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  •   A photon of wavelength is scattered from an electron, which was at rest.  The wavelengt

  A photon of wavelength \lambda is scattered from an electron, which was at rest.  The wavelength shift \Delta \lambda is three times of \lambda and the angle of scattering \theta is 600. The angle at which the electron recoiled is \phi.  The value of tan \phi is :

(electron speed is much smaller than the speed of light)

Option: 1

0.16


Option: 2

0.22


Option: 3

0.25


Option: 4

0.28


Answers (1)

best_answer

\Delta \lambda =\lambda _{f}-\lambda _{i}

\therefore \lambda _{f}=4\lambda

Conservation of momentum along x- axis give

p \cos \phi +\left ( \frac{h }{4\lambda } \right ).\cos 60=\frac{h}{\lambda }

or

p \cos \phi =\frac{h}{\lambda }-\frac{h}{8\lambda }=\frac{7\lambda }{8\lambda } -------------------(1)

Conservation of momentum along y axis

\Rightarrow p \sin \phi =(\frac{h}{4\lambda }).\sin60=\frac{\sqrt{3}\lambda }{8\lambda } ----------------(2)

Divide (1) and (2)

\Rightarrow \tan \phi=\frac{\sqrt{3}}{7}\simeq 0.25

 

 

 

 

 

 

Posted by

avinash.dongre

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