What is the speed of an electron orbiting around the nucleus of an atom?

In my opinion, the speed of an electron's movement in the electron cloud cannot be determined by direct measurement (electrons are too small for that), but we can use an analogy from astronomy — for example, the Moon orbits the Earth at a speed such that the magnitude of the centrifugal force is equal to the gravitational force. If we can calculate the gravitational force, we can easily calculate the speed of the Moon and even verify the result through measurement. In the case of an electron, the situation is similar; we just need to consider the electrostatic force instead of the gravitational force—this force attracts electrons to the nuclei, while gravity is negligible in the atom. By substituting into Coulomb's law, we find that the electrons in a hydrogen nucleus move at speeds on the order of a million kilometres per hour. Of course, in different atoms, due to their varying sizes and different core charges, the value of electron speeds is also different.

The above reasoning is based on the concepts of classical physics; if we look at this problem from the perspective of quantum physics, we come to the conclusion that we are unable to determine the speed of an electron precisely. In the micro-world, it is not possible to determine any value precisely (for example, the exact location of an electron), but only the probability of a given value. We are therefore able to determine what the most probable speed of the electron is.

In the case of larger atoms, the speed of the electrons is already so high that we must also take into account another theory of modern physics — the theory of relativity. In these atoms, electrons move at very high speeds (tens to hundreds of millions of meters per second, that is, a fraction to a tenth of the speed of light) and so, the theory of relativity also affects their mass—electrons in these atoms have a mass higher than that of electrons at rest due to relativistic effects.