 Now we could solve for the velocities if we wanted to, and get them as a function of n as well. But what we're really after here is to try and figure out the energies that the electron can take around the proton. Because it changes between those energies, those possible energies that the electron can have, that's giving the photon that's being emitted particular energies, and that photon having a particular energy means that the photon has a particular frequency. So these discrete frequencies are coming out of the energy levels for the electrons. Now there's two kinds of energy for the electron, kinetic energy and potential energy. Now the kinetic energy is just half mv squared, just like it normally is when we don't worry about relativity. Potential energy, well the force is attractive and is going as one on r squared, so the potential energy goes as one on r, and because the energy has to go up as they get pulled apart, there actually has to be a minus sign there. So to deal with the kinetic energy part, we notice that we have an mv squared up in that equation, so that's going to make that easier. Then those two terms look almost the same, and so you're just going to end up with, so the fact that we have quantized the radii means we're going to have quantized the energy. So we just substitute that radius into the energy and we get, so the electron has these discrete radii with discrete energies, and each possible state is characterized by a number n. So these two states here might have n1, this one up here that's a different state the electron can be in, that might be n2. And so what Bohr said was that this electron can't just emit radiation and decay, because it can only be in these particular levels. And so in order to emit a photon, it has to make a transition from one level to another level. And when it does that, it's going to change its energy in a very discrete amount, the difference between en2 and en1. And when it does that, it's going to emit a photon with that energy. And because that energy difference is going to be something times one on n1 squared minus one on n2 squared, then the frequencies, since the frequencies is proportional to the energy, we're going to get the Rydberg formula coming out of that. And so that's why Bohr's assumption gave him the Rydberg formula. And so Bohr's model worked. It explained why people saw discrete lines in spectra, and it gave quantitative reasons for why the particular lines were there in terms of fundamental parameters, rather than just some experimentally determined constant. But like Planck before him, Bohr didn't really change his idea of what electrons were. He just invented a crazy rule that got in the right answers. And just as Einstein took Planck's ideas about light and really changed our model for light to invent the photon, in 1924, De Broglie did the opposite. And he took Bohr's rule and he changed our ideas about all of matter.