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?

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Solution

## 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, $\mathrm{a}=\left(\frac{4}{\sqrt{2}}\right)\mathrm{r}=2\sqrt{2}\mathrm{r}$ $\mathrm{a}=2×\sqrt{2}×125\phantom{\rule{0ex}{0ex}}\mathrm{a}=2×1.414×125\phantom{\rule{0ex}{0ex}}\mathrm{a}=353.5\mathrm{pm}$Hence, the length of the side of the unit cell of the metal is $353.5\mathrm{pm}$

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