Answer:
2.07 pm
Explanation:
The problem given here is the very well known Compton effect which is expressed as
here, is the initial photon wavelength,
is the scattered photon wavelength, h is he Planck's constant,
is the free electron mass, c is the velocity of light,
is the angle of scattering.
Given that, the scattering angle is,
Putting the respective values, we get
Here, the photon's incident wavelength is
Therefore,
From the conservation of momentum,
where, is the initial photon momentum,
is the final photon momentum and
is the scattered electron momentum.
Expanding the vector sum, we get
Now expressing the momentum in terms of De-Broglie wavelength
and putting it in the above equation we get,
Therefore,
This is the de Broglie wavelength of the electron after scattering.