Question

In the recent Chem Activities, we have been learning about how Coulombic attractions and repulsions determine properties of atoms like ionization energy and atomic radius. We have made two assumptions not completely justified by the data we had up to this point: electrons are placed in discrete shells at fixed distances from the nucleus, and only a limited, never changing number of electrons can fit in a given shell. How can photoelectron spectra help us justify placing electrons into discrete energy levels (or shells) and determine the number of electrons that go in each energy level?