MadSci Network: Physics

Re: What is the volume (spacial region) of an electron?

Date: Mon Mar 22 13:55:10 1999
Posted By: Michael Ford, Staff, Radiation Safety/Health Physics/Plutonium/Nuke Weapons, Battelle Pantex, Pantex Plant
Area of science: Physics
ID: 919924727.Ph

As far as I have been able to determine, the volume of an electron
has not been determined.  One might be able to deduce the volume
of an electron from the effective radius of the Bohr hydrogen atom of
0.53 A or 0.53 x 1E -10 meters.  Since the hydrogen atom is made up
of one proton and one electron, one could assume a uniform
density of subatomic particles throughout the volume (for
argument's sake) where,

density (H atom) = (1.0079 AMU)/[(4/3)*PI*(0.53e-10 m)^3]

density (H atom) = 1.62 e30 AMU/m^3

Assume density (H atom) = density (e-), then

density (e-) = (5.49 e-4 AMU)/ e- Volume

and substituting and solving for the e- Volume, we find

e- Volume = (5.49 e-4 AMU)/(1.62 e30 AMU/m^3)

e- Volume = 3.4 e-34 m^3

or about 1800 times smaller than the volume of the Bohr hydrogen
atom which is consistent with the mass differences between the
proton and the electron.  Dependant upon your assumptions, the
same process could be used for other subatomic particles.
However, due to the homogenizations involved, those calculations
would also be plagued by the same inaccuracies.

My best guess.  'Hope this helps!

[Moderator note: Another approach is to equate the rest mass of the electron 
with the energy of a spherical distribution of an amount of charge equal to that 
 of the electron.  Doing this allows you to solve for the radius of the 

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