How can relativity affect the physical properties of heavy elements (such as gold and mercury) if the electrons do not orbit or move around the nucleus?

Answer 1

This is a great question! Outside of physics classes, physicists are insistent that electrons don't orbit the nucleus, and instead they occupy a sort of "cloud." Clouds can give the impression of stationariness, so it can be difficult to picture how relativity, which is known for affecting very fast-moving things, would matter.

So here's a modification to the "cloud" picture that can help make sense out of that: picture the electron as a wave within the cloud. A probability wave. At any given moment, in some places the cloud is denser, where the electron would be more likely to be found if you measured its location, and in other places it's sparser. As time passes, the dense parts may propagate around the cloud like a wave, just like if you stretch a slinky and hit one end of it. The movement of the probability wave is the quantum equivalent of the movement of classical particles. If the wave is moving fast enough, you could imagine that relativistic effects would become important for the quantum particle, just as they are for classical particles.

This tends to happen more as elements get heavier. Since the lowest-energy levels are filled first, the small number of electrons in lighter elements tend to have relatively small kinetic energies (which means the probability waves aren't moving as fast). Nuclei with more protons need more electrons to balance their charge, which means the electrons start to occupy energy levels in which they move faster—eventually relativistically fast.

The effect on physical properties happens primarily through adjustments of the electron's energy levels. The equation that works well for calculating the energy levels of lighter elements, called Schrödinger's equation, includes a term for the non-relativistic kinetic energy of the particle. The kinetic energy term becomes increasingly inaccurate as the particles approach the speed of light. For heavier elements, we can apply relativistic corrections to more accurately model the energy of very fast particles. The result is that energy levels in which the electrons move at speeds close to the speed of light have slightly different energies than they would otherwise. The modified energy levels affect how the atom interacts with light, applied electromagnetic fields, and subatomic particles, and the way it bonds with other atoms.