The structure of Fluorite, whose chemical formula is CaF2, can be described as cations Ca2+ arranged in FCC lattice and anions F- sited in the tetrahedral interstitial sites. It is known that the theoretical density of fluorite is equal to 3.18 g/cm3. Draw the unit cell of fluorite and highlight in the unit cell the crystallographic planes (200) and (040), reporting also the intersection between planes and unit cell and calculating the number of anions per unit area in those crystallographic planes. Calculate the Bragg angle 2 for the planes (111), (200) and (040) with diffraction analysis using a X-ray with = 0.1541 nm.