What is the maximum possible principal quantum number for an atom(any atom not a specific one) ?
closed as off-topic by A.K., Nuclear Chemist, Tyberius, Mithoron, Jon Custer Oct 3 '18 at 23:02
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Imagine a universe that is not expanding, and contains only one large star and one small planet. It is technically possible to put the two objects into orbit no matter how far apart they are. At some very large distance, the gravitational attraction is so small that it is nearly negligible, but if given infinite time you will be able to trace the orbits for the planet-star system. If, however, you introduce more planets and stars close to the planet, then the influence of the star that is very far away will become irrelevant to the motion of the planet.
We can see a similar case when we look at an electron around an atom. Each time you excite it, you move the electron into a higher-level orbital that is more weakly bound. Eventually you get the electron into orbitals that are nearly degenerate and asymptotically approach zero binding energy. If you have a universe that contains only the electron and the atom, and get rid of the vacuum fluctuations, then yes, it is theoretically possible to put an electron into an orbital with arbitrarily high level of n.
In practice, at some point the electron becomes so weakly bound that electromagnetic forces in the environment will dominate and take the electron away from the atom, ionizing it.
It is experimentally possible to isolate an atom from the environment quite well and then excite the electron to a pretty high n without ionizing it. An atom that is excited in this way is called a Rydberg atom.