The 1920s theory of matter was that electrons and nuclei are discrete things finite in size. You can reasonably test this theory by shooting a stream of smaller atoms at a thin film of bigger ones, and what you get is a scatter pattern consistent with most passing through, some being deflected back etc. This was alpha radiation at a gold sheet (alpha rays are helium atoms without electrons).
This essentially invalidated theory that atoms were one solid mass of protons and electrons together.
That 1920s understanding starts to come apart the more you ask questions like how big is a nucleus or an electron, and where is it, and what is it made of.
If the model of an electron orbiting a nucleus was correct you should be able to do experiments where you could see an electron on different sides of the atom for example.
Turns out, matter is much more complicated than that. Electrons, when bound to nuclei are much more like a charge distribution than a discrete blob orbiting a centre. Many electrons create a cloud of distribution.
Nuclei have the same issue, protons and neutrons are made of quarks exchanging gluons to stick together, meaning they have some internal structure as well, and the size of a nucleus is really the area with charge and forces in it.
So generally when we say atoms are mostly internally empty, we mean the nucleus is a small blob and electrons are small blobs orbiting it.
But electrons and nuclei (and protons and neutrons) are themselves not really finite discrete blobs.
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