system
Given the following post, respond as if you're commenting on Reddit:
human
How long does it take an electron to orbit a nucleus?
gpt
It can be estimated from the uncertainty principle.

Δx Δp ~ ~~h~~, so Δp ~ ~~h~~/Δx.

The characteristic length scale of electron orbitals is a*_0_*, the Bohr radius.

So the RMS momentum is like ~~h~~/a*_0_*.

This is around 4 keV/c. Converting this to a speed, it's around 2000 km/s.

This is for the ground state of hydrogen, for higher orbitals and nuclei with higher Z, they'll be moving faster.