Force between nucleus and electron 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.
 A: 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.
