Rentgen tube, De-Broile wavelength and Compton effect

[tigor]

Homework Statement

A Roentgen tube produces radiation with minimal wavelength. (λM)
De-Broglie Wavelength of electrons reaching Anode is λE.
Assuming electrons are not relativistic, what is the proper relation between wavelengths
λM, λE and Compton wavelength (λC)

Homework Equations

λE=h/p
λC=h/mc
I am not sure, minimal wavelength - what that is ?
This is multiple answers question, but any of the answers don't make sense to me.

The Attempt at a Solution

I think that relation between λC and λM can be wrote down through Compton effect:
λC=λE-λM=h/mc(1-cosα)
However, there is no angle given, so I cam confused about what to do?

Thank you in advance.

 

[anathema]

Thank you for your question. It seems like you are on the right track with your attempt at a solution. However, there are a few things that can be clarified to help you understand the proper relation between the wavelengths.

First, let's define the minimal wavelength (λM). This is referring to the shortest wavelength of radiation produced by the Roentgen tube. In other words, it is the smallest value for λE that can be achieved.

Now, let's look at the De-Broglie wavelength of the electrons reaching the anode (λE). As you correctly stated, this can be calculated using the equation λE = h/p, where h is Planck's constant and p is the momentum of the electron. This wavelength is related to the energy of the electron, which is determined by the potential difference in the Roentgen tube.

Next, let's look at the Compton wavelength (λC). This is the wavelength of a photon that is scattered off of an electron. It can be calculated using the equation λC = h/mc, where m is the mass of the electron and c is the speed of light. This wavelength is related to the mass of the electron.

Now, let's put all of this together. Since we are assuming that the electrons are not relativistic, we can use the non-relativistic equation for momentum, p = mv, where v is the velocity of the electron. We can also assume that the electrons are moving at the speed of light, so v = c. Substituting this into the De-Broglie equation, we get λE = h/mc. This is the same equation as the Compton wavelength!

Therefore, the proper relation between the wavelengths is that the De-Broglie wavelength (λE) and the Compton wavelength (λC) are equal. In other words, the wavelength of the electrons reaching the anode is equal to the wavelength of a photon scattered off of an electron.

I hope this helps clarify things for you. Please let me know if you have any further questions.