Compton scattering, angle of recoiled electron

In summary, the angle of the velocity vector from a recoiled electron after an impact from a photon is 110 degrees.
  • #1
Dawei
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Trying to find the angle of the velocity vector from a recoiled electron after an impact from a photon.

I have already found the initial energy of the photon, and the energy of the scattered photon, and so can calculate the momentums. I know the photon is scattered at an angle of 110 degrees, and I know from the Compton effect and the difference in the wavelengths what the electron's energy is.

Here is a relevant sketch:
http://upload.wikimedia.org/wikipedia/commons/e/e3/Compton-scattering.svg

Note that theta here is the 110 degrees. I want to know the angle of the velocity vector of that recoiled electron.

Please, if anyone can point a finger at where to go I'd be happy. I've been working on this for quite a long time, trying to turn the initial and final momentum into i and j components, but it is getting me nowhere. I have the feeling the answer is a lot more simple than what I've made it out to be!
 
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  • #2
In the derivation of the formula relating the scattering angle and the shift in wavelength, the electron is assumed to be at rest initially, so its final momentum will just be the difference of the photon's initial and final momenta. In the figure, the initial momentum is in the +x-direction, and you can calculate the components of the photon's final momentum since you know its energy and angle. I'm not sure what you're doing to make the problem so hard. Is there some specific form of the answer you're looking for?
 
  • #3
I just keep getting impossible answers for the cosine of theta (where theta is not the 'theta' in the above drawing, but rather the angle the electron makes with the horizontal).

I start out with initial photon momentum, equal to the final momentum in the x direction. That is,

hf1/c = (hf2/c)*(cos110) + (meve)*(cosθ)

And for the y direction:

0 = (hf2/c)*(sin110) + (meve)*(sinθ)

I don't know if this is right, and even if it is I can't figure out how to solve it.

Also, should hf2/c be negative?
 
Last edited:
  • #4
Dawei said:
I just keep getting impossible answers for the cosine of theta (where theta is not the 'theta' in the above drawing, but rather the angle the electron makes with the horizontal).

I start out with initial photon momentum, equal to the final momentum in the x direction. That is,

hf1/c = (hf2/c)*(cos110) + (meve)*(cosθ)

And for the y direction:

0 = (hf2/c)*(sin110) + (meve)*(sinθ)

I don't know if this is right, and even if it is I can't figure out how to solve it.

Also, should hf2/c be negative?
The equations are right. You're using hf2/c as the magnitude of the scattered photon's momentum, so it should be positive. The sign is taken care of by the sines and cosines. (In particular, cos 110<0.)

To solve for theta, move the hf2/c term to the other side in each equation, then divide one equation by the other.
 

1. What is Compton scattering?

Compton scattering is a phenomenon in which a photon (usually X-ray or gamma ray) collides with a charged particle, resulting in the photon losing some of its energy and changing direction.

2. How does Compton scattering relate to the angle of recoiled electron?

The angle of recoiled electron refers to the direction in which the electron is scattered after the collision with the photon. This angle is directly related to the energy and direction of the incident photon, as well as the characteristics of the charged particle it collides with.

3. What factors affect the angle of recoiled electron in Compton scattering?

The angle of recoiled electron is affected by the energy and direction of the incident photon, the mass and charge of the charged particle, and the energy and direction of the scattered photon.

4. Why is the angle of recoiled electron important in Compton scattering?

The angle of recoiled electron provides valuable information about the energy and direction of the incident photon, and can be used to study the properties of the charged particle it collided with. It also plays a crucial role in various applications of Compton scattering, such as in medical imaging and material characterization.

5. Can the angle of recoiled electron be predicted or controlled?

The angle of recoiled electron can be predicted using mathematical models and is influenced by the various factors mentioned earlier. However, it cannot be directly controlled as it is a result of the interaction between the photon and the charged particle. Scientists can manipulate the incident photon's energy and direction to indirectly influence the angle of recoiled electron.

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