Question

X-rays with a wavelength of .16 nm are scattered from a block of carbon. If the scattered radiation is detected at 89 degrees to the incident beam find the wave length of the scattered X-ray. (Part 2) Find the kinetic energy imparted to the recoiling electron.

Answer 1

Assuming the scattering is Compton scattering, the scattered x-ray wavelength is given by:\[\lambda '=\frac{ h }{ m _{e} c}\left( 1-\cos \theta \right)+\lambda \]where h is Planck's constant; me is the mass of an electron; c is the speed of light; θ is the scattering angle; and λ is the incident x-ray wavelength.

The kinetic energy of the scattered electron is just:\[KE=h \nu - h \nu '\]where ν is the incident x-ray frequency and ν' is the scattered x-ray frequency. This of course can be rewritten using:\[c=\lambda \nu \]