potential energy

1. Nov 13, 2011

### fluidistic

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 ($r<< a_0$) and for the most external ones ($r>>a_0$).

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

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?