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. $MX_{2}$
• C. $M_{2}X$
• D. $M_{5}X_{14}$

Answer 1

Answer: (B)

Contribution by $8 \,X$ atoms present at the corners
$=\frac{1}{8} \times 8=1$
Contribution by $6\, X$ atoms present at the face centres
$=6 \times \frac{1}{2}=3$
Total $X$ atoms $= 3 + 1 = 4$
Contribution by $4 \,M$ atoms present at edge centres
$=4 \times \frac{1}{4} = 1$
$1 \,M$ 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 $MX_{2}$