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Number of crystal systems from the following where body centred unit cell can be found, is ______.
Cubic, tetragonal, orthorhombic, hexagonal, rhombohedral, monoclinic, triclinic
Correct Answer: 3
We need to determine how many of the seven crystal systems can have a body-centred unit cell. The seven crystal systems are Cubic, Tetragonal, Orthorhombic, Hexagonal, Rhombohedral (Trigonal), Monoclinic, and Triclinic.
A body-centred unit cell has lattice points at the corners and one lattice point at the centre of the unit cell. In the Cubic system, a body-centred cubic (BCC) structure exists. In the Tetragonal system, a body-centred tetragonal structure exists. In the Orthorhombic system, a body-centred orthorhombic structure exists.
However, in the Hexagonal system only the simple (primitive) hexagonal structure exists, so no body-centred form is possible. Similarly, in the Rhombohedral system only the primitive rhombohedral structure exists, and in the Monoclinic system only simple and end-centred (base-centred) monoclinic structures exist—both without any body-centred form. Finally, in the Triclinic system only the primitive triclinic structure exists, and it has no body-centred form either.
Therefore, the crystal systems that allow body-centred unit cells are Cubic, Tetragonal, and Orthorhombic, giving a total of $$3$$.
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