Find max E of a photon in Compton Collision

In summary, to find the energy of an x-ray photon that can impart a maximum energy of 50keV to an electron by Compton collision, you need to use the equation ∆λ=h/mc(1-cos(theta)). After setting theta to 90, the corresponding change in frequency can be found using c/2.43*10^-12. However, this approach is incorrect as it assumes that f-f'=c/(lambda-lambda'), when in fact it should be f-f'=c/lambda-c/lambda'. This leads to a calculated energy of 510551 eV, which is greater than the 50keV energy delivered to the electron. Further clarification and hints are needed to solve this problem correctly
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Homework Statement



Find the energy of an x-ray photon that can impart a max energy of 50keV to an electron by compton collision

Homework Equations



∆λ=h/mc(1-cos(theta)) where m = mass of electron
E=hf
(to be honest, not entierly sure if these are all you need, or if you need them... sorry :( )

The Attempt at a Solution



∆λ=2.43*10^-12 (set theta to 90 because i am dealing with a maximum)

corresponding change in f = c/2.43*10^-12 from above
and since E=hf
∆E=510551 eV which is unfortunatly, larger than the E delivered to the electron... so CLEARLY I've stuffed up... I was planning on being able to say that the energy was 50keV + ∆E so i guess I'm on the wrong track... very wrong... any hints would be very greatly appreciated :!)
 
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  • #2
You are changing an equation like f-f'=c/lambda-c/lambda' into f-f'=c/(lambda-lambda'). This is WRONG! Right?
 

1. What is the Compton Collision process?

The Compton Collision process is a phenomenon in which a photon collides with an electron, resulting in a scattered photon and a recoiling electron. This process was first described by Arthur Compton in 1923 and is an important concept in quantum mechanics.

2. How is the maximum energy of a photon in Compton Collision calculated?

The maximum energy of a photon in Compton Collision is calculated using the equation Emax = Ei / (1 + (Ei/mec2)(1-cosθ)), where Ei is the initial energy of the photon, me is the mass of the electron, c is the speed of light, and θ is the scattering angle.

3. What factors affect the maximum energy of a photon in Compton Collision?

The maximum energy of a photon in Compton Collision is affected by the initial energy of the photon, the mass of the electron, and the scattering angle. The higher the initial energy of the photon, the higher the maximum energy of the scattered photon. The mass of the electron and the scattering angle also play a role in determining the maximum energy.

4. How does Compton Collision demonstrate the wave-particle duality of light?

Compton Collision demonstrates the wave-particle duality of light by showing that light can behave as both a wave and a particle. The photon is considered a particle in this collision process, as it interacts with the electron as a discrete unit. However, the scattered photon also exhibits wave-like properties, such as diffraction and interference, demonstrating the dual nature of light.

5. What are the real-world applications of understanding the maximum energy of a photon in Compton Collision?

Understanding the maximum energy of a photon in Compton Collision is important in fields such as medical imaging, where X-ray imaging involves the scattering of photons off of atoms in the body. It is also relevant in understanding the behavior of high-energy gamma rays in astrophysics and in developing advanced technologies such as particle accelerators.

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