Question

if the radius of a metal atom is 2.00 A⁰ & its crystal structure is fcc lattice, what is the volume(in cm³) of one unit cell?

Answer 1

$$\begin{gathered} \text{Hi,} \\ \mathrm{Radius}=2{\mathrm{A}}^{°}=2\times {10}^{-10}\mathrm{m} \\ \mathrm{We}\mathrm{Know}\mathrm{that}\mathrm{for}\mathrm{Fcc}, \\ \sqrt{2}\mathrm{a}=4\mathrm{r} \\ \mathrm{a}=\mathrm{side}\mathrm{of}\mathrm{crystal}\mathrm{lattice} \\ \mathrm{r}=\mathrm{radius} \\ \sqrt{2}\mathrm{a}=4\times 2\times {10}^{-10}\mathrm{m} \\ \mathrm{a}=\frac{8\times {10}^{-10}\mathrm{m}}{\sqrt{2}} \\ \mathrm{Volume}={\mathrm{a}}^3={\left(\frac{8\times {10}^{-10}\mathrm{m}}{\sqrt{2}}\right)}^3=181.04\times {10}^{-30}{\mathrm{m}}^3 \\ \mathrm{Regards} \end{gathered}$$