Answer to Question #139374 in Quantum Mechanics for Nadia

Question

A photon with wavelength 0.1385 nm scatters from an electron that is initially at rest. What must be the angle between the direction of propagation of the incident and scattered photons if the speed of the electron immediately after the collision is 8.90×10^6 m/s?

Answer 1

Solution

Here compton scattering in happening.

$\lambda'-\lambda=\frac{h(1-\cos \theta) }{mc}$ ................... eq1

Therefore for electron

$\lambda'=1.42\times 10^{-10}m$

Here given $\lambda=1.38\times 10^{-10}m$

$\lambda'-\lambda=0.06\times 10^{-10}m$

$\frac{mc}{h}=4.1\times10^{11}m^{-1}$

Therefore angle is given by using equation 1

$\theta=\arccos(1-\frac{mc(\lambda'-\lambda)}{h})$

$\theta=\arccos(1-1.442)$

$\theta=\arccos(-0.442)$

$\theta=116^°$