XRay Production and Bremsstrahlung

[Mazin Nasralla]

Hello,

I have been studying XRays recently in a general science course. It's about A Level standard but I want to take my interest further.

Anyway to the point. I thought I understood the release of XRays when an electron is slowed as it ploughs into a tungsten anode in an X-Ray Tube. Wiki and my teacher explained that a Continuous X-Ray spectrum is generated according to the Conservation of Energy. Loss of Kinetic Energy = Photon Released with the maximum energy of the photon being linked to the Voltage of the XRay Tube.

That all seemed to make sense, but now I'm doing Electrostatics and I'm thinking back to the electron moving into the anode. I must have misunderstood after all.

I appreciate that the electron will be slowed by the interaction with matter, but we drew a diagram of an electron interacting with a positively charged nucleus. It was bent around it and my teacher said it was braking and therefore a photon was released to compensate for the loss in kinetic energy.

I must have misunderstood the process. If there is an interaction with the positively charged nucleus surely that would accelerate the electron...not slow it down. I'm thinking now of a spacecraft using a planet to sling-shot around it and pick up speed.

I'm thinking maybe the electrons slow down when they hit the anode because of their interaction with the electron clouds, but if that is what slows them down then surely they are doing work against an electric field and there is no need to spontaneously fire off an X-Ray photon? A bit like when a free-wheeling bike slows as it goes up a hill. It's kinetic energy is being converted into gravitational energy. If the electron is slowed by its interaction with matter, which I would think would be electrostatic interaction then I am confused. What is the nature of the interaction. If it's against a negatively charged electron cloud then surely there's no need for a photon to be released as the loss of kinetic energy = work done by the electron against the field and it may gain electric potential? If the interaction is with the nucleus then surely that's not a braking effect. Sorry as you can see I am confused.

I know that X-Ray production is very inefficient and for the most part heat is released so maybe there's several processes going on. Could someone help me out? Thanks!

 

[mfb]

I must have misunderstood the process. If there is an interaction with the positively charged nucleus surely that would accelerate the electron...not slow it down. I'm thinking now of a spacecraft using a planet to sling-shot around it and pick up speed.

Spacecrafts do not pick up speed relative to the object of their fly-by. They accelerate while moving towards it, and get slower again while moving away from it. Energy conservation makes sure the velocity afterwards is the same as before.

In a purely classical picture the electron would do the same, but the electron also emits significant radiation in the process (a proper description needs quantum mechanics), so it slows down more than it accelerates. The gravitational equivalent would be the emission of gravitational waves, but those are negligible unless you let two neutron stars or black holes orbit each other closely.

 

[Mazin Nasralla]

Thanks for the reply but I don't understand

1) I know that NASA ESA use planetary orbits to accelerate their craft. Your argument would hold if the planet was stationary. Then the gravity field would be uniform and what speed the craft gained on approach I would be lost on exit, but if the planet moves as it does then that would not hold.

2) I don't get the argument that electron emit photons because of the conservation of energy. I know we can not use Newton mechanics to explain the atom or the electron but surely there is some connection? In macroscopic terms, a body would not lose energy and momentum unless a Force is acting against it. So if the electron enters a field or matter, it's loss of kinetic energy is due to the work done on it by a field, and therefore there is no need to release a photon?

X Ray production was presented to me as squaring Energy Conservation. The electron slows: And that loss of KE is converted to a Photon.

Experiment suggests this indeed is the process as Kinetic Energy = Max X-Ray Photon release as seen by the cut off of the Bremstrahlung spectrum at the X-Ray Tube Voltage. That suggests a link. But what slows the electron? Surely that's the field. And if that's the case then it's like friction. Work is done by the electron against the Field it loses energy and is slowed by that process...there's no need to spontaneously release a photon.

I know I am wrong and I missing something, just hoping it's something simple that I can get my head around. I did have a look at the Bremstrahlung explanation on Wiki and it was full of Integrals which I am not good enough to understand. Just doing that now as it happens in Maths.

 

[mfb]

1) I know that NASA ESA use planetary orbits to accelerate their craft. Your argument would hold if the planet was stationary.

The atoms are stationary in the material (to a very good approximation).
Yes you can use fly-bys to change (increase or decrease) the speed relative to the sun, but not relative to the planet. You need the relative motion of planets and sun, and this relative motion is negligible for solids (of the order of 1km/s, compared to your ~30000km/s electron).

2) I don't get the argument that electron emit photons because of the conservation of energy. I know we can not use Newton mechanics to explain the atom or the electron but surely there is some connection?

Not enough connection to explain the emission of a photon with classical mechanics. You can see that radiation is emitted in some way with classical mechanics - there are accelerated charges, and accelerated charges radiate. But the photon nature of the emission is purely quantum-mechanical.