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The pretty universally accepted model from the time we first began to suspect (with some actual evidence, as opposed to being ancient Greeks pulling theories out a posteriori) that there were such things as atoms was that they were small, indivisible ... well, probably spheres. At least some of them were probably spheres, anyway.

Around 1900 it became clear that while "small" was still true, "indivisible" was ... not so much. This lead to several competing theories that came out all about the same time (within a decade or so, anyway; 1902 to 1911): the cubic model, the "plum pudding" model, the "Saturnian" model, and the "Rutherford" model. All of these were attempts to explain the newly-discovered electrons and what exactly they were doing inside atoms.

In 1913 Niels Bohr modified the Rutherford model a bit (incorporating some pieces of the Saturnian model as well) and came up with the Bohr model, which proposed that the electrons orbited a concentration of positive charge in the center of the atom in well-defined circular orbits. The Bohr model accounted for the fact that the electrons didn't immediately radiate energy and spiral into the nucleus by proposing that they were confined by ... something ... into specific orbits having characteristic energies. An electron could jump from one orbit to another (provided there was a space open), but only by giving off energy exactly equal to the difference in energy between the two orbits. This accounted for the observed phenomenon that atoms did in fact give off energy of very specific, or quantized, values.

There were still problems with the Bohr model, one of which was that there didn't seem to be any particular reason the energy levels should happen to be what they were, so the Bohr model eventually disappeared in favor of the current quantum mechanical model, which describes the electrons as being in eigenstates of the time-dependent Hamiltonian equation, accounting precisely for their energies.

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