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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.

hsinghal
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Anubhav Goel
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  • Counter question: does the total energy of the system amount to $m_n c^2$ for $m_n$ the mass of a neutron and $c$ the speed of light (here we are neglecting the energy of the neutrino, because it just doesn't matter)? Or you could ask the anthropic question about the situation: in which casee would you be here to ask the question? – dmckee --- ex-moderator kitten Jun 08 '16 at 02:33
  • @dmckee Is it necessary to form neutron? Can't there be any other form of matter. Well, actual question is where does radial force for electron comes from? Can you suggest where I can find more? – Anubhav Goel Jun 08 '16 at 02:38
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    See this http://physics.stackexchange.com/q/238976/37364 – mmesser314 Jun 08 '16 at 03:15
  • @mmesser314 Can you tell where I can read more about how is this self inductance created and how it came to give perpendicular force? OP of accepted answer don't seem to be responsive. – Anubhav Goel Jun 08 '16 at 03:43
  • That isn't a well defined question.

    If you add up the total energy of the proton and electron then as long as it is less than zero they will form an excited state of a hydrogen atom then relax into the ground state by emission of one or more photons.

    But your question implies you know the precise separation of the two particles, in which case their momenta along that axis are competely uncertain so there is no way to answer.

     – John Rennie Jun 08 '16 at 10:18
  • Well you can leave if you want, that's your decision. In your place I'd use this as an opportunity to refine your thinking about what exactly you're asking. You can always discuss things in the chat if you don't want to post a question. – John Rennie Jun 08 '16 at 10:28
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    @AnubhavGoel No radial force is necessary because electrons do not orbit nuclei like planets around a sun. – Asher Jun 23 '16 at 16:16
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    Perhaps what this questioner is asking is how angular momentum is conserved if the electron and proton do combine to form an atom. – Physics Footnotes Jun 23 '16 at 20:14

2 Answers2

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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.

h2

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.

anna v
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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.

John Rennie
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Lawrence B. Crowell
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  • It is not necessary it can only release 13.6eV. There is a non-zero probability of electron being present near to the nucleus. In those cases more energy can be released. – Anubhav Goel Jul 05 '16 at 05:34