Question

In a particular case of Compton scattering, a photon collides with a free electron and scatters backwards. The wavelength after the collision is exactly double the wavelength before the collision. What is the wavelength of the incident photon?

Answer 1

Answer:

hence initial wavelength is $\lambda =4.86\times10^{-12}m$

Explanation:

shift in wavelength due to compton effect is given by

$\lambda ^{'}-\lambda =\frac{h}{m_{e}c}\times(1-cos\theta )$

λ' = the wavelength after scattering

λ= initial wave length

h= planks constant

m_{e}= electron rest mass

c= speed of light

θ= scattering angle = 180°

compton wavelength is

$\frac{h}{m_{e}c}= 2.43\times10^{-12}m$

$\lambda '-\lambda =2.43\times10^{-12}\times(1-cos\theta )$

$\lambda '-\lambda =2.43\times10^{-12}\times(1+1 )$  ( put cos 180°=-1)

also given λ'=2λ

putting values and solving we get

$\lambda =4.86\times10^{-12}m$

hence initial wavelength is $\lambda =4.86\times10^{-12}m$