# Energy of the electron

1. Dec 7, 2014

### gentsagree

The rest energy of the electron is E=m(0)*c^2=0.511MeV, where the rest mass m(0)=9.109x10^(-31)Kg multiplies c squared. This is the energy of the electron in its own frame, i.e. at rest.

When we say an electron gains (or has, I'm quite confused about this point too ) 1eV of energy when accelerated through a 1Volt potential, to which frame do we refer to?

Also, when we speak of low energy electrons, say one with energy of a few eV, we must mean in our frame (or the "laboratory frame"), as their energy in their own frame is bounded below by their rest energy of 0.511MeV. Correct?

Thanks!

2. Dec 7, 2014

### Staff: Mentor

This is in the frame in which the apparatus that accelerates the electron is at rest. In that frame, the electron gains 1 eV of energy. It now has 0.511 MeV of rest-energy plus 1 eV of kinetic energy (in that frame).

Here we mean the kinetic energy.

If by "their own frame" you mean the frame in which the electrons are at rest, in that frame they have only their rest-energy, i.e. 0.511 MeV, according to the definition of "rest frame". In the lab frame their energy is 0.511 MeV of rest-energy plus a few eV of kinetic energy.

In a situation like this people often use sloppy language and say just "energy" when they really mean "kinetic energy." You have to figure this out from the context. Clearly it is impossible for an electron to have only a few eV of (total) energy, because it must have 0.511 MeV of rest-energy.

3. Dec 12, 2014

### gentsagree

Thanks a lot!

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