X-rays of wavelength 0.071 nm scatter from electrons at 90°. (a) Calculate the wavelength shift. (b) Find the scattered wavelength and the energy lost by the photon. (c) What is the shift for backscattering (θ = 180°)? Solution: (a) Δλ = (h/mc)(1 − cos 90°) = 2.43×10⁻³ nm × (1 − 0) = 0.00243 nm. (b) λ′ = 0.071 + 0.00243 = 0.07343 nm. Photon energy lost: ΔE = hc(1/λ − 1/λ′) = 1240 × (1/0.071 − 1/0.07343) eV·nm/nm ≈ 1240 × (14.085 − 13.618) ≈ 579 eV — this energy goes to the recoiling electron. (c) Δλ = 2.43×10⁻³ × (1 − cos 180°) = 2.43×10⁻³ × 2 = 0.00486 nm — maximum shift.