Answer: 
Explanation:
The Compton Shift 
in wavelength when the photons are scattered is given by the following equation:
(1)
Where:
is a constant whose value is given by 
, being 
the Planck constant, 
the mass of the electron and 
the speed of light in vacuum.
the angle between incident phhoton and the scatered photon.
We are told the maximum Compton shift in wavelength occurs when a photon isscattered through 
:
(2)
(3)
Now, let's find the angle that will produce a fourth of this maximum value found in (3):
(4)
(5)
If we want 
, 
must be equal to 1:
(6)
Finding 
:
Finally:
This is the scattering angle that will produce 
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