My bullet-point summary is:

1. Geiger and Marsden studied the angle by which alpha particles were deflected when they passed through very thin sheets of gold foil.

2. The experiments were complex and pain-staking as they had to count hundreds of flashes of light caused by alpha particles striking a screen.

3. They observed that the vast majority of the alpha particles passed straight through the foil with almost no deflection.

4. A small fraction of the alpha particles were deflected by very large angles, which was a surprise.

5. Rutherford calculated that large deflections could not result from alpha particles being slightly deflected by several gold atoms after another in the foil. Instead, a large deflection must result from an interaction between an alpha particle and one gold atom only.

6. These results led to the replacement of the plum-pudding model by a nuclear model, in which virtually all of the mass of an atom and all of the positive charge are compressed into a miniscule nucleus at the centre.

7. The nucleus has a diameter in the region of one ten thousandth that of an atom.

8. Alpha particles that were deflected by large angles happened to get close to the nucleus of one gold atom when they travelled through the foil.

9. Most alpha particles show almost no deflection because they never get close to a nucleus on their way through the foil – they effectively pass through empty space.