We no longer regard the electron as a point-like particle. The electron has an internal structure, and the electric charge inside the electron has continuum distribution.
Here is one of our most basic assumptions about the electron; the electric charge distribution inside of the electron has the following equation:
We use the spherical polar coordinates in our book, in which r is the radial coordinate, is the polar angle, e is the electric charge of the electron, is the electron radius constant.
By integrating the electric charge density equation (2.1), we can find the volume electric charge:
In which , thus:
equation (2.6) is the electric charge space distribution equation.
From equation (2.6), we find out that:
When , therefore:
As we can see, the electric charge distribution is a kind of cumulative gamma distribution [B]
Equation (2.7) is the electric charge equation within the sphere of radius r.
When , thus:
Thus we can see that the electron as a whole has one unit negative electric charge e.