Problem 3
A photon of wavelength λ Compton-scatters from a free electron at rest; the scattered direction is at angle θ. Find final wavelength and maximum shift; electron mass mₑ. Use the stated ideal model: quantities are constant or vary only as specified, with no extra drag, losses, or external influences. State a sign convention, keep units consistent, and use a classical approximation only where appropriate. (a) Set up the governing equation from a fundamental law. (b) Solve for the requested quantity under the stated conditions. (c) Check the result using a suitable limit, sign, or unit test, and report both the expression and its physical meaning.Let E_i,E_f be the photon energies before and after scattering and p_i,p_f their momentum magnitudes; E_e,p_e are the scattered electron’s total energy and momentum magnitude.
problems.proof.stepOf
problems.proof.analysis
Solve the relation for the unknown while preserving algebraic signs and physical restrictions. Use any stated geometry or definition to express the result in the given data.
problems.proof.pitfall. Use the relativistic energy-momentum relation for the electron; do not use K=p²/(2m) for a high-energy photon collision.