Question

Barium has a body-centered cubic structure. If the atomic radius of barium is 222 pm, calculate the density of solid barium.

Short answer

The density of solid barium is $3.38\mathrm{gm}/{\mathrm{cm}}^3$.

Step-by-step solution

Edge length

$$\begin{gathered} 16{\mathrm{r}}^2=3{\mathrm{L}}^2 \\ \mathrm{L}=\frac{4\mathrm{r}}{\sqrt{3}} \\ \mathrm{L}=513\mathrm{pm} \\ \mathrm{L}=5.13\times {10}^{-8}\mathrm{cm} \end{gathered}$$

Density for a unit cell

There are two atoms per unit cell in a body-centered cubic unit cell.

$$\begin{gathered} \mathrm{Density}=\frac{2\times 137.3\mathrm{gm}/\mathrm{mole}}{6.023\times {10}^{23}\mathrm{atoms}/\mathrm{mole}\times {\left(5.13\times {10}^{-8}\mathrm{cm}\right)}^3} \\ \mathrm{Density}=3.38\mathrm{gm}/{\mathrm{cm}}^3 \end{gathered}$$