Question

Copper which crystallizes as a face – centred cubic lattice has a density of 8.93g/cm3 at 20o C. calculate the length of the unit cell.

Answer 1

Cu has a FCC structure , so the value of Z = 4.
Molar mass of Cu = 63.5 g
Density = 8.93 g cm^-3
$$\begin{gathered} \text{Volume of unit cell}=\frac{\text{Molar mass×Z}}{{\text{Density×N}}_A} \\ \text{Volume}=\frac{63.5\times 4}{8.93\times 6.022\times {10}^{23}}=1.1808\times {10}^{-23}{\text{cm}}^3 \\ {\text{Volume = a}}^3=2.277\times {10}^{-8}{\text{cm}}^3 \\ a=2.277\times {10}^{-8}\text{cm = 227.7 pm} \end{gathered}$$