In Compton scattering, what is the maximum possible wavelength shift (Compton shift delta lambda) when a photon collides with a free stationary electron?
Answer and explanation
Correct answer: D. 2 h / (m_e c) (approx. 0.0485 Angstroms at scattering angle 180°)
- Step 1: Compton shift formula: delta lambda = (h / (m_e c)) (1 - cos(theta)). Step 2. Maximum shift occurs when (1 - cos theta) is maximized. Step 3. cos(theta) has minimum value -1 at backscattering theta = 180°. Step 4. delta lambda_max = (h / (m_e c)) (1 - (-1)) = 2 h / (m_e c) = 2 0.02426 A = 0.0485 A. Answer: 2 h / (m_e c) (approx. 0.0485 Angstroms at scattering angle 180°). Why not the others: h/(m_ec) is the shift at 90 degrees.
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