After Thomson discovered and defined the negative portion of the atom, his attention turned to the positive portion which was ill-defined. One problem was that there was no simple tool to probe inside atoms. Electrons could be fired at matter, but so what? They just softly scattered off (it turns out that organized matter diffracts them but that came later).
The alpha particle was Rutherford's baby: he had named it and had shown that is was a helium atom stripped of electrons, i.e., He2+. By 1909, Rutherford and his students were firing alpha particles at everything in sight, looking for any new and unusual effects, but also testing theories about the positive part of Thomson's Plum Pudding Model.
Rutherford had earlier noted the thickness of sheets of materials needed to stop alpha particles. But why did they? There was nothing about JJ Thomson's atom that should get in the way. If the positively charged portion of each atom were a uniformly thin gruel, alpha particles should sail right through. But they noticed deflection--eppur si muove.
Eventually, they began measuring how much thin sheets of gold foil deflected beams of alpha particles. The experimental set-up involved aiming a beam of alpha particles at a gold foil and putting a detector on the other side to measure deflection angles of the "filtered" particles. In a sense, Rutherford was trying to quantify the density of the positive pudding portion. The more closely they looked, the more deflection they observed. Almost as an aside, Rutherford suggested putting the detector in front of the gold foil. When they did so, and to everyone's utter surprise, a detectable amount of alpha particles appeared to bounce off the gold foil rather than pass through it. It took Rutherford two years to digest, confirm, reconfirm and then to announce what this all meant. In Rutherford's words:
[Continued in part here]It was quite the most incredible event that has ever happened to me in my life. It was almost as incredible as if you fired a 15-inch shell at a piece of tissue paper and it came back and hit you. On consideration, I realized that this scattering backward must be the result of a single collision, and when I made calculations I saw that it was impossible to get anything of that order of magnitude unless you took a system in which the greater part of the mass of the atom was concentrated in a minute nucleus. It was then that I had the idea of an atom with a minute massive center, carrying a charge.