Question

Three elements $A, B$ and $C$ crystallise into a cubic solid lattice. Atoms $A$ occupy the corners, $B$ atoms, the cube centres and $C$ atoms, the edge. The formula of the compound is

• A. $ABC$
• B. $ ABC_{2} $
• C. $ ABC_{3} $
• D. $ ABC_{4} $

Answer 1

Answer: (C)

Number of atoms of $A$ per unit cell $=8 \times \frac{1}{8}$ (at the corners) $=1$
Number of atoms of $B$ per unit cell $=1$ (at the centre) $=1$
Number of atoms of $C$ per unit cell $=12 \times \frac{1}{4}$
(at the edge centre) $=3$
So, the formula of the compound is $A B C_{3}$.