Question

An ionic compound has a unit cell consisting of $A$ ions at the corners of a cube and $B$ ions on the centres of the face. What is the empirical formula for this compound?

• A. $A_3{B}_2$
• B. $A{B}_3$
• C. $A_2{B}_3$
• D. $A_{3}B$

Answer 1

Answer: (B)

$A{B}_3$

Unit cell consists of A ions at the eight corners.

Thus, the number of ions of the type,

$A=\frac{1}{8}\times 8=1$

Unit cell consists of B ions at the center of the six faces.

Thus, the number of ions of type,

$B=\frac{1}{2}\times 6=3$

Thus, the formula of unit cell is $A{B}_3$.