A solid crystal is composed of X, Y and Z atoms. Y atoms are occupying 50% of octahedral voids, whereas X atoms are occupying the 100% tetrahedral void with Z atoms present in the ccp array arrangement, then the formula of the compound in the given crystal is

X_{4} Y Z_{2}

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X_{5} Y_{10} Z_{8}

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X_{3} Y Z_{2}

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X Y_{4} Z_{2}

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Solution

The correct option is A $X_{4} Y Z_{2}$
Total number of atoms in ccp is 4. Number of octahedral voids is 4 and tetrahedral voids is 8.

Given,
Y occupies 50 % of the octahedral voids and hence the number of atoms is 2.
X ocupies 100 % of the tetrahedral voids and hence the number of atoms is 8.
Z occupies the ccp position and hence the number of atoms is 4

X: Y : Z = 8:2:4 = 4:1:2

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