Compton Scattering: Calculating Wavelength from Energy

In summary, the maximum energy imparted to an electron in Compton scattering is 45 keV. To find the wavelength of the incident photon, the equation Lambda = h/mc (1-Cos) can be used, but an angle is needed. The maximum energy transfer occurs when the rebound photon is straight back. In this scenario, the cue ball (photon) transfers all of its energy to the eight-ball (electron), making it move forward and the cue ball come to a halt. In the case of equal masses and no backspin, the cue ball simply comes to a stop, but with unequal masses, the cue ball would either rebound or continue moving forward.
  • #1
Jacob87411
171
1
If the maxmimum energy imparted to an electron in Compton scattering is 45 keV what is the wavelength of the incident photon?

So a compton scattering happens and the energy is 45 keV and I need to find the wavelength of the photon incident to this electron. I think I need to use

Lambda = h/mc (1-Cos), but I am not given an angle.
 
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  • #2
Jacob87411 said:
If the maxmimum energy imparted to an electron in Compton scattering is 45 keV what is the wavelength of the incident photon?

So a compton scattering happens and the energy is 45 keV and I need to find the wavelength of the photon incident to this electron. I think I need to use

Lambda = h/mc (1-Cos), but I am not given an angle.

Maximum energy corresponds to (minimum/maximum, you decide) wavelength change? Which angle gives the (minimum/maximum) wavelength change?

Your equation is missing something. It is not quite correct in two places. For one, the angle for the cos is missing. What else?
 
Last edited:
  • #3
Imagine you're playing billiards. You shoot the cue ball (photon) against the eight-ball (electron), with a certain amount of energy. What direction does the cue ball go after the collision, when it transfers the maximum amount of energy to the eight-ball?
 
  • #4
The cue ball will go in reverse fro mthe way it came?
 
  • #5
Jacob87411 said:
The cue ball will go in reverse fro mthe way it came?

Yes, although in the case of a cue ball that has no backspin there is no rebound because the masses of the balls are the same. But if you had a cue ball of lesser mass, it would bounce back. And if you had a cue ball of greater mass, it would keep going forward in a stratight line when the maximum energy is transferred.
 
  • #6
So there is the collision and there is no rebound, but the 8 ball (electron) does go forward and now has the energy from the cue ball (photon)
 
  • #7
correct! they have the same masses, so the cue ball transfers all of its energy to the eightball making it move forward and the cue ball come to a halt.
 
  • #8
Bleah, I forgot about the mass considerations... with equal masses and if topspin doesn't come into play, the cue ball simply comes to a dead stop in a head-on collision with a stationary eight-ball.

I should have specified something like a ping-pong ball hitting the eight-ball. After all, the photon is massless.
 
  • #9
Jacob87411 said:
So there is the collision and there is no rebound, but the 8 ball (electron) does go forward and now has the energy from the cue ball (photon)

There will be a rebound in the Compton effect problem, and the angle that will give the electron greatest energy is when the rebound photon is straight back.
 

Related to Compton Scattering: Calculating Wavelength from Energy

What is Compton Scattering?

Compton Scattering is a phenomenon in which a photon (electromagnetic radiation) interacts with an electron, resulting in a change in the wavelength and energy of the photon.

How is the wavelength of a photon calculated from its energy in Compton Scattering?

The wavelength of a photon can be calculated using the Compton Scattering equation: λ = h/mc(1-cosθ), where h is Planck's constant, m is the mass of the electron, c is the speed of light, and θ is the angle of scattering.

What is the significance of Compton Scattering in physics?

Compton Scattering is an important phenomenon in understanding the dual nature of light as both a wave and a particle. It also has applications in fields such as astrophysics, where it can be used to study the composition and energy of cosmic rays.

What factors affect the wavelength of a photon in Compton Scattering?

The wavelength of a photon in Compton Scattering is affected by the energy of the incident photon, the mass of the electron, and the angle of scattering.

Can Compton Scattering be used to determine the energy of an electron?

Yes, the energy of an electron can be determined using the Compton Scattering equation. By measuring the change in wavelength of the scattered photon, the energy of the electron can be calculated.

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