## Chemistry: Molecular Approach (4th Edition)

$1.47\,\,cm$
The molar mass of copper is 63.5 g/mol . Thus, the mass of copper containing$1.14\,\times \,{{10}^{24}}\,atoms$ is calculated as: \begin{align} & 1\,\,mol\,\,\,Cu\,\,=\,\,63.5\,\,g \\ & 1\,\,mol\,\,Cu\,\,=\,\,6.022\,\times \,{{10}^{23}}\ \ Cu\,\,atoms \\ & Thus,\,\,\,6.022\,\times \,{{10}^{23}}\ \ Cu\,\,atoms\,\,=\,\,63.5\,\,g \\ & \,\,\Rightarrow 1.14\,\times \,{{10}^{24}}\,\,Cu\,\,atoms\,\,=\,\,63.5\,\,g\,\,\times \,\frac{1.14\,\times \,{{10}^{24}}\,\,Cu\,\,atoms}{\,6.022\,\times \,{{10}^{23}}\ \ Cu\,\,atoms\,\,} \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,=\,\,120.2\,g \\ \end{align} Calculate the volume of copper as: \begin{align} & \,\,\,\,density\,\,=\,\,\frac{mass}{volume} \\ & \Rightarrow volume\,\,=\,\frac{mass}{density} \\ \end{align} Substitute density of copper $=8.96\ g/c{{m}^{3}}$ and mass of copper = 120.2 g in the above expression as: $volume\,\,=\,\,\frac{120.2\,\,g}{8.96\,\,g/c{{m}^{3}}}\,\,=\,13.41\ c{{m}^{3}}$ As copper atom is spherical, the volume of a copper atom is given by: \begin{align} & \left( \frac{4}{3} \right)\prod {{r}^{3}}\,\,\,13.41\,\,c{{m}^{3}} \\ & {{r}^{3}}\,\,\,\,=\,\,\frac{13.41\,\,c{{m}^{3}}\,\,\times \,\,\frac{3}{4}}{\prod } \\ & r\,\,\,\,\,\,\,\,\,\,\,=\,\,\sqrt[3]{\frac{13.41\,\,c{{m}^{3}}\,\,\times \,\,\frac{3}{4}}{\prod }} \\ & r\,\,\,\,\,\,\,\,\,\,=\,\,1.47\,cm \\ \end{align} The radius of a pure copper sphere containing $1.14\,\times \,{{10}^{24}}\,atoms$is 1.41 cm.