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This question already has an answer here:

Let's say we have a hydrogen atom in electric field. If the field is strong enough, electron will be separated from nucleus. How to determine the value of $E$ at which it happens?

To my understanding, field pulls electron with force $eE$ in one direction and proton with the same force to another. But how to determine the force holding them together?

EDIT: I am asking specifically how to calculate the value $E$ of external electric field which is "just enough" to ionize the atom.

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marked as duplicate by StephenG, ZeroTheHero, Sebastian Riese, user191954, John Rennie homework-and-exercises Sep 25 '18 at 7:21

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

  • $\begingroup$ See these duplicate answers: physics.stackexchange.com/q/384241 and this physics.stackexchange.com/q/44007 $\endgroup$ – Paul Sep 24 '18 at 18:06
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    $\begingroup$ Possible duplicate of Can electromagnetic fields be used to deconstruct and reconstruct atoms? $\endgroup$ – Paul Sep 24 '18 at 20:50
  • $\begingroup$ @Paul, I do not think any of the links you provided actually answers this question with all the math involved. All the answers are qualitative, not quantitative. See the EDIT. There is one answer by Emilio Pisanty which is good for Fermi estimation. Better than nothing, but still, I do not agree that this question is duplicate. $\endgroup$ – FiatLux Sep 24 '18 at 21:06
  • $\begingroup$ @FlatLux The answers in the links posted explain some possible different mechanisms and give estimates in at least one case in terms of the magnitude of an electric field. The point here is that there is more than one way to achieve what you've asked and the links indicate what you should look at next. Perhaps you could choose one of the mechanisms, try a calculation, and then post to receive further help if needed? $\endgroup$ – Paul Sep 26 '18 at 21:34
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First, the electron and proton are bound by the EM force. The electron exists around the nucleus at a certain stable energy level as per QM.

You are asking about the energy needed to knock the electron off the nucleus. This is the minimum thermodynamic work needed to remove an electron from a solid to a point in the vacuum immediately outside the nucleus. This energy is usually transmitted to the electron as kinetic energy from an absorbed photon.

You are asking how an external electric field could do the same thing. This EM field is mediated by virtual photons. You are asking whether the EM field can bo so strong that it will separate the electron from the nucleus.

One case where this happens, and I think you are asking about this is when electrons move in a conductor because of an external EM field. These electrons are not free, but they are loosely bound to the nucleus. In this case the force of the external field mediated by virtual photons is strong enough to separate the electron from the nucleus, and give it enough kinetic energy so that the electron moves to the next nucleus. This is called drift velocity, and is pretty slow. Though, the electrons are so densely packed in the metal, that the speed of electricity is almost the speed of light.

So the answer is yes, it is possible for an external electric field to separate the electron from the nucleus, by giving it kinetic energy in the form of virtual photons.

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