A compound is formed by two elements \(P\) and \(Q\). The element \(Q\) forms ccp and atoms \(P\) occupy \(1/3 \)rd of tetrahedral voids. What is the formula of the compound?
Answer & explanation
Correct answer: option 1
The correct answer is option 1. \(P_2Q_3\).
To determine the formula of the compound, we need to analyze the given information:
Element \(Q\) forms a ccp (cubic close-packed) structure.
In a ccp structure, there are 4 atoms of \(Q\) per unit cell.
Element \(P\) occupies \(\frac{1}{3}\)rd of the tetrahedral voids.
In a ccp structure, the number of tetrahedral voids is twice the number of atoms in the unit cell. Hence, there are \(2 \times 4 = 8\) tetrahedral voids per unit cell.
Since \(P\) occupies \(\frac{1}{3}\) of the tetrahedral voids:
\(\text{Number of } P \text{ atoms} = \frac{1}{3} \times 8 = \frac{8}{3} \approx 2.67 \text{ atoms per unit cell}\)
For \(Q\), there are 4 atoms per unit cell.
For \(P\), we have calculated approximately 2.67 atoms per unit cell.
To simplify, let's assume the smallest whole number ratio:
Multiply the number of \(P\) atoms by 3 to eliminate the fraction:
\(P : Q = 2.67 : 4 \approx 8 : 12\)
Simplifying the ratio:
\(P : Q = 2 : 3\)
The empirical formula of the compound based on the ratio is \(P_2Q_3\).
The correct answer is option 1: \(P_2Q_3\).