$\mathbf{fraction}\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{volume}\mathbf{\times}\mathbf{Avogadro}\mathbf{\text{'}}\mathbf{s}\mathbf{}\mathbf{number}}{\mathbf{volume}\mathbf{}\mathbf{at}\mathbf{}\mathbf{STP}}\phantom{\rule{0ex}{0ex}}\mathbf{fraction}\mathbf{}\mathbf{=}\mathbf{}\frac{\left({\displaystyle \frac{4{\mathrm{\pi r}}^{3}}{3}}\right)(6.022\times {10}^{23})}{\mathbf{22}\mathbf{.}\mathbf{4}}$

To derive the ideal-gas equation, we assume that the volume of the gas atoms/molecules can be neglected.

Given the
atomic radius of neon, 0.69 Å , and knowing that a sphere has a volume of 4/3 πr^{3}, calculate the fraction of space that Ne atoms occupy in a sample of neon at STP.

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