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Proton is a hydrogen atom without an electron.Since hydrogen has only one electron a collision between a proton and an electron will produce a hydrogen atom.

H(atom) + H(atom) = H2 (molecule)

1 e 1 e 2 es

Therefore H+ is a proton which does not have any electron in its shell.

So H+ + e = H (atom) only if a productive collision happens which is enough fot the nucleus to trap the colliding electron to its shell

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