How did the gold-foil experiment lead Rutherford to propose the atomic nucleus?

In 1909, Ernest Rutherford directed Hans Geiger and Ernest Marsden to conduct an experiment firing alpha particles at a thin sheet of gold foil.12

While most particles passed straight through—indicating that atoms are mostly open space—a small fraction were deflected at large angles, and some even bounced directly back toward the source. Rutherford famously remarked that this was as incredible as firing a shell at tissue paper and having it return to hit the shooter.12

Rutherford concluded that such significant scattering could only result from a single, intense collision with a target that was both extremely dense and positively charged. This led him to propose the Rutherford model in 1911, which described the atom as having a tiny, massive nucleus at its center, where nearly all of its mass and positive charge are concentrated.123