Lead metal has a density of $11.34 \mathrm{g}/{\mathrm{cm}}^3$ and crystallizes in a face-centered lattice. Choose the correct alternatives.

The following is the expression for density:

$\text{ Density }=\frac{\mathrm{Z}\times \mathrm{M}}{{\mathrm{N}}_{\mathrm{A}}\times \text{ volume }}$

$\text{ Volume }=\frac{4\times 207}{6.02\times {10}^{23}\times 11.34}=1.213\times {10}^{-22}{\mathrm{cm}}^3$

For FCC, we have $4\mathrm{r}=\mathrm{a}\sqrt{2}$

$\mathrm{r}=\frac{4.95\times {10}^{-8}\times \sqrt{2}}{4}=175\mathrm{pm}$

$\text{ Volume }=a^3=1.213\times {10}^{-22}{\mathrm{cm}}^3$

$$\begin{gathered} \text{ Edge length }=\mathrm{a}={\left({1.21310}^{-24}\right)}^{\frac{1}{3}} \\ \Rightarrow \mathrm{a}=4.95\times {10}^{-8}\mathrm{cm} \end{gathered}$$