A metal X has an atomic radius of 0.126 nm. If the density and molar mass of X are 7.87 g cm3 and 55.85 g mol1, respectively. (a) (i) Determine the number of atoms per unit cell and the crystal structure of metal X. (ii) Determine the volume of the unit cell. (ii) Determine its planar density in [100], [110] and [111] directions.

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Crystal Lattices and Unit Cell

Consider a crystal. The regular and repeating pattern of constituent particles is the most distinguishing feature of crystalline solids. A crystal lattice is formed when these particles are replaced with representative points. The three-dimensional arrangement of constituent particles is known as a crystal lattice. Unit cell is that the smallest portion of a space lattice which when repeated in several directions, generate the whole lattice. Unit cell is a building block of a lattice. It is the smallest unit of cell.