Compton Scattering- finding photon wavelength

In summary, an electron moving at 0.8c collides with an incoming photon and after the collision, the electron is moving at 0.6c and an outgoing photon is moving in the opposite direction. To find the wavelength of the incoming photon, we can use the equations for momentum and energy conservation, which result in a final expression with both the initial and final wavelength. To solve for the initial wavelength, we also need to take into account the correct expression for the energy of the electron.
  • #1

Homework Statement


An electron moving to the left at 0.8c collides with an incoming photon moving to the right. After the collision, the electron is moving to the right at 0.6c and an outgoing photon moves to the left. What was the wavelength of the incoming photon?

Homework Equations


p=γmv
Eγ=pc=h/λ

λ'-λ = (h/mec)(1-cosθ)

The Attempt at a Solution


*Defining left as positive*
I have the following expressions for the initial and final momentum of the system, and I set them equal to each other.

Pinitial= pe + pγ
Pi = -γimevei + Eγi/c
Pf = γfmevef - Ef/c

given Ei/c = h/λ

h/λ - γimevei = γfmevef - h/λ'

h(1/λ + 1/λ') = γfmevef + γimevei

I can plug in all the values for the electron and get some number, but I am still left with λ and λ'. I'm not sure if my approach is correct, but if it is, I don't see how I can find just λ (the initial wavelength).
 
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  • #2
Is the total momentum the only quantity that is conserved?
 
  • #3
Chandra Prayaga said:
Is the total momentum the only quantity that is conserved?
I presume energy would also be conserved, but writing out that expression also leaves me with λ and λ'

imevi2)/2 +mec2 - hc/λ = hc/λ' - (γfmevf2)/2 - mec2
 
  • #4
Your expression for the energy of the electron is wrong
 
  • #5
Would E= √(p2c2 + m02c4) be more accurate?
 
  • #6
That is correct
 

What is Compton Scattering and how is it related to finding photon wavelength?

Compton Scattering is a phenomenon in which a photon is scattered off an electron, resulting in a change in the photon's wavelength. This process is used to determine the wavelength of the scattered photon.

Why is Compton Scattering important in scientific research?

Compton Scattering is important because it helps us understand the nature of light and its interactions with matter. It also has various applications in fields such as astrophysics, nuclear physics, and medical imaging.

What factors affect the change in photon wavelength during Compton Scattering?

The change in photon wavelength during Compton Scattering is affected by the energy of the incident photon, the angle of scattering, and the mass of the scattering particle, which in this case is an electron.

How is Compton Scattering used to determine the energy of the scattered photon?

The energy of the scattered photon can be determined by measuring the change in its wavelength using a spectrometer. This change is directly related to the energy of the photon before and after scattering.

Can Compton Scattering be used to study the structure of atoms?

Yes, Compton Scattering can be used to study the structure of atoms by analyzing the energy and direction of the scattered photons. This information can provide insights into the distribution of electrons within an atom.

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