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JEE MainChemistrySolid State

A crystal system is characterised by the axial parameters a b c and = = = 90^ . The sum of the effective number of atoms ( Z ) present in one unit cell of each of the allowed Bravais lattices for this crystal system is ____.

Correct answer

9

Step-by-step solution

The given axial parameters ( a b c and = = = 90^ ) correspond to the Orthorhombic crystal system. The Orthorhombic system exhibits all four types of Bravais lattices. The effective number of atoms ( Z ) for each type is: 1. Primitive unit cell: Z = 8 1 8 = 1 2. Body-centred unit cell: Z = 8 1 8 + 1 = 2 3. Face-centred unit cell: Z = 8 1 8 + 6 1 2 = 4 4. End-centred unit cell: Z = 8 1 8 + 2 1 2 = 2 The sum of the effective number of atoms is 1 + 2 + 4 + 2 = 9 . Answer: 9

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