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In the "classical" model of an atom, with electrons orbiting the nucleus like planets around a star, electrons are travelling in a circle. Electrodynamics show that a charged particle doing so should radiate energy, thus resulting in a smaller radius. As the radius shrunk, the electron should continue to radiate energy until it had lost all its energy and was back into the nucleus -- and do all this in about 10^-11 seconds!!

In addition, the frequency of the light given off should be equal to the frequency of the electron's orbit. As the energy of the electron becomes smaller and the radius shrank, the orbital frequency should get progressively larger. As such, the emission should a range of frequencies, starting low and then getting higher -- much like the frequency produced by a Trombone as the player moves the slide while blowing the whole time. However, emission spectra are, instead, quite discrete in their frequencies.

To solve these problems, Bohr (rather arbitrarily) proposed that electrons did, indeed, orbit the nucleus in circles, but that orbits of certain radii resulted in no radiation be given off. Make this assumption, and the frequencies of hydrogen emission spectra are almost trivial to compute.

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