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In: Physics

A photon of wavelength 0.65037 nm strikes a free electron that is initially at rest. The...

A photon of wavelength 0.65037 nm strikes a free electron that is initially at rest. The photon is scattered straight backward. What is the speed of the recoil electron after the collision?

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Expert Solution

When a gamma ray photon collides with an electron, Compton scattering occurs. Compton scattering is a type of elastic scattering that results in a change in the photon's wavelength called a Compton shift sure to its transfer of energy and momentum to the electron. The Compton shift depends entirely on the scattering angle, so a photon scattered in a given direction will always have the same change in its wavelength.

In Compton scattering, the change in the wavelength of the incident photon depends only on the scattering angle

where is the Compton wavelength for an electron.

This means that the final wavelength of the photon is,

  

= 6.98896 × 10-11 m

where there angle is 180° since the photon scattered backwards and the wavelength of the photon is given.

By the conservation of energy, because Compton scattering is elastic, the energy lost by the photon is gained by the electron.

   J

= 2.16 × 107 m/s

genius_generous answered 1 day ago
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