Bohr's Atomic Model

Fig. 3390: Bohr hydrogen atom (with orbits drawn to scale) only allows electrons to inhabit discrete orbitals. Electrons falling from n=3,4,5, or 6 to n=2 accounts for Balmer series of spectral lines.

A pioneering researcher by the name of Niels Bohr attempted to improve upon Rutherford's model after studying in Rutherford's laboratory for several months in 1912. Trying to harmonize the findings of other physicists (most notably, Max Planck and Albert Einstein), Bohr suggested that each electron had a certain, specific amount of energy, and that their orbits were quantized such that each may occupy certain places around the nucleus, as marbles fixed in circular tracks around the nucleus rather than the free-ranging satellites each were formerly imagined to be (Fig. 3390). In deference to the laws of electromagnetics and accelerating charges, Bohr alluded to these “orbits” as stationary states to escape the implication that they were in motion.

Although Bohr's ambitious attempt at re-framing the structure of the atom in terms that agreed closer to experimental results was a milestone in physics, it was not complete. His mathematical analyzes produced better predictions of experimental events than analyzes belonging to previous models, but there were still some unanswered questions about why electrons should behave in such strange ways. The assertion that electrons existed in stationary, quantized states around the nucleus accounted for experimental data better than Rutherford's model, but he had no idea what would force electrons to manifest those particular states. The answer to that question had to come from another physicist, Louis de Broglie, about a decade later.

De Broglie proposed that electrons, as photons (particles of light) manifested both particle-like and wave-like properties. Building on this proposal, he suggested that an analysis of orbiting electrons from a wave perspective rather than a particle perspective might make more sense of their quantized nature. Indeed, another breakthrough in understanding was reached.

Fig. 3121: String vibrating at resonant frequency between two fixed points forms standing wave.

The atom according to de Broglie consisted of electrons existing as standing waves, a phenomenon well known to physicists in a variety of forms. As the plucked string of a musical instrument (Fig. 3121) vibrating at a resonant frequency, with “nodes” and “antinodes” at stable positions along its length. De Broglie envisioned electrons around atoms standing as waves bent around a circle as in Fig. 3122.

Fig. 3122: “Orbiting” electron as standing wave around the nucleus, (a) two cycles per orbit, (b) three cycles per orbit.

Electrons only could exist in certain, definite “orbits” around the nucleus because those were the only distances where the wave ends would match. In any other radius, the wave should destructively interfere with itself and thus cease to exist.