Physic Labs

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.
pe2c2=Ei2+Ef2−2EiEfcos⁡θ=(Ei−Ef)2+2mec2(Ei−Ef)p_e^2c^2=E_i^2+E_f^2-2E_iE_f\cos\theta=(E_i-E_f)^2+2m_ec^2(E_i-E_f)
problems.proof.analysis

Substitute the intermediate result into the expression for the requested observable. Keeping parameters symbolic until this step makes dependencies clear and avoids premature rounding.