Let's focus on the atom, starting from a historical perspective. Ernest Rutherford did a wonderful experiment in which he fired alpha particles (basically helium nuclei) at a very thin gold foil. He got a rather surprising result: rather than all the particle passing straight through the foil, many were scattered off at large angles, some even coming straight back.

Rutherford's comment: "It was almost as incredible as if you fired a fifteen-inch shell at a piece of tissue paper and it came back and hit you."

The results of the experiment were inconsistent with the plum-pudding model of the atom, in which the atom was viewed as tiny electrons embedded in a dispersed pudding of positive charge. Rutherford proposed that the positive charge must really be localized, concentrated in a small nucleus. This led to the planetary model of the atom, with electrons orbiting the nucleus like planets orbiting the Sun.