Physic Labs

Problem 3

A photon of wavelength λ\lambda scatters from an initially stationary electron; the scattered photon makes angle θ\theta with the incident direction. Find the wavelength shift Δλ\Delta\lambda and recoil-electron kinetic energy. Use electron mass mem_e, speed of light cc, and Planck constant hh. (a) Combine energy and momentum conservation with the electron’s relativistic relation to derive Compton shift Δλ\Delta\lambda. (b) Find the photon energy loss and identify it with recoil-electron kinetic energy. (c) Evaluate forward scattering θ=0\theta=0 and backscattering θ=π\theta=\pi, and state which gives the greatest recoil.
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p⃗γ=p⃗γ′+p⃗e\vec p_\gamma=\vec p_\gamma\prime+\vec p_e
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The photon momentum vectors enclose angle θ\theta, so recoil momentum is their vector difference. Squaring introduces −2pp′cos⁡θ-2pp\prime\cos\theta, the source of angular dependence.