A photon of wavelength 0.25 nm is scattered elastically by a stationary electron at an angle of 120°. Find the wavelength of the scattered photon.

medium 3 marks Class 12 · Physics · Dual Nature of Radiation and Matter

Answer

0.254 nm

The correct answer is 0.254 nm — Add to initial wavelength: $l amb d a^{'} = l amb d a + D e l t a l amb d a = 0.25 + 0.003639 = 0.253639,$ nm ≈ $0.254,$ nm.

Step-by-step solution

Use the Compton shift formula: $D e l t a l amb d a = \frac{h}{m _{e} c} (1 - cos θ)$ , where $θ = 12 0^{\circ}$ .
Compute $1 - cos 12 0^{\circ} = 1 - (- \frac{1}{2}) = 1.5$ .
Insert constants: $\frac{h}{m _{e} c} = 2.426 \times 1 0^{- 12},$ m = $0.002426,$ nm.
Calculate $D e l t a l amb d a = 0.002426 \times 1.5 = 0.003639,$ nm.
Add to initial wavelength: $l amb d a^{'} = l amb d a + D e l t a l amb d a = 0.25 + 0.003639 = 0.253639,$ nm ≈ $0.254,$ nm.

Common mistake: Using

s in θ

instead of

(1 - cos θ)

Concept tested: Compton wavelength shift

Published 14 September 2026 · Last updated 16 September 2026 · How this solution was prepared and checked

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