Determine the number of atoms fist:

$\overline{){{\mathbf{V}}}_{{\mathbf{sphere}}}{\mathbf{=}}{{\mathbf{s}}}^{{\mathbf{3}}}}$

${{\mathbf{V}}}_{{\mathbf{sphere}}}{\mathbf{=}}{(1.050\mathrm{cm})}^{{\mathbf{3}}}{\mathbf{=}}{\mathbf{1}}{\mathbf{.}}{\mathbf{157625}}{\mathbf{}}{{\mathbf{cm}}}^{{\mathbf{3}}}$

$\overline{){\mathbf{denstiy}}{\mathbf{=}}\frac{\mathbf{mass}}{\mathbf{volume}}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}(\mathrm{denstiy}=\frac{\mathrm{mass}}{\overline{)\mathrm{volume}}})\overline{)\mathbf{volume}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{mass}}{\mathbf{=}}{\mathbf{density}}{\mathbf{\times}}{\mathbf{volume}}}$

${\mathbf{mass}}{\mathbf{=}}(10.5\frac{g}{{\mathrm{cm}}^{3}}){\mathbf{\times}}(1.157625{\mathrm{cm}}^{3}){\mathbf{=}}{\mathbf{12}}{\mathbf{.}}{\mathbf{1550625}}{\mathbf{}}{\mathbf{g}}$

You are given a cube of silver metal that measures 1.050 cm on each edge. The density of silver is 10.5 g/cm^{3}.

Because atoms are spherical, they cannot occupy all of the space of the cube. The silver atoms pack in the solid in such a way that 74% of the volume of the solid is actually filled with the silver atoms. Calculate the volume of a single silver atom.

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What scientific concept do you need to know in order to solve this problem?

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