How did Rutherford's gold foil experiment yield new evidence about atomic structure?

The conclusion to Earnest was that the atom contained a dense positive core. This dense positive core is the nucleus.

In the experiment Rutherford shot alpha particles at a piece of gold foil. Alpha particles contain two protons and two neutrons. This is a helium atom with no electrons.

The majority of the alpha particles went straight through the gold foil, as expected from J.J. Thomson's model of the atom (the plum pudding model). However, some of the particles deflected at large angle. Some of the particles even deflected right back from where they were shot from.

Because of the deflections, it could be conclude that the alpha particles were hitting something dense inside the atom (the nucleus).