The discovery of the electron in 1897 was followed just 14 years later by the discovery of the atomic nucleus in 1911. In 1913 Bohr proposed a model of the hydrogen atom in which the electron made perfectly circular orbits around the newly discovered nucleus (proton) only to see his theory replaced by Schrödinger’s more general theory, wave mechanics, in 1926. Wave mechanics has dominated the thinking of chemists ever since, but it has hardly been the last word on the matter. More subatomic particles have been discovered, and other forms of quantum mechanics have been suggested over the years (matrix mechanics, density functional theory, …) including theories (quantum electrodynamics, quantum chromodynamics, …) that go far beyond the simplistic thinking of chemists.
So what really happens when two electrons, or perhaps an electron and a positively charged nucleus, get really, really close to each other? Wave mechanics turns to Coulomb’s law for help, and Coulomb states that the force between these particles varies inversely with the square of the distance between them, that is, the force is proportional to 1/r^2. This would imply that the force (and the potential energy associated with it) approaches infinity as r approaches zero. This can lead to disturbing thoughts (what keeps electrons from ‘falling into’ the nucleus?) and disturbing mathematical problems (how do I work with a formula that busts its way to infinity?).
Nautilus recently emailed me an old article (“The Trouble with Theories of Everything”, 1 Oct 2015) that looks into these disturbing corners of science and concludes, “There is no known physics theory that is true at every scale—there may never be.” Coulomb’s law, wave mechanics, you name it – are designed to explained certain phenomena that appear on certain scales of time, space, energy, and so. It may be possible to extrapolate them to other scales successfully, but there are no guarantees. Caveat extrapolator!