A compound is formed by 2 elements P and Q. Atoms of element Q (as anions) makes ccp and those of P (as cations) fill all tertrahedral voids and also occupy half of the octahedral voids. What is the correct formula of this compound?

\(P_5Q_2\)

The correct answer is option 2. \(P_5Q_2\).

Let us break down the process of determining the formula of the compound where elements \( P \) and \( Q \) form a cubic close-packed (ccp) structure:

Cubic Close-Packed (CCP) Structure:

In a cubic close-packed lattice (also known as face-centered cubic or FCC), the atoms are packed in a repeating pattern with each atom surrounded by 12 others.

Tetrahedral Voids: For every atom in a ccp lattice, there are 2 tetrahedral voids.

Octahedral Voids: For every atom in a ccp lattice, there is 1 octahedral void.

Counting Atoms and Voids:

The unit cell of a ccp lattice effectively contains 4 atoms.

In this structure:

Tetrahedral voids: Each unit cell contains \( 2 \times 4 = 8 \) tetrahedral voids.

Octahedral voids: Each unit cell contains 4 octahedral voids.

Given Conditions

Atoms of Q form ccp lattice:

The atoms of Q are arranged in the ccp structure, meaning there are 4 Q atoms per unit cell

Atoms of P fill all tetrahedral voids and half of the octahedral voids:

All the tetrahedral voids are filled by P atoms. Half of the octahedral voids are also filled by P atoms

Detailed Calculation

In a ccp unit cell, there are:

8 tetrahedral voids

4 octahedral voids

Tetrahedral Voids: All 8 tetrahedral voids are filled by P atoms. So, there are 8 P atoms filling tetrahedral voids.

Octahedral Voids: Half of the 4 octahedral voids are filled by P atoms, which means 2 P atoms are filling octahedral voids.

Total P atoms = 8 (from tetrahedral voids) + 2 (from octahedral voids) = 10 P atoms.

Total Q atoms in the unit cell = 4 (as Q forms the ccp lattice)

Total P atoms = 10

The empirical formula would be:

\(\text{Empirical Formula} = P_{10}Q_{4}\)

To simplify this formula, divide the subscripts by their greatest common divisor, which is 2:

\(\frac{P_{10}Q_{4}}{2} = P_{5}Q_{2}\)

Conclusion

The formula of the compound, where the atoms of \( P \) and \( Q \) are arranged according to the given structure and conditions, simplifies to \( P_5Q_2 \). Thus, the correct formula for the compound is (2) \( P_5Q_2 \)