Other answers have explained the second question well, but to the first, we know the atom is mostly empty space thanks to Ernest Rutherford’s experiments in the early 1900s (https://en.m.wikipedia.org/wiki/Geiger%E2%80%93Marsden_experiments). He had a sheet of gold foil 1 atom thick, and would fire alpha particles at it. Almost all of the particles went through, but some didn’t and would deflect in various directions. The particles that made it through obviously hit nothing, but the ones that deflected hit something, specifically the nucleus. These sets of experiments proved that the nucleus was at the center of the atom, and the electrons scattered widely around that. This experiment disproved the existing theory, also known as the “plum pudding model”.
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