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As this diagram shows, energy levels get closer together as they get higher. Is a free electron then truly free? Or is it in such a high (bound) state of energy that the transitions become nearly (but not actually) continuous?

If the latter is true, then wouldn't every electron in the universe in fact be bound to every nucleus, just mostly at very high energy levels? Or is this understanding wrong, and instead there is a clear cut distinction between the bound and unbound electron? In that case, what defines the transition?

Energy Levels

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Discrete excited states of electrons in an atom, as depicted, are usually bound states not states of "free" electrons. Unbound states, that could be considered as "free" electrons form an energy continuum.

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  • $\begingroup$ What happens when the electron goes from bound to free? Is there a finite number of bound states, and above that it is continuous? The picture in the diagram makes it seem as if there could be an infinite number of bound states. $\endgroup$
    – Arthur Fabian
    Commented May 4, 2018 at 1:05
  • $\begingroup$ @ArthurFabian - There is an infinite number of bound states with the limit of the ionization energy. Above this energy you have an infinite continuum of unbound electron states. $\endgroup$
    – freecharly
    Commented May 4, 2018 at 1:14
  • $\begingroup$ So above ionization energy, the electron behaves in a fundamentally different manner. But it can it still interact with light? I read somewhere that free electrons do not absorb photons. I am wondering how refraction takes place considering that it is not well explained by bound electrons absorbing photons, but I guess that's a separate question. $\endgroup$
    – Arthur Fabian
    Commented May 4, 2018 at 1:25
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    $\begingroup$ Well free electrons don't interact with photons in the same way as they do bound in discrete energy levels. But they do interact with photons, for instance Compton scattering is the scattering of charged particles and photons, or coulomb scattering where an electron is scattered off a potential via virtual photons $\endgroup$
    – Triatticus
    Commented May 4, 2018 at 2:48
  • $\begingroup$ Do both types of scattering result in random changes of direction for the photon? $\endgroup$
    – Arthur Fabian
    Commented May 4, 2018 at 18:39
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I suppose this is true in the same sense that every atom in the universe is gravitationally attracted to every other atom.

It's up to you to decide where the transition lies. It depends on what question you are asking, and how sensitive your equipment is, and how well your signal processing can sort out contributions from competing atoms.

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  • $\begingroup$ From what I understand, the distinction isn't entirely arbitrary. Free electrons cannot absorb a photon. If the electron is bound to a single nucleus, it can absorb photons which correspond to changes in the energy level defined by that bind. If there are numerous binds, including high energy binds to distant nuclei (what we generally regard as "free"), then there should be far more ways for the electron to absorb photons. $\endgroup$
    – Arthur Fabian
    Commented May 4, 2018 at 1:21
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For an electron to have energy levels it should be contained in a potential well.

For instance, an electron between two negatively charged plates would be in such potential well and its dynamics would exhibit energy levels.

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