# 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.

###### FREE Expert Solution

Determine the number of atoms fist:

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

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

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###### 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.

Frequently Asked Questions

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

Our tutors have indicated that to solve this problem you will need to apply the Density of Geometric Objects concept. You can view video lessons to learn Density of Geometric Objects. Or if you need more Density of Geometric Objects practice, you can also practice Density of Geometric Objects practice problems.

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Based on our data, we think this problem is relevant for Professor All Professors' class at HCC.