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the following question is extremely important so please reply!

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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# Total energy levels of the electron and rest energy

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