How electrons travel
In a femtosecond time frame, electrons are always moving around with a profusion of positions (aka orbitals) around the nucleus.
However, even with this ultrafast travel, electrons continue to look for ways to minimize their kinetic energy. The easiest way of doing this is through choosing shorter distance paths. When those paths are discovered, electrons will preferentially opt for those paths (least energy paths)
This is the default position of all objects in motion; they will opt for lower energy paths, unless an external force endows them with extra energy.
Shortest distance between two points
Like other minute particles, electrons follow shortest distance paths as they search for lower energy positions. On a sphere, the shortest distance between two points is that which follows one of the great circles of the sphere (geodesic).
An electron will move from one geodesic to the next looking for that which has the shortest distance between two points. If it bumps into an arc that is longer, it will revert back to one of the shorter arcs.
An equilibrium is reached when none of the geodesics is longer than the next.
Geodesics
An infinite number of geodesics
It is fine for an electron to travel along a great circle to minimize the distances it has to travel. But when there is only one electron in an energy shell, there are an infinite number of great circles that an electron can follow. This means that our electron can always be moving somewhere along a great circle in our real-world time frame of milli-seconds.
This is the basis for the spherical s-orbital. As much as the electron would like to minimize its kinetic energy, this is difficult when there is only 1 electron in the energy shell.
This is why elements in the first group of the Periodic Table (for example, sodium, potassium, and Cesium) are extremely reactive. Their electron is begging for lower energy paths. Consequently, they will attach to any other atom that allows more constrained travel paths.
A number of great circles
Picture credits:
- Grafixo. Geodesics, uploaded Nov 2021.
- NASA Hubble Space Telescope. Hubble Sees New Dark Spot on Neptune, uploaded July 1, 2016.
- Grafixo. Geodesics, uploaded Nov 2021.
- Grafixo. A number of great circles on a sphere, uploaded Nov 2021.