Proton and electron joining [duplicate]

Question

If I have a proton and an electron at rest at some distance apart.

Will they form an hydrogen atom when released or they will join together? My intuition says it will form H atom. But I cannot explain myself what prevents it from joining. Where does any radial force to encircle comes from? Is there some mechanism which I can read?

Uncertainty principle, how does it effect central forces and motion?

Edit: As questioned in comment for mass of neutron

Mass difference for proton and neutron mass is 1.293 MeV = $2.07 × 10^{-13} J$

Max Energy provided by electric field =$\frac{9×10^9 × 1.6×1.6×10^{-38}}{10^{-15}} ≈ 2.304 ×10^{-13} J$ which is much more than required.

Some part of this extra energy will be lost as radiations(I don't know how much) . Plus we have Mass energy of energy of electrons.

At appreciable conditions, forming neutron would be hence possible.

Answer 1

Let us make things clear. Protons and electrons are quantum mechanical entities and there is little meaning to project classical electrical attractive behavior to the micro framework of quantum mechanics, nor classical electric field calculations .

Classically, a negative charge attracted to a positive charge will experience acceleration, and accelerating charges classically radiate with a continuous spectrum. The creation of hydrogen atoms though demonstrated this as false . Here is what was seen, a spectrum appeared , and not a continuous radiation.

This required first the Bohr model and then the full panoply of the solutions of quantum mechanical equations for the given potential.

If the electron is at rest with respect to the proton, it will be captured in one of the energy levels and form a hydrogen atom. It cannot fall lower than the ground state. That is what quantization is about. There is not enough energy in the system for the electron to interact in inverse beta decay and form a neutron, even though there exists a probability for the electron for l=0 to pass through the proton.

In complex nuclei, where there exists energy in the nucleus, electron capture can happen for l=0 states.It is called electron capture.

For a scattering experiment, where the electron has extra kinetic energy, it will scatter in the continuum , and if enough energy is available new particles will be created as happens with proton proton scattering at the LHC. In electron proton scattering, a neutron may form through the weak interaction with small probability, accompanied by an electron neutrino in order to conserve lepton number.

Answer 2

The mass of a proton is $938.3$ MeV and the mass of a neutron is $939.6$ MeV. The difference is $1.3$ MeV. The electron mass is $.511$ MeV. So there is a deficit here greater than $.8$ MeV. I have ignored the neutrino mass, where we know the differences between neutrino types, but exactly their actual mass. However. the $\nu_e$ mass is thought to be at most a few $10$s of eV. If you have an electron far removed from the proton and let it fall towards the proton by electrostatic attraction it can only release $13.7$ eV. The reason is that there is the minimal S-shell configuration for the electron in the hydrogen atom. The electron can't get closer. Now if you have the elecctron heading towards the proton with considerable energy, greater than $.8$ MeV or $\gamma > 1.6$ you might form a neutron. The neutron is not stable and decays into a proton, an electron and its anti-neutrino.