Question

Consider an ionic solid $MX$ with $NaCl$ structure. Construct a new structure($Z$) whose unit cell is constructed from the unit cell of $MX$ following the sequential instructions given. Neglect the charge balance.
(i) Remove all the anions($X$) except the central one.
(ii) Replace all the face centered cations($M$) by anions($X$).
(iii) Remove all the corner cations($M$).
(iv) Replace the central anion($X$) with cation($M$).
The value of $\left(\frac{numberofanions}{numberofcations}\right)$ in $Z$ is ___________.

Answer 1

The answer is $3$.

$X^{-}\Rightarrow$ Octahedral void
$M^{+}\Rightarrow$ FCC point

(i) $M^{+}=4$ , $X^{-}=4-3=1$

(ii) $M^{+}=4-3=1$ , $X^{-}=1+3=4$

(iii) $M^{+}=1-1=0$ , $X^{-}=4$

(iv) $M^{+}=0+1=1$ , $X^{-}=4-1=3$

$\frac{no.ofanions}{no.ofcations}inZ=\frac{3}{1}=3$.