Compton shift = [h / (m₀ c)] x [1 - cos (theta)]
where, h = Planck's constant, m₀ = mass of electron, c = velocity of light and theta = scattering angle.

It is not observable in the visible region of electromagnetic spectrum because

Energy of X-rays or gama rays = 1000 eV nearly.
Energy of visible light photon = 2 eV
Energy of ultra-violet photon = 10 eV
Binding energy of electron in an atom = 10 eV
The above data shows that the electrons can be treated as free when X-rays or gama rays are incident but not for visible and ultra-violet radiation..
The Compton shift, in case of X-rays or gama rays is =
[h / (m₀ c)] [1 - cos (theta)] - nearly equal to - h / (m₀ c)
- nearly equal to - 2.43 x 10^-12 m. And this shift of about 2.43 x 10^-12 m in incident wavelength of about 10^-10 m X - rays and gama - rays can be easily measured.

In case of visible or ultra-violet radiation, the shift is nearly 2.43 x 10^-10 m. This much increase in wavelength of about 10^-7 m or more, means resolution resolution of 1 part in 10⁹. This certainly can not be obtained with optical and ultra-violet instruments.

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By :-   Dr. A. W. Pangantiwar