I'm honestly not sure how large atoms can be, since there are an arbitrarily large number of high-n states in the limit where the electron is tenuously bound to

I'm honestly not sure how large atoms can be, since there are an arbitrarily large number of high-n states in the limit where the electron is tenuously bound to the proton. I know that states with n ~ 100 are commonly observed (see Figure 3 of [1]) in Galactic and extragalactic star forming regions. This is because ionizing radiation creates a population of relatively recently recombined atoms where the electron happened to arrive in a high-n state. It's not that the electron has an infinitesimally small chance to be observed far away from the nucleus - it's quite likely actually if it lives in a high-n state - it's that collisions rates are so low that the system is out of thermodynamic equilibrium. Section III of these notes [2] describe the physics of Rydberg aroms and the radio recombination lines we observe from them quite nicely. [1] http://iopscience.iop.org/0004-637X/549/2/979/pdf/52126.web.pdf http://iopscience.iop.org/0004-637X/549/2/979/pdf/52126.web.... [2] http://www.ucolick.org/~krumholz/courses/spring10_ast230/notes9.pdf http://www.ucolick.org/~krumholz/courses/spring10_ast230/not...