Does a free neutron decay into a hydrogen atom?
While it is true that a proton and an electron make up a hydrogen-1 atom, the decay of the neutron is slightly different. The reason is that the electron leaves the decay event with a high kinetic energy, and it cannot be “held” by the proton (to create the hydrogen atom). Certainly the proton will “pick up” an electron from somewhere after is slows down a bit following its creation, as it, too, has some kinetic energy. The proton will have to release that kinetic energy through scattering, just like the electron that left the event. Links can be found below to related questions with descriptive answers.