Given :-
lamda (wavelength of incident photon) = 0.3 A⁰ = 0.3 x 10^-10m.
Scattering angle, theta = 45⁰

We know that, Compton shift = [h / (m₀c)] [1 - cos (theta)]
So, wavelength of scattered photon = lamda + [h / (m₀c)] [1 - cos (theta)]
i.e. wavelength of scattered photon = 0.3 x 10^-10m + [(6.6 x 10^-34 j.s) {1 - cos (theta)}] / [(9.1 x 10^-31 kg) (3 x 10⁸ m/s)]
i.e. wavelength of scattered photon = 0.3 x 10^-10m + [(6.6 x 10^-34 j.s) {1 - cos (45⁰)}] / [(9.1 x 10^-31 kg) (3 x 10⁸ m/s)]
i.e. wavelength of scattered photon = 0.3 x 10^-10m + 0.0071 x 10^-10m
i.e. wavelength of scattered photon = 0.3071 x 10^-10m = 0.3071 A⁰

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By :-   Dr. A. W. Pangantiwar