# Why is there a max radius for an orbit of an electron around a nucleus?

Why is there a max radius for an orbit of an electron around a nucleus ? I had a course in electromagnetism but I do not get this.

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The energy of the largest transition $n=\infty \rightarrow n=1$ is 13.6 eV, or half a Hartree (this is the energy of a photon with a wavelength of 912 Ångström). This is the binding energy of the hydrogen atom. Even the Lyman gamma line - representing a $n=4 \rightarrow n=1$ transition - is quite close to the ionisation limit. As n increases, from a strictly electrostatic point of view the orbital becomes far less stable, and this is reflected in the general negative trend of ionisation energies across the periodic table, however the complete picture is a bit more complex than that because electrons can interact with electrons as well as the nucleus.