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. $A_{2}B$
• B. $A{B}_3$
• C. $A{B}_2$
• D. $A_2{B}_3$
• E. $A_2{B}_5$

Answer 1

The correct option is C $A{B}_2$

Let number of octahedral holes in the lattice $=x$
$\therefore$ Number of tetrahedral holes in the lattice $=2x$
($\because$ 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 $=2x\times 25$% $=2x\times \frac{25}{100}=\frac{x}{2}$
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 $A{B}_2$