Solution : Hydrogen atom - Corrected Exericises on Gauss

 

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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.

 

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