Question

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

• A. $MX$
• B. $MX_2$
• C. $M_2X$
• D. $M_5X_{14}$

Answer 1

Answer: (B)

$MX_2$

Answer 2

$8\,X$ atoms present at the corners. Atoms contribute to $1$ unit cell $=\frac{1}{8}\times8=1$ $6 \,X$ atoms present at the face centres. Atoms contribute to $1$ unit cell $=6\times\frac{1}{2}=3$ Total $X$ atoms $= 3 + 1=4$ $4\,M$ atoms present at edge centres. Atoms present in $1$ unit cell $=4\times\frac{1}{4}=1$ $1\,M$ atom present at body centre and it contribute 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 $MX_2$.