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Formula of a compound in which the element Y forms hcp lattice and atoms of X occupy 2/3 of tetrahedral voids - Chemistry

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What is the formula of a compound in which the element Y forms hcp lattice and atoms of X occupy 2/3rd of tetrahedral voids?

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Solution

Suppose the number of atoms Y in hcp lattice = n

As the number of tetrahedral voids is double the number of atoms in close packing, the number of tetrahedral voids = 2n

As atoms X occupy 2/3rd of the tetrahedral voids, the number of atoms X in the lattice

`2/3xx2n=(4n)/3`

`:. "Ratio of X:Y"=(4n)/3:n=4/3:1=4:3`

Hence, the formula of the compound is X4Y3.

Concept: Close Packed Structures - Formula of a Compound and Number of Voids Filled
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