Hence the ionization energy of hydrogen is 13.6 eV, which is indeed found in experiment. If a hydrogen atom is in the ground state and absorbs a photon, it can only do so if the photon has just the right amount of energy to bring the electron to an allowed state in which it is happy. The frequency of a transition between two states l and n follows from This gives the correct frequencies as observed in experiment. Experimentally, the energy levels of the higher states have a width. This width is coupled to the life-time of the state by Heisenberg's uncertainty relation.
Typical lifetimes are very short, for example if then .
The radius of the orbit becomes large. It looks like the problem of a current in a loop. If a classical charge rotates around a center with period T, it radiates at a frequency . For large values of n the hydrogen atom looks like a classical problem. In this case the correspondence principle tells us that we should recover the classical results.