Maximum Kinetic Energy in Comton Scattering

In summary, the conversation discusses the maximum kinetic energy of a recoiling electron after being scattered by a photon with energy E. The equation for calculating this energy is K = (2E^2)/(2E + mc^2), but the expected answer is K = (E^2)/(E + mc^2). It is unclear which equation is correct, and it is possible that there is a typo in the conversation.
  • #1
samuelyee
1
0

Homework Statement


A photon of energy E is scattered off a stationary electron with rest mass m. What is the maximum kinetic energy of the recoiling electron?

Homework Equations


[tex]\lambda'-\lambda=\frac{h}{mc}(1-cos(\phi))[/tex]
[tex]E=\frac{hc}{\lambda}[/tex]

The Attempt at a Solution


The maximum kinetic energy gained is when [tex]\phi=180^{o}[/tex] , so
[tex]\lambda'-\lambda=\frac{2h}{mc}[/tex]
After some manipulation, I finally get
[tex]K = \frac{2E^2}{2E+mc^2}[/tex]
But the answer is supposed to be [tex]K = \frac{E^2}{E+mc^2}[/tex] , which would be the case if the cosine term is zero. Am I making the wrong assumption at the start?

Thanks for the help!
 
Last edited:
Physics news on Phys.org
  • #2
I am getting the same as you. I'm guessing a typo somewhere?

Cheers -- sylas
 

What is Compton scattering and how does it relate to maximum kinetic energy?

Compton scattering is a process in which an incident photon interacts with an electron, resulting in a decrease in the photon's energy and an increase in the electron's energy. The maximum kinetic energy in Compton scattering refers to the highest possible energy that the electron can gain from this interaction.

How is the maximum kinetic energy in Compton scattering calculated?

The maximum kinetic energy in Compton scattering can be calculated using the formula: Ek,max = Eγ (1-cosθ), where Ek,max is the maximum kinetic energy, Eγ is the energy of the incident photon, and θ is the scattering angle.

What factors affect the maximum kinetic energy in Compton scattering?

The maximum kinetic energy in Compton scattering is affected by the energy of the incident photon, the mass of the electron, and the scattering angle. Higher energy photons, lighter electrons, and smaller scattering angles result in a higher maximum kinetic energy.

Why is the maximum kinetic energy in Compton scattering important in physics?

The concept of maximum kinetic energy in Compton scattering is important in understanding the behavior of photons and electrons in interactions, and it has applications in fields such as medical imaging, materials science, and astrophysics.

How does the maximum kinetic energy in Compton scattering relate to the conservation of energy?

The maximum kinetic energy in Compton scattering is an example of the law of conservation of energy, which states that energy cannot be created or destroyed but can only be transferred or transformed. In Compton scattering, the decrease in energy of the photon is balanced by the increase in kinetic energy of the electron, thus conserving the overall energy of the system.

Similar threads

Replies
8
Views
1K
  • Introductory Physics Homework Help
Replies
19
Views
629
  • Introductory Physics Homework Help
Replies
3
Views
2K
  • Introductory Physics Homework Help
Replies
4
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
11
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
1K
  • Introductory Physics Homework Help
Replies
1
Views
4K
  • Introductory Physics Homework Help
Replies
12
Views
1K
  • Introductory Physics Homework Help
Replies
3
Views
3K
Back
Top