A photon of wavelength 3.7 nm Compton scatters from an electron at an angle of 90°. What is the modified wavelength? (Enter your answer correct to 5 significant figures.)

3.70242 nm

Explanation:

Using Compton effect formula

Δλ = ( h / mec) ( 1 - cosθ)

where h is planck constant = 6.62607 × 10 ⁻³⁴ m²kg/s

me, mass of an electron = 9.11 × 10⁻³¹ kg

c is the speed of light = 3 × 10⁸ m/s

Δλ = 6.62607 × 10 ⁻³⁴ m²kg/s / (9.11 × 10⁻³¹ kg × 3 × 10⁸ m/s ) ( 1 - cos 90°) =   0.242 × 10 ⁻¹¹ m = 2.42 × 10⁻¹² m  = 0.00242 nm

modified wavelength = 3.7 nm + 0.00242 nm = 3.70242 nm

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