Problem: You are given a cube of silver metal that measures 1.050 cm on each edge. The density of silver is 10.5 g/cm3.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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FREE Expert Solution

Determine the number of atoms fist:

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

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

Problem Details

You are given a cube of silver metal that measures 1.050 cm on each edge. The density of silver is 10.5 g/cm3.

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.