A x.ray photon of wavelength 1.82 exponent-10m is scattered at angle θ.if fractional change in wavelength is 2% then what is value of scattering angle?



A x.ray photon of wavelength 1.82 exponent-10m is scattered at angle θ.if fractional change in wavelength is 2% then what is value of scattering angle?

Data:
λ = 1.82 x 10 -10 m
Δ λ / λ = 2%
θ = ?

Solution:
According to Compton’s Shift we can write as
Δ λ =(h / mo c) ( 1- Cos θ) ----------(1)
Finding Δ λ
Δ λ = 2 % x  λ
Δ λ = 2 /100 x 1.82 x 10 -10 =   3.64 x 10 -12   m
Now using equation (1)
 1- Cos θ = Δ λ x mo c /h
or
Cos θ = 1- (Δ λ x mo c /h) = 1 – (3.64 x 10 -12  x 3 x 10 8 x 9.1 x 10 -31 / 6.63 x 10 -34)=-0.4988
Or
θ=Cos-1 (-0.4988) =120 0 Answer

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