🤓 Based on our data, we think this question is relevant for Professor Castaneda's class at UMICH.

${\mathbf{V}}_{\mathbf{a}}\mathbf{=}\frac{\mathbf{4}{\mathbf{\pi r}}^{\mathbf{3}}}{\mathbf{3}}\mathbf{=}\frac{\mathbf{4}(3.14)(69\mathrm{pm}){\left({\displaystyle \frac{{10}^{-11}\mathrm{dm}}{1\mathrm{pm}}}\right)}^{\mathbf{3}}}{\mathbf{3}}\mathbf{=}\mathbf{1}\mathbf{.}\mathbf{37536}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{27}}\mathbf{}{\mathbf{dm}}^{\mathbf{3}}$

${\mathbf{V}}_{\mathbf{Ne}}\mathbf{=}(1.37536\times {10}^{-27}\overline{){\mathrm{dm}}^{3}})\left(\frac{1\overline{)L}}{1\overline{){\mathrm{dm}}^{3}}}\right)\left(\frac{2.69\times {10}^{22}\mathrm{atoms}}{1\overline{)L}}\right)\mathbf{=}\mathbf{3}\mathbf{.}\mathbf{6997}\mathbf{\times}{\mathbf{10}}^{\mathbf{-}\mathbf{5}\mathbf{}}\mathbf{atoms}$

A sample of gaseous neon atoms at atmospheric pressure and 0 ^{o}C contains 2.69×10^{22} atoms per liter. The atomic radius of neon is 69 pm.

What fraction of the space is occupied by the atoms themselves?

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Based on our data, we think this problem is relevant for Professor Castaneda's class at UMICH.