Question

Aluminum crystallizes in an FCC structure. The atomic radius of the metal is $125\mathrm{pm}$. What is the length of the side of the unit cell of the metal?

Answer 1

For a cubic close-packed structure, let a be the edge and r is the radius of the atom.

Given that $\mathrm{r}=125\mathrm{pm}$

Length of the side of the unit cell in FCC structure, $\mathrm{a}=\left(\frac{4}{\sqrt{2}}\right)\mathrm{r}=2\sqrt{2}\mathrm{r}$

$$\begin{gathered} \mathrm{a}=2\times \sqrt{2}\times 125 \\ \mathrm{a}=2\times 1.414\times 125 \\ \mathrm{a}=353.5\mathrm{pm} \end{gathered}$$

Hence, the length of the side of the unit cell of the metal is $353.5\mathrm{pm}$