Question

In a crystal lattice, anions A form hcp array. \(\dfrac{2}{3}\) of the tetrahedral voids are occupied by cations C. What is the formula of crystal?

• A. \(C_3A_4\)
• B. \(C_4A_3\)
• C. \(C_2A_3\)
• D. \(C_3A_2\)

Hint:

In close-packed structures, if there are \(N\) atoms or ions, then octahedral voids are \(N\) and tetrahedral voids are \(2N\).

Answer 1

The Correct Option is B

Step 1: Relate voids to anions in hcp.
N anions → 2N tetrahedral voids. Cations fill 2/3 of them → (2/3)(2N) = 4N/3 cations. Ratio C:A = (4N/3):N = 4:3.

Step 2: Final Answer:
C₄A₃ (option 2).