An incident photon of wavelength 0.0100 nm is Compton scattered; the scattered photon has a wav

step 1 In this exercise, we have an incident photon, incident on an electron, and it scatters off this

An incident photon of wavelength 0.0100 nm is Compton...

An incident photon of wavelength $0.0100 \mathrm{~nm}$ is Compton scattered; the scattered photon has a wavelength of $0.0124 \mathrm{~nm}$. What is the change in kinetic energy of the electron that scattered the photon?

Key Concepts

Conservation of Energy in Photon-Electron Collisions

This principle states that the total energy before and after a collision remains constant. In the context of Compton scattering, the decrease in a photon's energy (due to an increase in its wavelength) is exactly compensated by an increase in the kinetic energy of the electron. Applying energy conservation allows one to calculate the kinetic energy imparted to the electron by determining the difference between the energies of the incident and scattered photons.

Photon Energy-Wavelength Relationship

This concept refers to the fundamental connection between a photon's energy and its wavelength, given by the equation E = hc/?, where h is Planck's constant and c is the speed of light. In scattering processes like the Compton effect, a change in wavelength directly corresponds to a change in energy. This relationship is essential for determining how much energy is exchanged during interactions between photons and electrons.

Compton Scattering

This concept describes the inelastic scattering of a photon by an electron. When a photon collides with an electron, a portion of the photon’s energy is transferred to the electron, causing a shift in the photon’s wavelength. The phenomenon is indicative of the particle nature of light and is quantitatively explained by the Compton formula, which relates the change in the photon’s wavelength to the scattering angle and fundamental constants.

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