As far as I know, Rutherford's atomic model says that atoms have a center (the nucleus) of concentrated positive charge and this center is very very small compared to the actual size of the atom.
The electrons on the other hand, orbit this nucleus thus, completing the model of the atom.
This may seem obvious (we see that in most elementary textbooks). Before this, J.J Thomson proposed his own atomic model: The atom is made out of a positive sphere with electrons in it. Admirable but it is still a flawed model.
Rutherford's one is an improvement.
The problem is, atoms emit and absorb certain wavelengths of light which shows that the atom has different energy levels. Rutherford's model cannot explain this phenomenon.
Next, the electron as proposed by Rutherford moves in circular orbit. According to Maxwell, charges in circular motion must emit radiation. In Rutherford's model, the atom would eventually cease to exist because the electron would collapse into the nucleus (something which we never observe).
Hope this would suffice.
This is an article about an electron moving in circular motion. Physicists manage to detect electromagnetic radiation from an electron. This is not coming from an electron in an atom mind you.