Don't forget that angular momentum should be conserved, too. If I remember my atomic physics correctly, the absorption of a photon involves not only increasing the energy (from the ground state E_1 to some excited state E_n) but also provides the difference in angular momenta of the states, which is related to the l = +-1 criterion for the quantum number l.
KC
-----Original Message-----
From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of Antti Savinainen
Sent: Thursday, 27 October, 2016 02:28
To: phys-l@www.phys-l.org
Subject: [Phys-L] Photons vs. electrons in excitation
Hi,
it is well known that the excitation of an electron in the ground state (e.g. in hydrogen) requires a photon with a certain energy. The energy must match with the energy difference between some excited state and the ground state. If the incoming photon does not have the "right" energy it does not cause excitation; instead, scattering takes place.
However, if the incoming particles are electrons with a certain kinetic energy which does not match the energy difference between any excited state and the ground state, they nevertheless cause excitation as long as the electrons have enough energy to do so. Why is it so that the bound electron is so "picky" with photons but when it comes to electrons, anything goes as long as there is enough energy? This means that the electron loses part of its kinetic energy in the interaction with the atom and the "lost" energy appears in the excitation.