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The orbitals define the volume of an atom or molecule not of an electron (singular). A truly "free" electron is a plane-wave solution of the Schrodinger equation, and therefore technically occupies the full volume of the universe :-/
If you want to use the deBroglie wavelength as an argument for volume, then you're claiming that the effective size of an electron is a function of its momentum. Not what we normally do when we mean "size" as a property of an object.
I'm thinking specifically of the Rutherford method of measuring the effective radius of an object from the scattering angular distribution. From Bhahba (e- - e-) scattering, we know that the inteaction radius of a free electron (the radius where the electrical repulsion would stop being pointlike, and start to look more like a billiard ball) is less than 10-20 m, and is entirely consistent with zero.
From deep inelastic scattering, in particular at HERA, we know that the interaction radius of an individual quark is less than 10-18 m, and also consistent with zero.
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Posted:Aug 28, 2010
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