In a compound, atoms of element Y form ccp lattice and those of element X occupy 2/3rd of tetrahedral voids. The formula of the compound will be - [AIEEE 2008]a)X2Y3b)X2Yc)X3Y4d)X4Y3Correct answer is 'D'. Can you explain this answer?

Question

Answer

Concept:No. Of tetrahedral voids =2 x no. Of octahedral voids.Let no. Of octahedral voids be N then no. Of tetrahedral voids=2N.
Number of atoms of Y = N = 4
Number of atoms of X = 2/3 × 2N=2/3 × 8=16/3
∴∴ Formula of the compound will be X4Y3
Hence answer is (d)

Answer

Let no of atoms of Y =n therefore no of particles of X=2n(tetrahedral void =2*no of atoms in crystal) As 2/3voids are occupied therefore X=2/3*2n = X4n/3 Yn and we get X4Y3

Answer

Answer

Explanation:
In a compound, atoms of element Y form a ccp (cubic close-packed) lattice. This means that the atoms of element Y are arranged in a face-centered cubic structure, with Y atoms located at each of the corners and face centers of the unit cell.

Formation of tetrahedral voids:
Within this ccp lattice, there are voids or empty spaces present. These voids can be classified into two types: tetrahedral voids and octahedral voids.

In this compound, atoms of element X occupy 2/3rd of the tetrahedral voids. This means that for every 2 tetrahedral voids, 3 atoms of element X are present.

Determination of formula:
To determine the formula of the compound, we need to consider the ratio of atoms of element X to Y in the compound.

Number of tetrahedral voids:
In a ccp lattice, the number of tetrahedral voids is equal to the number of atoms of element Y.

Number of atoms of element X in tetrahedral voids:
Given that atoms of element X occupy 2/3rd of the tetrahedral voids, the number of atoms of element X in the compound is (2/3) * (number of tetrahedral voids).

Number of atoms of element Y in the compound:
Since atoms of element Y form the ccp lattice, the number of atoms of element Y in the compound is equal to the number of tetrahedral voids.

Ratio of atoms:
The ratio of atoms of element X to Y in the compound can be determined by dividing the number of atoms of element X by the number of atoms of element Y.

Simplifying the ratio:
Let's assume that there are 'a' atoms of element X and 'b' atoms of element Y in the compound. Therefore, the ratio of atoms is given by (2/3)*a/b.

To simplify this ratio, we can multiply both the numerator and denominator by 3, yielding 2a/3b.

Final formula:
Since the ratio of atoms is 2a/3b, the formula of the compound will be X2Y3. Therefore, the correct answer is option D.

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