Module 5 : MODERN PHYSICS
Lecture 25 : Derivation of Compton's Formula
Example 12
  A photon of frequency $ \nu_0$ scatters from an electron at rest and moves in a direction making an angle of 60 $ ^\circ$ with the incident direction. If the frequency of scattered photon is half that of incident photon, calculate the frequency of the incident photon.
  Solution
 
Since frequency is halved, wavelength is doubled. Thus change in wavelength $ \lambda-\lambda_0$ is equal to $ \lambda_0$. Using Compton's formula
 
$\displaystyle \lambda_0 = 2.4\times 10^{-12}(1-\cos 60^\circ)= 1.2\times 10^{-12}\ \ {\rm m}$
 
The corresponding frequency is $ \nu_0 = c/\lambda_0 = 2.5\times 10^{20}$ Hz., which is a gamma ray photon.
 

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