Electron Velocity

(Created prior to 1993)

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

Topper
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