Question

An ionic compound crystallises in FCC type structure with 'A' ions at the centre of each face and 'B' ions occupying corners of the cube. The formula of compound is __________ .

• A. $A{B}_4$
• B. $A_{3}B$
• C. $AB$
• D. $A{B}_3$

Answer 1

The correct option is B $A_{3}B$

'A' ions are at the centre of each face . There are six face centres and each contributes one half to the unit cell. Total number of A ions present per unit cell
$=6\times \frac{1}{2}=3$.
'B' ions occupy corners of the cube. There are 8 corners and each contributes one eight to unit cell.
Total number of B ions present per unit cell
$=8\times \frac{1}{8}=1$.
The formula of compound is $A_{3}B$
Hence, the option B is the correct answer.