If the Hydrogen atom had certain preferred energies, and the emitted light is what comes out when the atom shifts from one such energy state to another, then the Balmer series tells us that Hydrogen has energies of . These are all Balmer lines, with increasing frequency, except the one at the bottom, which is not a Balmer line, but does exist. And, one predicts certain combination rules. Neils Bohr in 1913 tried to piece together Rutherford's results, and the quantization of light, and the clues from spectra, to make the first Quantum Model of the atom. These are Newtonian electron orbits, but they do not radiate.
Radiation is emitted only when an electron changes orbits.
The photon energy is just the classical energy difference of the initial and final states. But, let us at least first see how these simple postulates yield the Balmer formula. So, combining with the equations above, . Let's first figure it out empirically, using Balmer's formula. This means that the energy corresponding to that radius is .