Question

Which of the following has highest number of formula units per unit cell ?

• A. $NaCl$ type structure
• B. $N{a}_{2}O$ type structure
• C. $Ca{F}_2$ type structure
• D. All have Same Number of formula unit

Answer 1

The correct option is D All have Same Number of formula unit

(A) In $NaCl$ $\text{Anion}C{l}^{-}\to \text{Forms FCC lattice}\text{(Corner + face centre)}$
$\text{Cation}N{a}^{+}\to \text{Present in octahedral void}\text{+ body centre + edge centre}$
$\text{So,}C{l}^{-}=6\times \frac{1}{2}+8\times \frac{1}{8}=4$
$N{a}^{+}=1+12\times \frac{1}{4}=4$
So it is $N{a}_{4}C{l}_4$ and formula unit is $NaCl$
Thus number of formula unit is $4$
(B)
$\text{In}N{a}_{2}O$
$\text{Anion}{O}^{2-}\to \text{Forms FCC lattice}$
$\text{Cation}N{a}^{+}\to \text{Present in all tetrahedral voids}$
So it is $N{a}_4{O}_8$ and formula unit is $N{a}_{2}O$
Thus number of formula unit is $4$
(C)
$\text{In}Ca{F}_2$
$\text{Cation}C{a}^{2+}\to \text{Forms FCC lattice}$
$\text{Anion}{F}^{-}\to \text{Present in tetrahedral void}$
So it is $C{a}_4{F}_8$ and formula unit is $Ca{F}_2$
Thus here also number of formula unit is $4$
$\text{All of the three options have same formula unit}.$