[Physics] The mass change of electron after absorbing photon

particle-physicsquantum mechanicsquantum-field-theory

If a photon is absorbed by an electron, will the rest mass of the electron increase? Or will the relativistic mass of the electron increase?

There are good answers, but I want to introduce the representation of Feynman diagrams, because that is what is being used when studying the behavior of elementary particles, and both the photon and the electron are elementary particles. These diagrams are used to calculate the probability of interaction , a strict mathematical operation implied by it.

The squiggly line represents the four momentum of a photon , and the dark the four momentum of the electron. The interaction happens at the points called vertices. What happens is that for a tiny interval of the variable the photon is absorbed completely in a summed four vector in the internal dark line , and the electron and photon reappear with the scattered momenta/energies at a second vertex. Between the two vertices An integral is applied over the variables and the boundary conditions of the problem.

The incoming and outgoing electron have the invariant mass given by the four vector they are carrying. Only energy and momentum change with the absorption of part of the energy of the incoming photon.

It has to be stressed that for a free electron there will always be a scattered off photon, even of very low energy, because of momentum conservation at the center of mass, there cannot be two particles coming in and one going out.

If a photon is absorbed by an electron, will the rest mass of the electron increase?

The answer is no, it is not called an invariant mass in vain.

Or will the relativistic mass of the electron increase?

Yes, the relativistic mass will increase. The concept is not really useful at the particle level. It is useful where newtonian mechanics is assumed, and newtonian forces are estimated, as with starships and the velocity of light, but it is confusing terminology at the particle level.

The case of electrons bound in an atom is covered by other answers.