Question

A photon of wavelength 4 Å strikes an electron at rest and is scattered at an angle of 150° to its original direction. Find the wavelength of the photon after collision.​

Answer 1

Photon has the speed of light(c) in vacuum.

Speed of light(c)=$3\times 10^{8} \frac{m}{s}$

The wavelength can be obtained by using the COMPTON effect.$\lambda'=\lambda+\frac{h}{mc} (1-cos\theta)$

Here, $h=planck's\ constant(6.63\times 10^{-34} J-s)\\m=mass\ of\ electron(9.1\times 10^{-31} kg)\\c=speed \ of \ light(3\times 10^{8} )$

Given $\lambda=4\times 10^{-10} \\\theta=150 \textdegree$

Wavelength=$4\times 10^{-10} m+\frac{6.63\times 10^{-34}J-s }{(9.1\times 10^{-31}kg)(3\times 10^{8} m/s) }(1-cos150\textdegree)=0.4045\times 10^{-9}$

Hence, the wavelength of the photon after the collision is 0.4045nm.