Modern Physics

Olympiad (NSEP) level, single correct, hard

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Question 4 of 5

In the Compton scattering of an X-ray photon of wavelength λ\lambda by a free stationary electron, the maximum fractional increase in wavelength Δλλ\frac{\Delta\lambda}{\lambda} occurs at scattering angle θ=180∘\theta = 180^\circ and equals:

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Answer: (A) 2hmecλ\frac{2 h}{m_e c \lambda}

Δλ=hmec(1−cos⁡θ)\Delta\lambda = \frac{h}{m_e c} (1 - \cos\theta). At θ=180∘\theta = 180^\circ, cos⁡180∘=−1  ⟹  Δλ=2hmec\cos 180^\circ = -1 \implies \Delta\lambda = \frac{2h}{m_e c}, so fractional shift is 2hmecλ\frac{2h}{m_e c \lambda}.
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