# Charge distribution of the Hydrogen atom

Please see the attach file for the full question.

The time-averaged potential of a neutral hydrogen atom is given by 4s (1 + 7) wo r where q is the magnitude of the electronic charge, and cx-' = ao/2, ao being the Bohr radius. Find the distribution of charge (both continuous and discrete) that will give this potential and interpret your result physically.

It is taken from "Classical Electrodynamic 3rd" by Jackson and I know it will use the Poisson Equation.

© BrainMass Inc. brainmass.com October 10, 2019, 7:39 am ad1c9bdddfhttps://brainmass.com/physics/em-waves/charge-distribution-hydrogen-atom-590061

#### Solution Preview

Hello and thank you for posting your question to Brainmass.

Please see the attached solution for the complete solution.

The solution is attached below in two files. the files are identical in content, only differ in format. The first is in MS Word format, while the other is in Adobe pdf format. Therefore you can choose the format that is most suitable to you.

111Equation Chapter 1 Section 1

Lets rewrite the potential as:

(Please see the attached file)

Poisson equation states that:

(Please see the attached file)

Therefore:

(Please see the attached file)

The Del operator in spherical coordinates is:

(Please see the attached file)

The ...

#### Solution Summary

The solution shows, step by step, how to apply the Poisson Equation in order to find both the discrete and continuous charge distribution.