(Solved): Question 1: X-ray Diffraction \( x \)-ray diffraction is a method used to identify different types ...

Question 1: X-ray Diffraction \( x \)-ray diffraction is a method used to identify different types of materials. While this is usually quite a complex process, however for a simple cubic structure, as seen below, we can find the distance between neighboring atoms. The below image shows the diffraction of \( x \)-rays passing through a cubic structure and illustrates a change in distance of \( 2 d \sin \theta \) If the wavelength of the \( x \)-ray is equal to an integer multiple of this change in distance, we will get constructive interference: \[ m \lambda=2 d \sin \theta \] X-rays of wavelength \( 0.103 \mathrm{~nm} \) reflects off a crystal and a second-order maximum is recorded at a Bragg angle of \( 25.5^{\circ} \). (a) What is the spacing between the scattering planes in this crystal? (b) At what angle will the third-order maximum occur?