Question

In a face-centre cubic arrangement of A and B atoms whose A atoms are at the corner of the unit cell and B atoms at the face-centre, one of A atom is missing from one corner in the unit cell. The simplest formula of the compound is:

• A. $A_{24}{B}_7$
• B. $A_7{B}_{24}$
• C. $A_7{B}_4$
• D. $A{B}_2$

Answer 1

Answer: (B)

$A_7{B}_{24}$

No. of atoms of $A$ from corners of unit cell $=\frac{7}{8}$
No. of atoms of $B$ from faces of unit cell$=3$
$\therefore A:B=\frac{7}{8}:3=7:24$
Thus, formula of the compound is $A_7{B}_{24}$.