X-rays with an energy of 265 kev undergo compton scattering from a target. if the scattered rays are deflected at 41.0° relative to the direction of the incident rays, find each of the following. (a) the compton shift at this angle (b) the energy of the scattered x-ray (c) the kinetic energy of the recoiling electron

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 scattered X-rays (photons) are deflected at :

  (2)

  (3)

But we are asked to express this in , so:

 (4)

The initial energy of the photon is given by:

     (5)

From this equation (5) we can find the value of :

   (6)

   (7)

Knowing the value of and , let's find :

Then:

 (8)

 (9)

Knowing the wavelength of the scattered photon  , we can find its energy :

   (10)

   (11) This is the energy of the scattered photon

If we want to know the kinetic energy of the recoiling electron , we have to calculate all the energy lost by the photon in the wavelength shift, which is:

 (12)

Finally we obtain the kinetic energy of the recoiling electron:

frequency or wavelenth of em radiation in a vacuum