Atoms A, B, C are located at fcc, tetrahedral voids and octahedral voids respectively. If 50% of T-voids are occupied, then what is the formula of the compound?

A₄B₄C₄

The correct answer is option 3. A₄B₄C₄.

To determine the formula of the compound with atoms A, B, and C located at fcc, tetrahedral voids, and octahedral voids respectively, and given that 50% of the tetrahedral voids are occupied, let us proceed step by step:

Atoms in FCC Unit Cell: In a face-centered cubic (fcc) lattice, there are 4 atoms per unit cell.

Tetrahedral Voids: The number of tetrahedral voids in an fcc unit cell is twice the number of atoms, so there are \( 2 \times 4 = 8 \) tetrahedral voids. Since 50% of the tetrahedral voids are occupied, the number of occupied tetrahedral voids is \( 0.5 \times 8 = 4 \)

Octahedral Voids: The number of octahedral voids in an fcc unit cell is equal to the number of atoms, so there are 4 octahedral voids.

Composition Calculation:

Atoms A (located at fcc lattice points): There are 4 atoms of A per unit cell.

Atoms B (located in tetrahedral voids): There are 4 atoms of B per unit cell, as 50% of 8 tetrahedral voids are occupied.

Atoms C (located in octahedral voids): There are 4 atoms of C per unit cell.

Formula of the Compound: From the above information, we have:

4 atoms of A, 4 atoms of B, 4 atoms of C

Thus, the formula of the compound is A4B4C4.