Question

The face diagonal length of $f.c.c$. cubic cell is $660\sqrt{2}$ pm. If the radius of the cation is $110pm$, the radius of the anion in $(pm)$ is

Answer 1

Answer: 220

$\sqrt{2}a=660\sqrt{2}pm$
so $a=660pm$
Now if tetrahedral void is occupied by cations than
$\frac{\sqrt{3}}{4}a=\left(r_{+}+r_{-}\right)$
$r_{-}=\left(\frac{\sqrt{3}\times 660}{4}-110\right)=110\left[\frac{3}{2}\sqrt{3}-1\right]=1.598$
so $\frac{r_{+}}{r_{-}}=\frac{1}{1.598}\simeq \frac{1}{1.6}=\frac{10}{16}=0.625$
but $\frac{r_{+}}{r_{-}}>0.414$ so it must not be occupying tetrahedral
void then
$a=2\left(r_{+}+r_{-}\right)$
$\Rightarrow 330=r_{+}+r_{-}$
$r_{-}=220pm$
$\{\frac{r_{+}}{r_{-}}=0.5$ it can occupy octahedral void $\}$