513.001 Molecular and Solid State Physics

Interference of scattered x-rays

Two identical atoms are in the y - z plane and are separated by 3.2 Å. The line connecting the atoms makes an angle of 60° measured from the z - axis. X-rays with a wavelength of 1.54 Å are incident along the z-axis and scatter off the atoms. The amplitude of the electric field componenet of the x-rays is E₀. A detector in the y - z plane can be moved in a circle around the atoms with a radius that is many times the wavelength of the x-rays.

(a) Find one angle (measured from the z-axis) where constructive interference will be observed.

(b) What is the amplitude of the electric field component of a wave scattered at an angle of 35°? Give the amplitude in terms of the amplitude of the unscattered wave E₀.

(c) What is the intensity of the x-rays scattered at an angle of 35°? Give the intensity in terms of the intensity of the unscattered wave I₀.