Electrons will absorbed into the proton. We call this electron capture or K capture. This will turn one proton into a neutron with emissions of an electron neutrino.

It is called K capture because the lowest electron shell in a many electron atom is called the k shell. This will also result in X-rays when that lower orbital is filled again.

This process is greatly suppressed with just one proton and electron. Though it is still possible just unlikely.

so the answer might be that the proton will swallow the electron

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