system
Given the following post, respond as if you're commenting on Reddit:
human
I'm confused - Do electrons orbit the nucleus or not? On one hand you've got orbitals and MO theory saying no, and on the other hand you have quantum mechanics and Feynman saying they move fast enough in heavy elements to have relativistic effects. Which is it?

Feynman specifically has said that no element higher than 137 can exist because the electrons would haven to move faster than c. It's even jokingly called "Feynmanium". Earlier on reddit I read that Osmium is so heavy that the electrons on the lower levels start to obey relativistic effects due to having to move so fast as to not be pulled into the nucleus. 

And yet chemistry consistently teaches that electrons don't actually orbit and only exist in specific areas (Orbitals). So I'm confused. Which is it? Can someone weigh in?
gpt
Both. Electrons have angular momentum due to their orbitals, but if you were to zoom in with a magic microscope you wouldn't see them rotating around like planets.

The electrons have kinetic energy as well. In quantum mechanics, you write down the total energy (technically, the Hamiltonian) and then figure out what it implies about the behaviour of the particle. Normally you'd write something like 1/2 mv^2 - ke^2 /r (the second term is electrostatic attraction, Coulomb's law. Also, the kinetic terms are written in terms of momentum, not velocity) but here the kinetic energy is non-relativistic. If you suspect that electrons are moving fast enough for this to be important, you can change the kinetic energy to include a correction due to relativity: 1/2 mv^2 + 3/8 mv^4 /c^2 . This changes the expected behaviour of the system somewhat, in accordance with experiments (typically the frequency of atomic spectra).