Physic Labs

Problem 3

A photon of wavelength λ\lambda is backscattered through 180° by a free electron initially at rest. Given electron mass mem_e, Planck's constant hh, and light speed cc, find the scattered wavelength, the energy transferred to the electron, and the condition for the electron kinetic energy to equal the incident photon energy. Model each stage with the appropriate conservation law or equation of motion; quantities stated as constant remain fixed during that stage. (a) Establish the governing physical relation for each stage. (b) Determine the requested observables from the stated initial conditions and constraints. (c) Check signs, dimensions, and the physical limiting behavior of the results.
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Eγ=hcλ,Eγ′=hcλ′,Ke=hc(1λ−1λ′)E_\gamma=\frac{hc}{\lambda},\quad E'_\gamma=\frac{hc}{\lambda'},\quad K_e=hc\left(\frac1\lambda-\frac1{\lambda'}\right)
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Energy conservation says the electron receives the photon's energy loss: Ke=Eγ−Eγ′K_e=E_\gamma-E'_\gamma. This follows from the chosen physical model and the stated initial conditions; the sign convention must remain consistent throughout. A dimensional check catches algebraic errors before the result is interpreted.