Compton Scattering Homework: Find Energy & Angles

E (photon's initial energy). Sorry for the confusion.In summary, the conversation discusses a relativistic collision between a photon and an electron, where the electron is initially at rest. The resulting energies and angles of the scattered particles are calculated using the conservation of energy and momentum equations. There is a discrepancy in the calculations, which is clarified in the end.
  • #1
Jukai
13
0

Homework Statement



In a relativistic collision between a photon and an electron, the recoiling electron has an energy of 40keV and the scattered photon an energy of 120keV. Find the energy of the photon before the collision, find the angles at which the photon and the electrons are scattered. The electron is initially at rest.

Homework Equations



Conservation of energy dictates that E + Ee = E' + Ee'
where E is the photon's energy before impact, E' its energy after impact, Ee the electron's initial energy and Ee' the electron's energy after impact.

I should put the conservation of momentum, but my problem lies with the conservation of energy.

The Attempt at a Solution



So, Ee is the rest energy of the electron, therefore 511keV. When I plug these values in my function, I get that E is -351keV. This raises 2 questions: why is it negative, and why is it smaller than E' when the theory says that E' < E. When I find the corresponding wavelength of the initial photon, it's also negative of course.

Could someone help me in figuring out what I've done wrong.
 
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  • #2
How did you get E=-351 KeV?
 
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  • #3
E + mec² = 120keV + 40keV

==> E = -351keV no? (I assume E'=120keV and Ee'=40keV, and that mec² = 511keV)
 
  • #4
right so the electron has suddenly lost over 90% of it's mass after it was supposed to gain energy from the photon. I'm guessing that that energy is referring to the kinetic term only
 
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  • #5
I see, that would make more sense. Then E is 160keV, which is bigger than E' as expected. Thank you
 
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  • #6
I trust you are referring to the initial energy of the photon being bigger than the final one rather than the electron which your post suggests
 
  • #7
Yes, I didn't mean to write Ee
 

1. What is Compton Scattering?

Compton scattering is a phenomenon in which a photon (particle of light) collides with a free charged particle (usually an electron) and transfers some of its energy to the particle, resulting in a change in the photon's wavelength and direction of propagation.

2. How is energy calculated in Compton Scattering?

The energy of the scattered photon can be calculated using the formula Escattered = Eincident / (1 + Eincident/m0c2(1-cosθ)), where Eincident is the energy of the incident photon, m0 is the rest mass of the electron, c is the speed of light, and θ is the scattering angle.

3. What are the possible angles of Compton Scattering?

The scattering angle in Compton scattering can range from 0° (forward scattering) to 180° (backward scattering).

4. How does Compton Scattering contribute to our understanding of the structure of matter?

Compton scattering allows scientists to study the microscopic structure of matter by observing changes in the wavelength and direction of photons as they interact with electrons. This helps us understand the distribution and behavior of electrons within atoms and molecules.

5. What are some real-world applications of Compton Scattering?

Compton scattering has various applications in fields such as medicine, materials science, and astrophysics. For example, it is used in medical imaging techniques such as X-ray computed tomography (CT) scans to create detailed images of the body's internal structures. It is also used in materials analysis to determine the composition and structure of materials. In astrophysics, Compton scattering is used to study the properties of cosmic rays and the structure of stars and other celestial bodies.

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