# Total energy levels of the electron and rest energy

#### relativityfan

hi,

in an atom, the energy levels of the electrons are negative and the velocity of the electron increases when the energy decreases.

however, this cannot be the total energy(in relativity) because it does not includes the rest energy of the electron
what I really dont know is the formula for the total (relativistic) energy of the electrons. With the binding energy, the mass of the electron decreases(mass deficit) but its speed increases, therefore its relativistic mass too...

For example, in heavy elements (for example Z>90), the velocity of electrons is relativistic. In such case, should the total energy of the elecrons (binding energy) be higher or lower than the rest energy?

and I suppose that such energy can be reached by absorbing photons.
in an particle accelerators, I suppose that the relativistic mass is increased by absorbing photons.
I also suppose that the only photons absorption and emission of photons by electrons drops from an energy level to another energy level. (where are the virtual photons???)

Am I correct with thiese sentences?

so why in some case absorbing photons increases the velocity and in other cases it decreases the velocity?

Please reply, any help for one of these questions is very welcome!

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#### alxm

however, this cannot be the total energy(in relativity) because it does not includes the rest energy of the electron
Well that's mostly just a shift of $$m_0c^2$$.
what I really dont know is the formula for the total (relativistic) energy of the electrons.
That'd be the http://en.wikipedia.org/wiki/Dirac_equation" [Broken] (if you ignore QED effects)
For example, in heavy elements (for example Z>90), the velocity of electrons is relativistic. In such case, should the total energy of the elecrons (binding energy) be higher or lower than the rest energy
The total energy is usually lower and the binding energy higher. Both for relativistic effects overall, and for the mass-velocity correction specifically. However, some relativistic effects raise the energy (e.g. the Darwin term), but these are obviously smaller.
I also suppose that the only photons absorption and emission of photons by electrons drops from an energy level to another energy level. (where are the virtual photons???)
No, there are atom-photon interactions which leave the energy level unchanged; Rayleigh scattering for instance.
so why in some case absorbing photons increases the velocity and in other cases it decreases the velocity?
Huh? The absorption of a photon by an electron can only increase its energy and velocity.

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