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The "infinity" level is theoretical! From my understanding, if the level were to reach infinity, it would just mean the electron is as far as possible from the nucleus as chemically possible, while (just barely) being a part of the atom. I would assume n=infinity could be approached, but not necessarily reached by electrons (basically an upper limit). Electrons would be rejected from the atom at this theoretical point.
Physically, it is impossible for an electron to reach n = infinity. As long as there is a "distance" between an electron and an atom, there will be some attraction, though it would be EXTREMELY small. So unless there is a way to reach a length of "infinity" between an atom and an electron (or anything really), there will be no 0 energy. :)
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