The closest distance between $\mathrm{Si}$ and $\mathrm{C}$ in $\mathrm{SiC}$ is $0.866Å$. What will be the molar volume of unit cell?

$\mathrm{SiC}$$\Rightarrow$ alternate tetrahedral voids Corners

closest distance $=\frac{\sqrt{3}}{4}a$

a= length of side of a= length of side of unit all

$\text{ Given }=0.866A^{\circ }=\frac{\sqrt{3}}{2}$

$\frac{\sqrt{3}}{2}=\frac{\sqrt{3}}{4}a$

$a=2A^{\circ }$

$\begin{array}{r}=2\times {10}^{-10} \mathrm{m}\\ =2\times {10}^{-8} \mathrm{cm}\end{array}$

$\text{ volume }=a^3\Rightarrow \text{ Molar volune }=a^3\times N_A$

$\text{ Molar volume }={\left(2\times {10}^{-8}\right)}^3\times 6\times {10}^{23}$

$=8\times {10}^{-24}\times 6\times {10}^{23}$

$=48\times {10}^{-1}$

$=4.8 ml$