The Charge distribution of an Atom

We were given the potential of an Hydrogen atom as follows:

Phi=q exp(-alpha*r)/r (1 +alpha*r/2

Where r is the distance from the center of the atom and alpha is 2/ao {a0 being the Bohr radius. Setting q=1 and measuring r in angstroms reduces the formula to :

Phi=(1+r)/r*exp(-2r) We expect a symetrical distribution of charge that should resemple a delta function as you get closer to the center of the atom. As a check of the function it was graphed.

This is a slice of the 3 dimentional potential along the plane of the atom. This fits the expectation so I'll assume Phi was calculated correctly.

The next step is to caluclate the charge distribution. using this Phi and the formula:

Rho=-del^2(Phi)

This solution was graphed in 4 different slices, above and below the atom at equal distances to check for symmetry, on the plane of the atome, and just above the atom where neither positive nor negative charge dominates absolutly. Here is the graph for above the atom:

And here is the graph below:

As you can see, they are identical except for graphing styles (I wouln't want you to think I'd used the same graph twice now, whould I ?) On the plane of the atom We expect the positive nucleus to dominate. It does. Just above the plane of the atom, we get effects from both the positive and the negative charges. If the charge distribution were only due to the electron, as can be argued from the first two graphs, this effect wouldn't be seen. It can be surmised there are more charges present than an electron that would produce a delta function like this :