Solid State

Given Values:The edge length $a=288\ \mathrm{pm}$. The density $(\rho)$ is $7.2\ \mathrm{g}/\mathrm{cm}^3$. The mass given is 208 g .Step 1: Find volume of one unit cellThe edge length must be changed to centimeters: $1\ \mathrm{pm}=10^{-10}\ \mathrm{cm}$. So: $a=288 \times 10^{-10}\ \mathrm{cm}$.The volume of one unit cell is: $V=a^3= (288 \times 10^{-10})^3\ \mathrm{cm}^3=2.389 \times 10^{-23}\ \mathrm{cm}^3$Step 2: Find total volume that 208 g will occupy$V_{\text{total}} = \frac{m}{\rho} = \frac{208}{7.2} = 28.89\ \mathrm{cm}^3$Step 3: Find the number of unit cells in $208\ \mathrm{g}$$\text{Number of unit cells} = \frac{V_{\text{total}}}{V_{\text{unit cell}}} = \frac{28.89}{2.389 \times 10^{-23}} = 1.209 \times 10^{24}$Step 4: Find the total number of atomsA body centered cubic (bcc) unit cell has 2 atoms per unit cell.So, Total atoms $=$ Number of unit cells $\times 2=1.209 \times 10^{24} \times 2=2.42 \times 10^{24}$ which is the same as $24.2 \times 10^{23}$.