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Electron Spin and Kinetic Energy
Name: Aarmin
Status: student
Age: N/A
Location: N/A
Country: N/A
Date: N/A
Question:
Is there a kinetic energy ascribed to an electron's spin?
If there is, why doesn't it appear in annihilation of electron and
positron?
Replies:
Dear Aarmin,
Since the spin of a particle is quantized, it is always the same. For
example, the spin angular momentum of a "spin 1/2" particle, such as an
electron is sqrt (3/4) h/2pi = 0.138 h, where h is Planck's constant.
Any kinetic energy associated with this spin is therefore always the
same and always contributes the same to the rest mass energy of the
particle.
The amount of that kinetic energy is not known, since the structure of
the electron is not known, but it certainly appears when the electron
annihilates.
Best, Dick Plano, Professor of Physics emeritus, Rutgers University
In the collision of an electron and positron, several things can happen
depending upon the speed (kinetic energy) of the particles. The site:
http://en.wikipedia.org/wiki/Electron-positron_annihilation
#See_also
gives a general answer to your question. The site:
http://hyperphysics.
phy-astr.gsu.edu/hbase/particles/lepton.html
gives a more general answer.
So far as is known the electron is a "fundamental" particle. (I back off
from "always" or "never" -- there may be undiscovered cases.). The
"simple" case requires that a number of conservation laws are applied to
the process. In this "low energy" case -- i.e. relative speeds of the
particles is much less than the speed of light, two gamma ray photons
are created, each with energy 0.511 mev traveling in exactly opposite
directions. This is required to conserve linear momentum before and
after the "collision".
It turns out that the reverse process can also occur but the details
of that interaction are a bit more complicated. See:
http://www.answers.com/topic/pair-production.
Since electrons and positrons both have spin 1/2 (Fermions) that spin
is also conserved before and after collision. Remember photons also
have spin.
The properties that are "conserved" are not always different ways
of expressing kinetic or potential energy. In the subatomic world
there are other variables (e.g. "color") that have conservation
rules that must be obeyed (usually).
Vince Calder
Uh, no, because to measure that kinetic energy,
you'd have to compare spinning and non-spinning states,
and the electron never has a non-spinning state.
So, in effect, we lump that kinetic energy (if it is such)
into the rest mass of the electron.
Thus, when an electron is annihilated, sure, lots of energy
comes out, and some of it always kinetic, but there has been lots of mixing.
The kinetic part of the energy coming out could come from any part
of the electron's total mass-energy going in.
By the way, ask yourself this:
The energy of a photon, is it kinetic or electromagnetic?
Or both? It does carry momentum....
Jim Swenson
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Update: June 2012
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