# Charged Particle Radiation

• I
Good morning all, I was just wondering the following question. When an electron is accelerated it emits electromagnetic radiation, depending on how much it is accelerated the energy varies so the frecuency does and the electromagnetic wave emitted would be of different colors or maybe even x-rays if the velocity is high enough. If this happens inside an x-ray machine, then why is it neccesary for the process of Bremstrahlung to occur? or K-shell emision? Would the electron alone be enough to generate x-rays or it is enough and the other fenomena occur only to generate more of them?

## Answers and Replies

gleem
Science Advisor
Education Advisor
In an X-rays tube depending on the composition of the anode X-rays are mainly the result of Bremsstrahlung production due to the rapid deceleration of the electrons or the emission of characteristic X-rays due to the excitation of the atoms in the anode from the electron beam. Thus a Tungsten anode (Z= 74) produces mostly Bremsstrahlung while an anode of Molybdenum (Z=42) will have a larger percentage of characteristic X-rays.

The acceleration of the electrons due to the potential difference between the anode and cathode is insufficient to produce significant radiation.

• AndresPB
In an X-rays tube depending on the composition of the anode X-rays are mainly the result of Bremsstrahlung production due to the rapid deceleration of the electrons or the emission of characteristic X-rays due to the excitation of the atoms in the anode from the electron beam. Thus a Tungsten anode (Z= 74) produces mostly Bremsstrahlung while an anode of Molybdenum (Z=42) will have a larger percentage of characteristic X-rays.

The acceleration of the electrons due to the potential difference between the anode and cathode is insufficient to produce significant radiation.

Totally awesome thanks, how can i do a fast estimation of why the accelaration due to the potential diference is insufficient?

mfb
Mentor
The acceleration in bremsstrahlung happens within the size of an atom. The acceleration between the electrodes happen within centimeters, the acceleration is about 9 orders of magnitude smaller.

gleem
Science Advisor
Education Advisor
how can i do a fast estimation of why the accelaration due to the potential diference is insufficient?

Classically the rate of radiation emitted in an acceleration varies as the acceleration squared. In the case of a typical X-ray tube the anode cathode distance is a couple of centimeters while the distance it take an electron to decelerate in an anode say of Tungsten is a small fraction of a millimeter.

Classically the rate of radiation emitted in an acceleration varies as the acceleration squared. In the case of a typical X-ray tube the anode cathode distance is a couple of centimeters while the distance it take an electron to decelerate in an anode say of Tungsten is a small fraction of a millimeter.
Thanks a lot, could you put the formula?

gleem
Science Advisor
Education Advisor
could you put the formula

total radiated power = (2/3)(e2/c3)a2 in the Gaussian unit system.

Where e is the electronic charge
c is the velocity of light
a is the acceleration

• AndresPB
total radiated power = (2/3)(e2/c3)a2 in the Gaussian unit system.

Where e is the electronic charge
c is the velocity of light
a is the acceleration
Thanks a lot, where can i read about its deduction?

gleem
Science Advisor
Education Advisor
Thanks a lot, where can i read about its deduction?

Google "Larmor formula"

• AndresPB
Classically the rate of radiation emitted in an acceleration varies as the acceleration squared. In the case of a typical X-ray tube the anode cathode distance is a couple of centimeters while the distance it take an electron to decelerate in an anode say of Tungsten is a small fraction of a millimeter.
That would be all thanks, you are the best. Just to get all clear, could you explain why is the distance important here? Is it because the desaceleration/aceleration happen faster when distances are short so they have to be bigger? It doesnt matter one happens via bremstrahlung and the other happens for a potential diference?

mfb
Mentor
Right.

You can see the acceleration around an atom as potential difference as well - just with much higher field gradients. Well, quantum-mechanical effects can become relevant there, but let's ignore them for now.