A compound formed by elements X, Y, Z . Atoms of Y forms ccp lattice and X occupies half the octahedral voids and Z occupies half the tetrahedral voids. Find the formula of the compound?

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Solution

Let, the number of close packed spheres be N,
then:
The number of octahedral voids generated = N
The number of tetrahedral voids generated = 2N
Number of atoms of Y = N = 4
Number of atoms of X =1/2×N
=1/2×4
=2
Number of atoms of Z = 1/2 $\times$ 2N
=1/2×8
=4
The formula of the compound is $X_{2} Y_{4} Z_{4}$
Also can be written as $X Y_{2} Z_{2}$ .

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