  Question

How many lattice points are there in one unit cell of each of the following lattice?(i) Face-centred cubic(ii) Face-centred tetragonal(iii) Body-centred

Solution

(i) Face-centred cubic$$8$$ lattice points at corners and $$6$$ lattice points at face centres are present in face-centred cubic.A corner lattice point contributes one eight to the unit cell and a lattice point at face centre contributes one half to the unit cell.Total number of lattice points per unit cell: $$\displaystyle 8 \times \frac {1}{8} + 6 \times \frac {1}{2} = 1 + 3 = 4$$(ii) Face-centred tetragonal$$8$$ lattice points at corners and $$6$$ lattice points at face centres.A corner lattice point contributes one eight to the unit cell and a lattice point at face centre contributes one half to the unit cell.Total number of lattice points per unit cell: $$\displaystyle 8 \times \frac {1}{8} + 6 \times \frac {1}{2} = 1 + 3 = 4$$(iii) Body-centred$$8$$ lattice points at corners and $$1$$ lattice point at body centre.A corner lattice point contributes one eight to the unit cell and a lattice point at body centre contributes one  to the unit cell.Total number of lattice points per unit cell: $$\displaystyle 8 \times \frac {1}{8} + 1 \times 1 = 1 + 1 = 2$$ChemistryNCERTStandard XII

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