An X-ray photon with a wavelength of 0.240 nm scatters from...

An X-ray photon with a wavelength of 0.240 nm scatters from
a free electron at rest. The scattered photon moves at an angle of
$125^{\circ}$ relative to its incident direction. Find (a) the initial momentum and (b) the final momentum of the photon.

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Key Concepts

Photon Momentum

Photon momentum is a key concept in quantum physics where the momentum of a photon is directly related to its wavelength by the equation p = h/?, with h being Planck's constant. This relationship reflects the dual nature of light, exhibiting both wave-like and particle-like properties, and is fundamental in analyzing phenomena such as scattering and diffraction.

Compton Scattering

Compton scattering is the process in which a photon collides with a free electron, resulting in a change in the photon's wavelength and momentum. The change in wavelength is described by the Compton formula, ?? = (h/(m?c))(1 - cos?), illustrating how momentum and energy are conserved during the interaction and showing how the scattering angle influences the photon's final state.

Momentum Conservation in Particle Collisions

The principle of conservation of momentum plays a critical role in photon-electron interactions, ensuring that the total momentum before and after the collision remains constant. In scattering events, the momentum vectors change direction, and analyzing these changes—often by decomposing the vectors—helps in understanding the dynamics of the collision.

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