All the sentences are practically correct (except the 1st has to be slightly changed to derive meaning from it), but have different meanings.
An electron is scattered from a nucleus. should be An electron is scattered away from a nucleus. and would mean that an electron was on its way to hitting the nucleus, but was scattered in a different direction by something in its path before arrival.
Similarly, An electron is scattered against a nucleus. would mean that it was 'flying' in space and hit some object by which it was scattered in the direction of the nucleus and hit it.
An electron is scattered by a nucleus. means that the electron hit the nucleus which resulted in a change of direction of the electron.
Note that only the 3rd option describes/clarifies the cause of the electron being scattered (namely the nucleus), while the other two refer to the effect of the scattering (the electron hitting or not hitting the nucleus).