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Is the speed of electrons in Atoms consistent in all Atoms or clusters/groups/individual elements, and if it is consistent in any atom, is that speed constant?

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Quantum mechanically bound particles (like electrons in an atom or molecule) do not have well defined momentum.1 What they do have is a well defined distribution of momenta. This is one of the reasons that we say electrons are bound in "orbitals" and not in "orbits".

That distribution is the same for the orbital around the same type of atom (or in the same type of molecule). Now, for atoms heavier than helium, there are more than one type of occupied orbital in the atom even in the ground state. So, it is not true that every electron in the atom has the same momentum distribution.2 All the 1s in carbon electrons have the same distribution. All the 1p electrons in carbon have the same distribution as each other but a different one than the 1s electrons. The 1s electrons in oxygen have a different distribution than the 1s electrons in carbon. And so on.

Molecular orbitals are distinct from atomic orbitals.


1 Physicists usually talk about momentum instead of speed in this context, but as almost all of these speeds remain much lower than the speed of light we can connect the two ideas by $p = mv$.

2 I've been talking as if you can tell electrons apart, but in reality you can't so there is room for some hemming and hawing about the way I am writing this. The distributions are associated with the state and not with the particle.

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No, the speed is not consistent from atom to atom. Electrons nearest the nucleus of highly charged nuclei move the fastest.

In the simplistic Bohr model of a single electron atom (H, He+, Li2+...), speed is proportional to charge of the nucleus.

As a consequence, relativistic effects are much more pronounced in heavy atoms.

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