Photons need specific energy levels, equal to the difference between two energy levels to excite an electron in an atom. Is this the same case with electrons that collide with atoms?

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    $\begingroup$ In short: yes. The energy needed to excite an electron is independent of the manner of excitation, be it the absorption of a photon or the absorption of (part of) another electron's kinetic energy (which can be thought of as being transferred by means of a virtual photon). $\endgroup$ – Wouter May 12 '13 at 23:13
  • $\begingroup$ I ask because I am doing an A level Physics paper which is saying that an electron collides with an atom, excites one of the electrons, and the KE of the electron before is 9eV and after the collision it is 1eV. This just seemed counter to what I learnt about colliding photons needing energies equal to the differences between the discrete energy levels of the atom. If it is the same case with electrons, wouldn't all of the electrons KE have to be absorbed? $\endgroup$ – user85798 May 13 '13 at 0:13
  • $\begingroup$ Nope, the important difference is this: in the case of the photon, the photon is absorbed (remember that a photon is really just a packet of energy). Contrarily, in the case of the electron, the 'free' electron and the bound one interact and due to this interaction the 'free' one loses some energy while the bound one gains some energy (ideally the same amount that was lost by the 'free' one). Because the 'free' electron can have any continuous amount of KE, it only needs at least the amount necessary to excite the bound electron in order to actually excite it. $\endgroup$ – Wouter May 13 '13 at 0:57
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    $\begingroup$ @Wouter remember that a photon is really just a packet of energy - this is not true, a photon is a full-fledged particle. It's only that its only interaction vertex absorbs photon - a purely electromagnetic fact. And there could be another photon emitted immediately, as in the scattering of light on a free electron, or in the propagadion of light through refracting media. Why atoms are not involved in such processes, that has something to do with selection rules. $\endgroup$ – firtree May 13 '13 at 5:11
  • $\begingroup$ @firtree I agree it's usually considered a valid elementary particle. But considering some of the possible problems with the photon as an elementary particle (e.g. Lorentzinvariance: different observers don't necessarily agree on the number of photons; one manifestation of this is the Unruh effect), I went back to the original (Einstein) interpretation of the photon as a packet of energy being transferred from the EM field to the particle, which is the important aspect in this story anyway. $\endgroup$ – Wouter May 16 '13 at 15:15

Energy and momentum has to be conserved. That the electron / photon has to have enough energy for the excitation is obvious. What is interesting is what happens when they have too much energy.

For radiative transitions between bound states the orbital anuglar momentum has to change by 1. This means that the photon has to be absorbed which in turns means that the photon has to have exactly the right energy (otherwise the extra energy has nowhere to go). For transitions to unbound states (so atom is oxidized) this is no longer true. A photon with 9 eV energy could very well give rise to an oxidised atom and an 1 eV photon.

Electrons can take away (and give) momentum easier so they only need enough energy for the transition. Since the electron is not absorbed it can take away any extra energy if it has too much.


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