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Sum

In ionic crystalline solid atoms of element Y form hcp lattice. The atoms of element X occupy one-third of tetrahedral voids. What is the formula of the compound?

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#### Solution

**Given:** Atoms of element Y form hcp structure.

Atoms of element X occupy 1/3rd of tetrahedral voids

**To find:** Formula of the compound

**Calculation:** The atoms of element Y form hcp structure.

The number of tetrahedral voids generated is twice the number of Y atoms.

Thus, number of tetrahedral voids = 2Y

The atoms of element X occupy (1/3) of these tetrahedral voids.

Hence, number of X atoms = 2Y × `1/3 = 2/3"Y"`

Ratio of X and Y atoms = `2/3`Y : 1Y = `2/3`: 1 = 2: 3

∴ Formula of compound = X_{2}Y_{3}

Concept: Packing Efficiency

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