In a compton scattering experiment, a beam of x-rays of wavelength 0.07 nm scatters of nearly free electrons. the scattered radiation is investigated as a function of the angle theta between it and the primary beam. the scattered radiation
a) a component shifted in wavelength by an amount that decreases as the scattering angle increases.
b) a component shifted in wavelength by an amount that is independent of the scattering angle.
c) a component shifted in wavelength by an amount that is independent of the wavelength of the primary beam.
d) two components with wavelength shifted up and down by an equal amount.
e) no wavelength other than that of the primary beam.

Option (e).

Explanation:

The Compton's equation is:

(1)

where λ': is the wavelength scattered, λ: is the initial wavelength, h: is Planck's  constant, : is the electron rest mass, c: speed of light, Θ: scattering angle (between λ and λ'), and : is a constant known as the Compton wavelength of the electron = 0.00243 nm.          

From equation (1), the scattered radiation is directly proportional to the scattering angle, having the maximum value when Θ=90°:

And the minimum value when Θ=0°:

Hence, the options (a) and (b) are incorrect.

Similarly, we can see from equation (1) that the scattered radiation depends also on the wavelength of the primary beam and no wavelength other than that (since is a constant), so the correct option is (e).  

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