Question

Light of wavelength 1.7x10^-11m undergoes Compton scattering. What
is the kinetic energy, momentum magnitude, speed, and de Broglie wave-
length of the electron which is emitted when the light scatters through an
angle of 90degrees?

Answer 1

Compton scattering : $\lambda_f = \lambda_i + \frac{h}{m_o c} (1 - \cos \theta)$

$\Rightarrow \lambda_f = 1.7* 10^{-11} + \frac{6.626 * 10^{-34}}{9.1 * 10^{-31} * 3* 10^8} (1 - \cos 90^o) =1.943 * 10^{-11} m$

Kinetic Energy, $K = \frac{h^2}{2 \lambda^2 m} = \frac{(6.626*10^{*-34})^2}{2 * (1.943 * 10^{-11})^2 * 9.1 * 10^{-31} } = 6.39 * 10^{-16} J$

Momentum, $p = \frac{h}{\lambda} = \frac{6.626 * 10^{-34}}{1.943 * 10^{-11}} = 3.41 * 10^{-23} kgm/s$

Speed,

р = 3.41 * 10- 9.1 * 10-31 = 3.75 * 10 m/s

de Broglie Wavelength, $\lambda_f = 1.943 * 10^{-11} m$