Chapter 39

It is possible for atoms to be excited into states with very high values of the principal quantum number. Electrons in these so-called Rydberg states have verv small ionization energies and huge orbital radii. This makes them particularly sensitive to external perturbation, as would be the case if the atom were in an electric field. Consider the \(n=45\) state of the hydrogen atom. Determine the binding energy, the radius of the orbit, and the effective cross-sectional area of this Rydberg state.

Suppose that the spectrum of an unknown element shows a series of lines with one out of every four matching a line from the Lyman series of hydrogen. Assuming that the unknown element is an ion with \(Z\) protons and one electron, determine \(Z\) and the element in question.