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