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In a solid compound, atoms of element Y are arranged in a ccp lattice, and atoms of element X fill two-thirds of the tetrahedral voids. What is the empirical formula of the compound?

1. X4Y3
2. X2Y3
3. X2Y
4. X3Y4

Correct answer: X4Y3

Solution

In a cubic close-packed (ccp) lattice, there are 4 atoms of Y per unit cell. Since two-thirds of the tetrahedral voids are filled by X, and there are 8 tetrahedral voids in a ccp structure, this results in approximately 5.33 atoms of X. The simplest ratio of X to Y, when reduced, gives the empirical formula X4Y3.

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