Atoms of element X forms fcc lattice and those of the element Y occupy...
Number of atoms of X per unit cell = 4
Number of atoms Y per unit cell = (1/3) x 8
(∵ Number of tetrahedral voids = 2 x N)
Hence, Formula of the compound is X
3, Y
2
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Atoms of element X forms fcc lattice and those of the element Y occupy...
Given information:
- Atoms of element X form fcc lattice
- Atoms of element Y occupy 1/3rd of the tetrahedral voids
To determine the formula of the compound formed between X and Y, we need to consider the ratio of X and Y atoms in the crystal lattice.
Explanation:
1. The fcc lattice consists of 4 atoms per unit cell. Each corner atom is shared by 8 unit cells, while each face-centered atom is shared by 2 unit cells. So, the total number of atoms in one unit cell can be calculated as:
Number of atoms = (8 × 1/8) + (6 × 1/2) = 4
2. The tetrahedral voids in an fcc lattice are located at the center of each tetrahedron formed by 4 atoms. The number of tetrahedral voids per unit cell can be calculated as:
Number of tetrahedral voids = 2 × Number of atoms
= 2 × 4 = 8
3. Since the atoms of element Y occupy 1/3rd of the tetrahedral voids, the number of Y atoms per unit cell can be calculated as:
Number of Y atoms = 1/3 × Number of tetrahedral voids
= 1/3 × 8 = 2.67 ≈ 3
4. The remaining voids are occupied by atoms of element X. Since each tetrahedral void is surrounded by 4 atoms, the number of X atoms per unit cell can be calculated as:
Number of X atoms = 4 - Number of Y atoms
= 4 - 3 = 1
5. Therefore, the ratio of X and Y atoms in the compound is X:Y = 1:3. The formula of the compound can be written as X3Y2, which is option B.
Conclusion:
The formula of the compound formed between element X and Y, where X atoms form an fcc lattice and Y atoms occupy 1/3rd of the tetrahedral voids, is X3Y2.
Atoms of element X forms fcc lattice and those of the element Y occupy...
See for fcc z=4 .tetrahedral voids is 2×4.but in question they asked 1/3×8 then u will get answer
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