Question

If in a cubic cell, atoms $A$ present at all corners and atoms $B$ at the center of each face. What will be the molecular formula of the compound, if all the atoms present in one body diagonal are replaced by atom $C$?

• A. $A_3{B}_{12}C$
• B. $A{B}_{12}{C}_3$
• C. $A_2{B}_{12}{C}_3$
• D. $A_3{B}_{12}{C}_4$

Answer 1

The correct option is A $A_3{B}_{12}C$

Atoms $A$ are present at corners,
Atoms $A$ per unit cell$=8\times \frac{1}{8}=1$
If atoms present on one body diagonal are replaced by atom $C$, then atoms $A$ per unit cell $=\frac{6}{8}=\frac{3}{4}$
Atoms $B$ are at centre of each face $=6\times \frac{1}{2}=3$
Atoms $C$ at corners, atoms $C$ per unit cell will be $=2\times \frac{1}{8}=\frac{1}{4}$

A	B	C
$\frac{3}{4}$	$3$	$\frac{1}{4}$
$3$	$12$	$1$

So, molecular formula $A_3{B}_{12}C$.