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Now many physics courses do suppose a point particleIn any point-like particle model, a stable classical Hy atom would be point-like. At best (assuming the known finite size of the proton), it would have the size of the order of 1 Fermi. No classical model with Coulomb interaction between the nucleus and the electron can explain the actual size (the Bohr radius) of a Hy atom. Paradoxically as it may sound, but in the final run, it is the QM indeterminacy that determines the exact atomic size.
model, but I don't think they say that the atom has to have zero size
classically. Isn't the size of an atom just a parameter in a given
classical model?