Problem 9: A 50 keV X-rays is scattered through an angle of 900. What is the energy of the X-rays after Compton Effect?

Solution

Given Energy of the incident X-rays photon, E_{i} = 50 keV
Scattering angle of photon after collision, θ = 90^{0}
Value of Planck’s constant, h = 6.63 × 10^{-34} J s

Asked: Energy of X-rays photon after collision, E_{f}

The Compton’s equation in terms of frequencies is

Dividing throughout by h and putting cosθ = cos90^{0} = 0, we have from equation (A),

Here f’ is the frequency of photon (X-rays) after collision. Now the rest mass energy of electron is

Converting to eV, using the conversion equation,

We have

Put this and the value of hf = E_{i} = 50 keV in equation (1)

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