What Is the Wavelength of the Incident X-ray Photon in Compton Scattering?

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The discussion focuses on calculating the wavelength of an incident X-ray photon in a Compton scattering scenario, where the photon is scattered at an angle of 180° and the electron achieves a speed of 4.67 x 10^6 m/s. The relevant equations include the conservation of energy and momentum, leading to the relationship between the wavelengths before and after scattering. The user attempts to derive the wavelength of the incident photon using algebraic manipulation of the equations but seeks confirmation on their calculations. Key points include the conservation of momentum and the need to correctly apply the equations to find the wavelength. The discussion emphasizes the importance of verifying algebraic steps in physics problem-solving.
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Homework Statement



An X-ray photon is scattered at an angle of θ = 180.0° from an electron that is initially at rest. After scattering, the electron has a speed of 4.67 x 106m/s. Find the wavelength of the incident X-ray photon.

Homework Equations



hc/λ = hc/λ′ + KE

λ′ = λ + h/mc (1-cosθ)


The Attempt at a Solution



Ok, I solved the first equation for λ′and set both equal to each other:


hc/λ = hc/λ′ + KE
λ′= λ + (λ/hc)KE (hopefully my algebra isn't off...could somebody check?:confused:)

λ + (λ/hc)KE = λ + h/mc (1-cosθ) (subtract λ from both sides)

(λ/hc)KE = h/mc (1-cosθ) (multiply both sides 1/KE)

λ/hc = [h/mc (1-cosθ)]/KE (multiply both sides by hc/1)

λ = [h∧2/m(1-cosθ)]/KE

then plug in numbers...
But, do I have it right so far?
 
Physics news on Phys.org
Momentum is conserved, so all the new momentum of the electron came from the photon.
momentum of the electron = m v
momentum of the photon = h f = h c / wavelength.
 

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