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

A **simple cubic unit cell** is composed of a cube with one atom at each of its corners.

$\mathbf{\#}\mathbf{}\mathbf{of}\mathbf{}\mathbf{atoms}\mathbf{=}\left(\mathbf{8}\mathbf{\times}\frac{\mathbf{1}}{\mathbf{8}}\right)$

**# of atoms = 1 atom per 1 unit cell**

$\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{unit}\mathbf{}\mathbf{cell}\mathbf{=}\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{cube}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{volume}}{\mathbf{}}{\mathbf{of}}{\mathbf{}}{\mathbf{unit}}{\mathbf{}}{\mathbf{cell}}{\mathbf{=}}{{\mathbf{a}}}^{{\mathbf{3}}}}\phantom{\rule{0ex}{0ex}}\overline{){\mathbf{a}}{\mathbf{=}}{\mathbf{2}}{\mathbf{r}}}{f}{o}{r}{}{s}{i}{m}{p}{l}{e}{}{c}{u}{b}{i}{c}{}{u}{n}{i}{t}{}{c}{e}{l}{l}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{volume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{unit}\mathbf{}\mathbf{cell}\mathbf{}\mathbf{=}{\left(2r\right)}^{\mathbf{3}}\phantom{\rule{0ex}{0ex}}\phantom{\rule{0ex}{0ex}}\mathbf{v}\mathbf{olume}\mathbf{}\mathbf{of}\mathbf{}\mathbf{unit}\mathbf{}\mathbf{cell}\mathbf{}\mathbf{=}{\mathbf{(}\mathbf{2}\mathbf{\times}\mathbf{167}\mathbf{}\overline{)\mathbf{pm}}\mathbf{\times}\frac{\mathbf{10}{}^{\mathbf{-}\mathbf{12}}\mathbf{}\overline{)\mathbf{m}}}{\mathbf{1}\mathbf{}\overline{)\mathbf{pm}}}\mathbf{)}}^{\mathbf{3}}\mathbf{\times}{\left(\frac{1\mathrm{cm}}{{10}^{-2}\overline{)m}}\right)}^{\mathbf{3}}$

**volume of unit cell = 3.7259 x 10 ^{-23} cm^{3}**

Polonium crystallizes with a simple cubic structure. It has a density of 9.3 g/cm^{3}, a radius of 167 pm, and a molar mass of 209 g/mol.

Use these data to estimate Avogadros number (the number of atoms in one mole).

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