Calculating Energy of Scattered Photon in Compton Effect

In summary, the energy of the scattered photon in Compton effect is related to the angle between the scattered photon and the incident photon. This angle can be derived from conservation of energy and momentum in relativistic mechanics, or by looking it up. The equation to calculate the angle involves the energy of the incident photon, the rest mass of the electron, and the angle of the recoiling electron. Other approaches to solving this problem may involve using the HyperPhysics resource or using the principle of conservation of momentum. With some work, a solution can be obtained for this problem.
  • #1
nelufar
32
0
How to calculate energy of scattered photon when the energy of incident photon is equal to the rest energy of an electron and the angle between the direction of the recoiling electron and the incident photon is 40 degrees?
In compton effect the energy of scattered photon is related to angle
between the scattered photon and the incident photon. How to relate the angle between the direction of the recoiling electron and the incident photon and angle between the scattered photon and the incident photon?
 
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  • #2
Derive this from conservation of energy and momentum in relativistic mechanics. Or look it up. I know it is on HyperPhysics.
 
  • #3
Can't we use derivation for Compton effect?
 
  • #5
I tried solving the problem using relativistic approach but there also the relation is for angle of the scattered photon not for angle of recoiling electron.So,can there be any other way to solve it.
 
  • #6
Momentum is conserved. The transverse component was zero before the interaction, so theta and phi are related by
[tex]0 = \frac{h}{\lambda '} \sin \theta - p_e \sin \phi[/tex]
 
  • #7
But we only know the energy of the incident photon and rest mass of electron. Recoiling electron will also have energy which is not given.So how to calculate P_e and what about /theta?
 
  • #8
Is there no solution to the problem? Can there be any other approach to solve it?
 
  • #9
nelufar said:
Is there no solution to the problem? Can there be any other approach to solve it?
This looks like a homework problem, so of course there is a solution.
You just need to work on it a bit.
 
  • #10
I have tried a lot but the equation which you have provided, I got stuck there. So, if you can help , it would be really helpful. Atleast tell me can there be some other approach which probably I am not thinking of.
 
  • #11
I referred you to HyperPhysics. Momentum is conserved so
[tex]\vec{p_i} = \vec{p}_f + \vec{p_e} \Leftrightarrow \vec{p}_f= \vec{p_i}-\vec{p_e}[/tex]

[tex]p_f^2 = p_i^2 + p_e^2 - 2\ p_i\ p_e \cos{\phi}. [/tex]
That is how you can get it as a function of the electron angle, I think.
If you now proceed along similar lines as Nave, I think you should get there.
 
Last edited:
  • #12
Pieter Kuiper said:
I referred you to HyperPhysics. Momentum is conserved so
[tex]\vec{p_i} = \vec{p}_f + \vec{p_e} \Leftrightarrow \vec{p}_f= \vec{p_i}-\vec{p_e}[/tex]

[tex]p_f^2 = p_i^2 + p_e^2 - 2\ p_i\ p_e \cos{\phi}. [/tex]
That is how you can get it as a function of the electron angle, I think.
If you now proceed along similar lines as Nave, I think you should get there.

Thanks. I will try with this.
 

1. What is the energy of a scattered photon?

The energy of a scattered photon depends on the type of scattering process and the energy of the incident photon. It can be calculated using the formula Es = Ei / (1 + (Ei/mec2)*(1-cosθ)), where Ei is the energy of the incident photon, me is the mass of the electron, c is the speed of light, and θ is the scattering angle.

2. How does the energy of a scattered photon change with different scattering angles?

The energy of a scattered photon decreases as the scattering angle increases. This is due to conservation of energy and momentum in the scattering process. The higher the scattering angle, the more energy is transferred to the scattered electron, resulting in a decrease in energy of the scattered photon.

3. Can the energy of a scattered photon be measured?

Yes, the energy of a scattered photon can be measured using various techniques such as Compton scattering experiments or spectroscopy. These methods involve measuring the energy and direction of the scattered photon to determine its energy.

4. What happens to the energy of a scattered photon in different materials?

The energy of a scattered photon can be affected by the properties of the material it is scattered in. This can include factors such as the atomic structure, density, and composition of the material. In some cases, the energy of the scattered photon may increase or decrease depending on the material and scattering process.

5. How does the energy of a scattered photon relate to the wavelength of light?

The energy of a scattered photon is directly proportional to the frequency (and inversely proportional to the wavelength) of the incident light. This is described by the equation E = hν = hc/λ, where h is Planck's constant, ν is the frequency, c is the speed of light, and λ is the wavelength. As the energy of the photon changes, so does its frequency and wavelength.

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