In 1905, Ernest Rutherford did an experiment to test the plum pudding model. His two students, Hans Geiger and Ernest Marsden, directed a beam of alpha particles at a very thin gold leaf suspended in a vacuum.
The vacuum is important because any deflection of the alpha particles would only be because of collisions with the gold foil and not due to deflections off anything else.
Gold was used because it was the only metal that could be rolled out to be very, very thin without cracking.
It was thought that the alpha particles could pass straight through the thin foil, or possibly puncture it. If the plum pudding model had been correct then all of the fast, highly charged alpha particles would have whizzed straight through undeflected. The scientists were very surprised when other things happened:
Rutherford considered these observations and he concluded:
Rutherford had discovered the nuclear atom, a small, positively-charged nucleus surrounded by empty space and then a layer of electrons to form the outside of the atom.
The discovery of the make-up of the nucleus (protons and neutrons) came much later, and was not made by Rutherford. The nucleus was calculated to be about 1/10,000th the size of the atom.