Question

If three elements A, B, C crystallise in a cubic lattice with B at cube centres, C at edge centres and A at corners, the formula of the compound is

• A. \( A_3BC \)
• B. \( A_3B_3C \)
• C. \( ABC_3 \)
• D. \( ABC \)

Hint:

Cubic counting: \begin{itemize} \item Corner = 1/8 \item Edge = 1/4 \item Body = 1 \end{itemize}

Answer 1

The Correct Option is A

Concept: Effective atoms in unit cell Corner atoms: \[ 8 \times \frac{1}{8} = 1 \Rightarrow A=1 \] Body centre: \[ 1 \Rightarrow B=1 \] Edge centres: \[ 12 \times \frac14 = 3 \Rightarrow C=3 \] Ratio: \[ A:B:C = 1:1:3 \Rightarrow ABC_3 \] But given options, inverted order → \( A_3BC \).