An incident x-ray photon of wavelength 0.0900 nm is scattered in the backward direction from a f

step 1 For this question we have an x -ray coming in with wave length of 0 .09 nanometers and it's scat

An incident x-ray photon of wavelength 0.0900 nm is...

An incident x-ray photon of wavelength 0.0900 $\mathrm{nm}$ is scattered in the backward direction from a free electron that is initially at rest. (a) What is the magnitude of the momentum of the scattered photon? (b) What is the kinetic energy of the electron after the photon is scattered?

Key Concepts

Photon Momentum

Photon momentum is determined by the relation p = h/?, where h is Planck's constant and ? is the wavelength of the photon. This concept is essential for analyzing interactions involving photons, as it provides a measure of the momentum carried by electromagnetic radiation despite its lack of mass.

Compton Scattering

Compton scattering describes the collision process in which a photon scatters off a free or loosely bound electron, resulting in a change in the photon's wavelength. This phenomenon demonstrates the particle-like behavior of light and is analyzed using the principles of momentum and energy conservation.

Conservation of Energy and Momentum

In collision processes such as Compton scattering, both energy and momentum are conserved. Conservation of energy involves equating the total energy before and after the collision, while conservation of momentum involves balancing the vector momenta of the photon and electron. These principles underpin the derivation of quantitative relationships in the scattering process.

Kinetic Energy of Electron

The kinetic energy of the recoiling electron is determined by the energy transferred from the photon during the scattering process. It is calculated by considering the difference between the incident photon's energy and the energy of the scattered photon, reflecting how the electron gains motion as a result of the interaction.

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