At the center of an atom you have protons and neutrons. The strong nuclear force holds these particles together, tightly packed, with a distance of about 1 femtometer.
The electromagnetic force gives protons in the nucleus a positive charge. This means the atom attracts a cloud of electrons. Because electrons have little mass, the speed (momentum) they have when they’re close to the nucleus means their position around the nucleus is fuzzy. The most likely places you’ll find the first couple of electrons is roughly around 50,000 femtometers away from the nucleus, depending on the atom.
Two atoms usually interact through their electron clouds, and don’t get any closer than that.
So when people say an atom is almost entirely empty space, they’re trying to talk about the distances that exist between protons and neutrons (1fm) and then between those and their electrons (50,000x). None of these particles have a true size in the sense that we think that a ball has a size, but they do have locations and momentum, which gives us a way of describing a kind of size for them when they’re bound together in something like an atom. It’s just that sometimes it gets fuzzy and we have to talk about averages and probabilities.
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