Question Detail
Question
The wavelength of Compton scattered photons is measured at θ = 90°. If Δλ/λ is to be 1%, what should the wavelength of the incident photons be?
Correct Answer
Option C is the correct answer.
Detailed Explanation
The Compton shift at θ = 90° is Δλ = h/mc = 2.426 × 10⁻¹² m. If Δλ/λ = 0.01, then λ = Δλ/0.01 = 2.426e-12 / 0.01 = 2.426 × 10⁻¹⁰ m = 0.2426 nm = 242.6 pm. None of the options match. If Δλ/λ = 1%, λ = 100 × Δλ = 100 × 2.426e-12 = 2.426e-10 m = 0.2426 nm. Not in options. If the question is asking for the wavelength for which Δλ/λ = 0.01, then λ = 2.426e-10 m = 0.2426 nm. The closest is 24.2 nm, which is 100 times larger. There might be a misprint.
Hint
Use the Compton shift formula: Δλ = (h/mc)(1 - cos θ).