A gamma-ray photon scatters off a free proton (initially at...

A gamma-ray photon scatters off a free proton (initially at rest) at an angle of $45^{\circ} .$ The wavelength of the scattered light is measured to be $6.20 \times 10^{-13} \mathrm{~m}$. (a) What was the energy of the incoming photon? (b) How much kinetic energy did the proton receive? (You may need to carry an extra figure or two in your intermediate answers.)

Key Concepts

Compton Scattering

Compton scattering is the interaction in which a photon collides with a particle, typically a charged particle like an electron or proton, resulting in a change in the photon’s wavelength and a transfer of energy and momentum to the particle. This phenomenon is a cornerstone of quantum mechanics, illustrating the dual wave-particle nature of light and providing insight into how photons interact with matter.

Energy-Wavelength Relationship

This concept refers to the fundamental relationship between the energy of a photon and its wavelength, expressed by the equation E = hc/?, where h is Planck’s constant and c is the speed of light. In scattering processes, this relationship is vital for converting measured wavelengths into corresponding energies.

Conservation of Energy

Conservation of energy is a fundamental principle in physics stating that the total energy in an isolated system remains constant. In the context of photon scattering, the energy initially carried by the photon is redistributed between the scattered photon and the kinetic energy acquired by the target particle, allowing calculations for the energy changes involved in the process.

Conservation of Momentum

In scattering interactions, the law of conservation of momentum asserts that the total momentum of the system before the collision equals the total momentum after the collision. This principle is essential for analyzing the momentum exchange between the photon and the target particle and is used in conjunction with energy conservation to determine the outcomes of scattering events.

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