Since protons and electrons are oppositely charged, what prevents them from attracting to each other and just sticking together?
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An electron and a proton getting stuck together is called a “hydrogen atom”.
As others have mentioned, quantum mechanics puts a limit on how tightly they can get stuck, because there’s a single lowest-energy state, the ground state, or what a chemist would call the 1s state.
The answer to why there’s a lowest-energy state is less ELI5, but: electrons obey the Schrödinger equation. If you plug into the Schrödinger equation the force on the electron due to attraction by a proton and solve it, the solutions are a set of functions called the [spherical harmonics](https://en.wikipedia.org/wiki/Spherical_harmonics), and out of that set of functions there’s one which has the lowest energy, so that’s the ground state.
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