Question

A researcher fires a stream of X-rays with a frequency of 3.50 x 1018 Hz at a target where they undergo Compton scattering. A circular detector is set up to detect X-rays at all possible scattering angles. (a) An X-ray scatters, resulting in the maximum possible wavelength being detected. What is the magnitude of the momentum of the electron scattered during this process? 7.31619e-24 X Your response differs from the correct answer by more than 10%. Double check your calculations. kg m/s (b) An X-ray scatters, resulting in the minimum possible wavelength being detected. What is the magnitude of the momentum of the electron scattered during this process? 1.50e-23X Consider carefully whether the correct answer is exactly zero, or just a very small number. kg·m/s

Answer 1

Frequency of x ray = 3.50 times 10^18 Hz (v) Wave length of x ray = c/v = 3 times 10^8/3.50 times 10^18 = 0.857 times 10^- 10 m a) Compton wave length shifting is given as lambda' = lambda + h/m e c (1 - cos theta) for maximum possible wave length, theta = 180 degree and cos theta = -1 so lambda' = lambda + h/m e c^2 = 0.857 times 10^- 10 + 2 times 2.43 times 10^- 12 m Kinetic energy of electron = energy post by photon so k middot E = h f - h f' = h c/ lambda - h c/ lambda' k middot E = h c (1/ lambda - 1/ lambda') = h c (1/0.857 times 10^- 10 - 1/0.9056 times 10^- 10) = 6.626 times 10^- 34 times 3 times 10^8 times 0.0625 times 10^10