Module 5 : MODERN PHYSICS
Lecture 25 : Reason for the unshifted peak in the spectrum
  Example 11
A photon of wavelength 6000 nm collides with an electron at rest. After scattering, the wavelength of the scattered photon is found to change by exactly one Compton wavelength. Calculate (i) the angle by which the photon is scattered, (ii) the angle by which the electron is scattered and (iii) the change in the energy of the electron due to scattering.
  Solution :
Since the change in wavelength is one Compton wavelength, $ (1-\cos\theta) =1$, i.e. $ \theta = 90^\circ$. Thus the
  photon is scattered at right angles to the incident direction.
Initial momentum of the photon is
 
$\displaystyle \frac{h\nu_0}{c} = \frac{h}{\lambda_0} = \frac{6.63\times 10^{-34}} {6\times 10^{-12}}= 1.105\times 10^{-22}\ \ {\rm kg m/s\ \ along}\ \hat \imath$
  The final momentum of the photon is
 

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