While atomic orbitals are often understood in the Bohr model as if they were analogous to planetary orbitals, or are explained as wave motions in quantum mechanical terms, there is an unpublished approach to understanding electronic orbital structures which might be of interest to some chemistry teachers or theorists. This “3-D Pendulum Model” as a theoretical approach for electronic orbitals, is very easily understood and makes perfect sense. Although it was used in his classes by a chemistry teacher in North Carolina in about 1961, it never seems to have gotten into the literature as any part of science theory.
The idea is this, an electron attracted to a proton, or a nucleus, would move toward it at an ever increasing velocity, much as a pendulum is attracted to the center of the Earth, but would pass right through the center of the proton or nucleus, changing direction slightly in the passage, as both the protons in the nucleus and the electron are spinning bodies, go out the other side slowing down to a “stop” then turn back to repeat the process, after a number of turns a pattern would be established of electron motions. Since the greatest amount of time of the electron would be spent very near where it “stops,” a probability picture of where the electron could be found would be a “shell” or “orbit.” This, of course, is exactly the same conclusion as is reached by other models of electronic structure. This seems to be quite strange if one considers the nucleus of an atom as a very hard ball and the electron as being something light and fluffy. If, however, one does the mathematics on the listed masses and volumes of electrons and protons, it can be shown that the electron actually has a far greater mass density per unit volume than the proton and could easily pass through protons, and hence atomic nuclei. Once this is understood the idea of the electron moving much like a “three dimensional pendulum is more easily understood than the more abstractly mathematical approach of quantum mechanics.
To understand the idea better, one can imagine some sort of alternate reality in which something dropped on the surface of the Earth could be attracted by gravity to the center of the Earth and pass right on through without being impeded by friction. Exactly the same type of motion would result. The object would pass through the Earth to a distance equivalent to its starting point, and then fall back though again, and again, forever.
The idea of a body moving in three-dimensions in this manner is most easily understood, in discussion, as above, where but two bodies are involved as would be the case with an object and our “alternate earth” or an electron and a proton in the Hydrogen atom, but can be extended to describe situations where in two objects will repel each other while being attracted to a third. This would be a simple model of a Hydride ion. It can be seen seen that the idea can be extended almost indefinitely and should be possibly useful in computer modeling.
A mathematical wizard student of the aforementioned chemistry teacher said that the mathematics of this 3-D pendulum model works out to be the same as the quantum mechanical model. This writer is not a good enough mathematician to verify this, and the present address of Douglas Rogers Sandy Dymphus Christoper Messer is unknown, if he still be alive.
