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Name: Aarmin
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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?

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:

gives a general answer to your question. The site:


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:

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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