Chemistry - Solid State Question with Solution | TestHub

For a simple cubic unit cell, the edge length $a$ and the radius of the particle $r$ are related by $a=2r$.

Given $r=400\mathrm{pm}=400\times 10^{-10}\mathrm{cm}=4\times 10^{-8}\mathrm{cm}$.

Substituting the value of $r$:

$a=2\times 4\times 10^{-8}\mathrm{cm}=8\times 10^{-8}\mathrm{cm}$

The volume of the unit cell is given by $V=a^3$.

$V=(8\times 10^{-8}\mathrm{cm}{)}^3$

$V=512\times 10^{-24}{\mathrm{cm}}^3=5.12\times 10^{-22}{\mathrm{cm}}^3$

Answer: $5.12\times 10^{-22}{\mathrm{cm}}^3$