<h2>
Answer: 37.937 keV</h2>
Explanation:
<u>Photons have momentum</u>, this was proved by he American physicist Arthur H. Compton after his experiments related to the <u>scattering of photons from electrons</u> (Compton Effect or Compton Shift). In addition, energy and momentum are conserved in the process.
In this context, the Compton Shift  in wavelength when the photons are scattered is given by the following equation:
 in wavelength when the photons are scattered is given by the following equation:
 (1)
     (1)
Where:
 is a constant whose value is given by
 is a constant whose value is given by  , being
, being  the Planck constant,
 the Planck constant,  the mass of the electron and
 the mass of the electron and  the speed of light in vacuum.
 the speed of light in vacuum.
 the angle between incident phhoton and the scatered photon.
 the angle between incident phhoton and the scatered photon.
We are told the scattered X-rays (photons) are detected at  :
:
 (2)
   (2)
 (3)
   (3)
Now, the initial energy  of the photon is given by:
 of the photon is given by:
   (4)
    (4)
From this equation (4) we can find the value of  :
:
 (5)
    (5)
 
    
 (6)
    (6)
Knowing the value of  and
 and  , let's find
, let's find  :
:
 
 
Then:
 (7)
  (7)
 
  
 (8)
  (8)
Knowing the wavelength of the scattered photon  , we can find its energy
  , we can find its energy  :
 :
  (9)
    (9)
  
    
  (10) This is the energy of the scattered photon
    (10) This is the energy of the scattered photon
So, if we want to know the energy of the recoiling electron  , we have to calculate all the energy lost by the photon, which is:
, we have to calculate all the energy lost by the photon, which is:
 (11)
   (11)
 
   
Finally we obtain the energy of the recoiling electron:
