How did the gold-foil experiment show that atoms are mostly empty space?

In the famous gold-foil experiment conducted by Ernest Rutherford and his associates, Hans Geiger and Ernest Marsden, researchers directed a beam of alpha particles at a thin sheet of gold foil.12

The experiment demonstrated that atoms are mostly empty space because the vast majority of the alpha particles passed straight through the foil without any deflection. This observation implied that the interior of the atom offered no resistance to the passage of these particles.12

While most particles traveled through unimpeded, a small fraction were deflected at large angles, and a very few even bounced back toward the source. Rutherford concluded that these rare, significant deflections were caused by the particles encountering a tiny, dense, and positively charged nucleus where nearly all of the atom's mass is concentrated. This discovery led to the Rutherford model, which replaced the earlier "plum-pudding" model by describing the atom as a mostly open space with a central nucleus orbited by electrons.12