a-Mn has a cubic structure with a = 0.8931 nm and a density of 7.47 g/cm³. B-Mn has a different cubic structure, with a = 0.6326 nm and a density of 7.26 g/cm³. The atomic weight of manganese is 54.938 g/mol and the atomic radius is 0.112 nm. Determine the number of atoms in each unit cell for a-Mn and B-Mn.

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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.