Question

A compound $M_p{X}_q$ has cubic close packing $(ccp)$ arrangement of $X$. Its unit cell structure is shown below. The empirical formula of the compound is

• A. $MX$
• B. $M{X}_2$
• C. $M_{2}X$
• D. $M_5{X}_{14}$

Answer 1

Answer: (B)

Contribution by $8X$ atoms present at the corners
$=\frac{1}{8}\times 8=1$
Contribution by $6X$ atoms present at the face centres
$=6\times \frac{1}{2}=3$
Total $X$ atoms $=3+1=4$
Contribution by $4M$ atoms present at edge centres
$=4\times \frac{1}{4}=1$
$1M$ atom present at body centre contributes completely to $1$ unit cell
Thus, total $M$ atoms in one unit cell $=1+1=2$
Ratio is $M:X=2:4=1:2$
Thus, empirical formula is $M{X}_2$