Question

A binary solid has a primitive cubical structure with $B^-$ ions constituting the lattice points and $A^+$ ions occupying $25\%$ of its tetrahedral holes. The molecular formula of the crystal is

• A. $AB$
• B. $A_2B$
• C. $AB_2$
• D. $AB_4$

Answer 1

Answer: (C)

$AB_2$

Answer 2

Let number of octahedral holes in the lattice $=x$
$\therefore$ Number of tetrahedral holes in the lattice $=2 x$
$(\because$ Number of tetrahedral holes $=2 \times$ number of octahedral holes)

Now, $A^{+}$ ions occupy $25 \%$ of tetrahedral holes. Hence, number of tetrahedral holes occupied in the lattice $=2 x \times 25 \%=2 x \times \frac{25}{100}=\frac{x}{2}$

Since, number of octahedral holes $=$ Number of lattice points.

$\therefore$ Number of octahedral holes $=x$
$\therefore$ Molecular formula of the crystal is

$A_{x / 2} B_{x}$ or $A B_{2}$