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Date: Around 1993

How fast do electrons move (under typical circumstances in a typical atom)?

We tend to think of atoms in electrons in an atom as like planets rotating around the sun. While this view is attractive, the basis of semiweeklies of the first theories of atom structure by Bohr, is a simplification. Really, the electron should be considered as smeared out over a large volume surrounding the atom. In this sense, the electron does not move inside the atom.


Well, that is all strictly true, but still it is possible to ascribe approximate velocities to electrons in bound states. This is done all the time to ascribe whether relativistic effects are important in calculating these bound states; for example, relativistic contraction of the inner core of electrons is the explanation typically used to explain the unique properties of transition metals, and relativistic corrections to calculations are currently a frontier area in theoretical atomic and chemical physics. A sort of gross model for "speeds" of electrons in bound states can be obtained from the Bohr model. This model predicts that the electron associated with a hydrogen nucleus would be moving at 2.42 x 10^8 cm /sec, which you may wish to compare with the speed of light: c = 3.00 x 10^10 cm/sec. So the velocity of an electron in the first Bohr orbit (ground state) is a tiny fraction of the speed of light, which is why non relativistic forms of quantum theory work quite well for hydrogen. However, start increasing Z (the charge on the nucleus) and the Bohr velocity for the inner electrons starts to get huge...and experimentally, there is a considerable contraction of the spatial extent of these electrons relative to H. So, although velocities are not strictly defined for electrons whipping around a nucleus, an approximate model (the Bohr model) does give one a sense of when one might need to start formulating relativistic corrections to quantum mechanics.


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