If the incident electron loses all of its energy in the collision with an atom,what happens to it after the collision?

Question

I was studying the production of X-rays and there was this line that "If an electron loses all its energy in a single collision with a target atom, an x-ray photon with the maximum energy or the shortest wavelength is produced. This wavelength is known as the short-wavelength limit" So the question goes like this.The incident photon collides with the atom and ejects the electron from the K-shell.if the incident electron loses all of its energy in the collision what happens to it after the collision? and why wouldn't this incident electron fill the vacancy created in the K-shell.?as it is more prone to fall in the vacancy.Rather it is filled by another electron i.e. from L-shell.

Answer 1

There are a few things here

First in the quote you mentioned, for the maximum energy the incident electron loses all its energy (more or less) and a photon is generated - in this process no electrons in the target atom are knocked out, it is just the free electron slowing down that makes the X-ray photon. Given that electrons in this experiment start with at least 1000 eV energy or 1 keV normally and that a 1 eV electron moves at a speed of 60 cm per microsecond the electron will be able to fly away even if it only has 1 eV left. If the target is metal the electron might be captured into the conduction band of the metal. In the end something will happen where the electron will be lost otherwise the target will charge up with all the electrons hitting it

The incident photon collides with the atom and ejects the electron from the K-shell.if the incident electron loses all of its energy in the collision what happens to it after the collision?

Here you are talking about two different things - the first is photoemission of an electron by an X-ray (The incident photon collides with the atom and ejects the electron from the K-shell) where a core electron is knocked out by the absorption of a high energy photon. The second thing (if the incident electron loses all of its energy in the collision what happens to it after the collision?) is the process I describe above where an electron hits a target and loses its energy by generating an X-ray.

and why wouldn't this incident electron fill the vacancy created in the K-shell.?

As noted you are talking about two different things - when the slowed down electron is present no K-shell hole is present.

Rather it is filled by another electron i.e. from L-shell.

This is Auger emission where an X-ray photon knocks out a K-electron and then an L-shell electron drops into the hole. Note this can also happen when a high energy electron knocks out a K-shell electron, but in this case the incident electron will have many 100s of eV left over because in this case the electron is not stopped with close to zero energy.