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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

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Solution

Number of corner atoms per unit cell

= 8 corners atoms ×18 atom per unit cell

=8×18=1 atom

Number of face face centred atoms per unit cell

= 6 face centred atoms ×12 atom per unit cell

6×12=3 atoms

Total number of atoms (lattice point) = 1 + 3 = 4

(ii) As in (i)

No. of lattice points = 4

(iii) In bcc unit cell, number of corner atoms per unit cell

=8 corners×18 per corner atom

=8×18=1 atom

Number of atoms at body centre =1×1 = 1 atom

Total number of atoms (lattice points) = 1 + 1 = 2


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