1) Explain how X-ray diffraction arises from the scattering of X-rays in a crystal. 2) Derive the Bragg scattering equation. 3) Outline how cubic crystals may be used to measure the wavelength of X-rays. 4) Outline how X-rays may be used to determine the structure of crystals. 1) X-ray diffraction can be seen by directing X-rays at a regular arrangement of atoms in a crystal. From this, an interference pattern can be observed that is similar to the diffraction of light by diffraction grating.
2) nλ = AB + BC AB = BC nλ = 2AB AB sin θ = d AB = d sin θ nλ = 2d sin θ 3) In X-ray diffraction, the interatomic distances in the crystal are of the same magnitude as the wavelength of X-ray. This property enables the crystal to function as the slits in the diffraction grating with visible light. After measuring the lattice plane distances with x-rays of a specific wavelength, and by using cubic crystals of a known lattice plane distance, the wavelengths of x-rays can be measured. 4) X-ray crystallography can be used from Bragg’s law in which X-rays of known wavelengths are used to explore the crystal structure of different elements and compounds. In this method, crystalline atoms cause a beam of X-rays to diffract into many specific directions. By measuring the angles and intensities of these refracted beams, a crystallographer can calculate the density of electrons within the crystal. From this method, chemical bonds of the crystal will be known.