 The Rutherford model of the atom left one outstanding problem. In the Thomson model, the electrons were stationary in the positively charged pudding, but what keeps a negatively charged electron from falling into the positively charged nucleus, given that the opposite charges attract each other? The first proposed solution was to assume that the electron is in orbit around the nucleus, like the earth around the sun. Just as we can use gravitational and centripetal forces to calculate the radius and velocity of a planet around the sun, we can use electric and centripetal forces to calculate the radius, circumferences, velocity, and revolutions per second of an electron around the nucleus. For hydrogen, we get a very small circumference of around a third of a nanometer, and a very large velocity, almost one percent of the speed of light. That combination gives us a fantastically large 660 trillion revolutions per second. Now think about that for a second. But classical electromagnetic theory points out that an accelerating charge radiates energy. Theoretically, the electron should collapse into the nucleus in less than a trillionth of a second. And yet, we see that it does not collapse. You'll recall from our How Far Away Is It segment on Distant Stars that the light spectrum from stars was covered by thousands of dark lines called Fraunhofer lines or spectral lines. Although these lines had been studied for over a hundred years, no one understood what they were. In 1885, Johann Ballmer broke out a subset of these lines for hydrogen and developed some mathematical interrelationships between them. Then almost 30 years later, Nielus Bohr developed a quantized momentum theory for the atom. It partially explained these lines. His model still had the electrons orbiting the nucleus, but they could only orbit at certain specific distances from the nucleus, called shells. Each shell had its own unique energy level, N, where N was a positive integer, equal to one, two, three, etc. These were called the atom's quantum numbers. Electrons radiate or absorb energy when they change energy levels. The emitted or absorbed light has the energy difference between the two levels. This energy is equal to Planck's constant times the frequency of the light. Here's how it works. When a photon with an energy E hits an electron in a shell around a nucleus that has a higher shell it can reach with the same exact energy, the photon's entire energy is transferred to the electron instantaneously. This jumps the electron to a higher energy level with a larger quantum number. The photon is eliminated. This creates absorption lines in a star's spectrum as light from the star travels through the star's atmosphere. When the electron drops from this excited state back to a lower energy level, a photon with the exact difference between energy levels is emitted. This creates emission lines that we can see in the lab. Bohr's model explained the Ballmer series for hydrogen spectra. In addition, it provided the physical mechanism for Planck's quantized emission blackbody radiation and Einstein's quantized absorption photoelectric effect. There was also momentous for astronomy. By observing the absorption lines in a star's spectrum we can tell what the star is made of. And not only that, by analyzing how these lines shift, we can calculate star radial velocities via the Doppler effect and even use them to measure their distances and the expansion of the universe. Indeed, Bohr's model explained a great deal, but there was no explanation for why the shell distances from the nucleus were as described. And there was no explanation for why the orbiting electrons didn't radiate away their energy and collapse into the nucleus.