Since protons and electrons are oppositely charged, what prevents them from attracting to each other and just sticking together?
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You’ve opened up the can of worms that’s called Quantum Mechanics. Simply put, there’s a minimum amount of energy that physics allows in any system, and that minimum is always greater than zero. In an atom, that zero energy would be with the electron and proton being in the same spot. So, instead, it stays just outside the nucleus, hovering just above that zero that it can never reach.
When scientists first discovered that electrons are situated around a dense atomic nucleus, they had the same question as you. It was the quantum equations, ironically derived from some of the conclusions of the Theory of Relativity which is famously incompatible with them, that showed science how this could work.
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