 So the main problem with the Rutherford model of the atom where the electrons are circling around the nucleus is that as they accelerate around the nucleus they should be giving off electromagnetic radiation losing energy and that means that all atoms should be decaying quite fast as the electrons spiral in towards the nucleus. And the frequency of the radiation they emit will essentially be the orbiting frequency of the electrons going around the nucleus. And as the electrons lose total energy, which is mainly potential energy, they'll actually gain kinetic energy and so they'll circle faster and faster and so that frequency will go up just as it goes into its death spiral. So the Rutherford model is contradicted by two main pieces of experimental evidence. The first is that atoms do not decay very quickly and the second is the light coming off them looks very different to that frequency chirp and indeed it contains some rather interesting structure. So if we look at something like the Sun to a first approximation we get this kind of spectrum, the continuous spectrum. Indeed the Sun isn't actually made of atoms, it's made of a plasma, all the nuclei and the electrons are all stripped off each other and swirling around and so we tend to get a thermal distribution of light which is just like the Planck spectrum. So there are no mysteries there provided we do believe in the existence of photons and the discrete energies that light can take. But in 1802 Walliston noticed that the solar spectrum actually had a bunch of dark features on it. And in 1814 Fraunhofer did a careful study where he noted all the frequencies at which it happens. And it wasn't until 45 years later that people noticed that some of these special frequencies were the ones that showed up if you took a hot gas of atoms and look at its spectrum. In fact when you take a hot gas of atoms rather than a plasma you see very sharp emission lines. Now this is rather odd because in the Rutherford model the electrons can go around the nuclei at any speed they like, they can rotate around at any frequency and therefore they should be able to emit radiation at any frequency. But instead each kind of atom gives off a very specific fingerprint of lines. So a given gas gives off a particular set of lines and if you have a different gas say instead of hydrogen you had helium or neon or something you get a different set of lines. And in the mid 1800s Kirchoff and Bunsen noticed that these lines that they saw in the solar spectrum that Fraunhofer characterized corresponded to particular sets of the fingerprints from the bright lines you would get if you were looking at hot gases of atoms. And they realized that what was happening there was that the bright thermal continuous light from the plasma in the sun was then passing through an atmosphere of atomic gas. And obviously there's a gas of atoms and molecules in the earth's atmosphere but turns out the sun also has an atmosphere of gas at the edges of the corona. And those atoms were scattering away some of the light but only at their special frequencies and so their fingerprints were represented in the light as dark absorption lines. And this was easily replicated in the lab by looking at bright light passing through cold gases. So the real mystery then was what's so special about these frequencies? Is there a reason for them? Is there a pattern to them? So in the 1880s Barma found a very simple formula that described every line in the visible spectrum that comes from atomic hydrogen. The formula had two good properties. The first was that it was so accurate that when they went back and re-measured some of the lines that were just off it it turns out that it was the measurement that was wrong rather than the formula. And furthermore it predicted more lines down in the infrared that turned out to be there when people looked very carefully. And so that was a very good sign that they'd found one of the patterns. And then shortly after that Rydberg generalised that formula and found that all the lines in atomic hydrogen could be described by the following formula. In other words the frequency of every single line in hydrogen was just proportional to some number that you get from taking two integers n1 and n2 where n2 is bigger than n1 and they just started one and got to infinity and that gives you the entire family of lines. And the Barma series was just the subset of these Rydberg series for which n1 was two and the full series also predicted some ultraviolet lines that turned out to be there when people looked and gave the entire spectrum. Now importantly no one had any idea why the Rydberg formula was correct. It was just an empirical formula that they found by looking at the lines and the frequencies themselves. It wasn't until 1913, two years after Rutherford proposed his model of the atom that Niels Bohr revised it to finally explain the atomic spectrum of hydrogen. Bohr's model combined Planck and Einstein's idea of photons along with an assumption about the possible electron orbits that was to pave the way for the rest of quantum mechanics.