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A crystalline compound is made of elemen...

A crystalline compound is made of elements X and Y. Y atoms form hexagonal close-packed (hcp) structure with X atoms occupying half of the octahedral voids in the structure. Determine the empirical formula of the compound.

Text Solution

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Number of octahedral voids in a hexagonal close-packed (hcp) structure is equal to the number of close-packed atoms. Suppose, numberof Y atoms in hcp structure = n.
So, the number of octahedral voids in the structure = n
Since hlaf of the octahedral voids are occupied by X atoms, the number of X atoms in the hcp array of Y atoms = `n/2`
Therefore, the ratio of number of X and Y atoms in the unit cell of the crystal lattice = `n/2:n=1:2`
Hence, the empirical formula of the compound is `XY_(2)`.
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