When an electron absorbs a photon, it remains an electron and the photon disappears. The electron energy and momentum are altered to account for the energy and momentum the photon was carrying. For a free electron, it will not be possible to balance energy and momentum simultaneously. There will have to be another interaction to make that work. If the electron is part of an atom, it can transfer some of the momentum to the rest of the atom and it can balance.

Scenario 1: Will an atom absorb an electron with kinetic energy greater than the difference of the initial and final energy levels or must it absorb an electron with kinetic energy similar to that of the energy difference only?

Let us talk of free atoms, gas.

If the atom is ionized, there will be an available energy level that an electron could occupy. A free floating electron at rest relatively to the atom can fall on that energy level and release a photon. In the case of an ionized hydrogen atom ( called a proton),

it will release a photon of energy 13.6 eV .

If the electron is not at rest with the nucleus, the probability of capture is very low, though computable, the excess energy released in the interaction as a photon carrying away the difference and bringing it at rest so as to be captured. The probability is low because extra electromagnetic vertices will be needed to compute the interaction crossection.

So the answer is that predominantly the electron must be at rest to be captured.

Scenario 2: I've read the following statement in my textbook, but I find it hard to believe since we were told that an atom can absorb a photon with the exact amount of energy to the energy difference. Statement: "A photon can be absorbed and cause ionisation if its energy is greater than or equal to the difference between the ionisation level and the ground state, although excitation requires photons with specific energies."

I read this as : in a neutral atom where the electron is bound , as with the hydrogen example above, in the ground state , the electron can be kicked out of the ground state if the energy is equal or larger than 13.6 eV. The electron will carry the balance of the energy of the photon.

Excitation means that the electron is hanging around in the higher than ground state levels, it is still bound by the potential of the nucleus. Ionization is where the electron becomes free of the potential of the nucleus, and since over the 13.6 eV in the example above, there exists a contiuum, it can carry all the left over energy as kinetic energy from the kick.

## Best Answer

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.

The answer is no, it is not called an

invariant massin vain.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.