### Solution : Hydrogen atom - Corrected Exericises on Gauss

Hydrogen atom.

1. electrostatic field.
As the vector electrostatic field is opposite the gradient of the potential V and it depends only on r (the distribution having spherically symmetrical) are obtained:
2. Feed field.
The flow of the electrostatic field is defined by:
As the field's radial component and constant over a sphere of radius r:

The study gives limits:
to r tends to 0
Φ = 0  for r approaching infinity.
According to Gauss, a domestic load sphere of radius r expressed as:
.
We can therefore conclude that the total charge distribution is zero and that at point O we have a positive point charge q.

3. Volumetric charge density.
The charge contained between the spheres with center O and radius r and r + d r is:

Is then obtained:

This charge density is negative and has a total charge - q.

4. Function
The Studied function is the radial charge density and passes through an extremum at r = a.

5. Hydrogen.
The distance a is the Bohr radius which is the distance to the kernel for which the probability of presence of the electron is maximum.