Copper has the fcc crystal structure. Assuming an atomic radius of 130 pm for copper atom (Cu = 63.54):the density of Cu is

Expression of density:

$\rho =\frac{n\times M_{\mathrm{m}}}{N_{\mathrm{A}}\times a^3}$

For fcc structure, edge length is calculated as:

$\begin{array}{l}4r=\sqrt{2}a\\ a=2\sqrt{2}r\\ =2\sqrt{2}\times 130\mathrm{pm}=367.64\mathrm{pm}=3.67\times {10}^{-8}\mathrm{cm}\end{array}$

Volume of unit cell is:

$\begin{array}{l}{a}^3={\left(3.67\times {10}^{-8}\right)}^3{\mathrm{cm}}^3\\ =49.43\times {10}^{-24}{\mathrm{cm}}^3\end{array}$

For FCC, Z= 4. Substitute the given values in the density expression:

 $\rho =\frac{4\times 63.54}{6.023\times {10}^{23}\times \left(3.67\times {10}^{-8}{\mathrm{cm}}^3\right)}=8.54 \mathrm{g}/{\mathrm{cm}}^3$