Question

A crystalline solid has $A^-$ ions at the corners and face centres whereas $B^+$ ions are at the body centre and edge centres of the unit cell. The simplest formula of the compound will be

• A. $A_2B$
• B. $AB_2$
• C. $AB_3$
• D. $AB$

Answer 1

Answer: (D)

$AB$

Answer 2

Number of $A^-$ ions= {\underset{\text{(at corners)}}{ {\frac{1}{8} \times 8 + }}$$\underset{\text{(at face centres)}}{ {\frac{1}{2} \times 6 = 4 }} }
Number of $B^+$ ions = {\underset{\text{(atbody centre)}}{ {1 + }}$$\underset{\text{(at edge centres)}}{ {12 \times \frac{1}{4} = 4 }} }
${ (A^-)_4 (B^+)_4 = A_4 B_4 = AB}$