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If we know the molar mass of a certain element and Avogadro's constant, how can we calculate the mass of a single atom? Do we need to multiply the molar mass with Avogadro's constant?

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For most atoms it's around Ryan's answer.

E.g. Carbon-12:

$$\frac{\ce{12 g}~\ce{C}}{\pu{1 mol}~\ce{C}} \times \frac{\pu{1 mol}~\ce{C}}{\pu{6.022E23 atoms}} = \pu{1.993E-23 g//atom} = \pu{1.993E-27 kg//atom}.$$

That was the molar mass $M$ multiplied by $1/N_\mathrm{A}$, where $N_\mathrm{A}$ is Avagadro's constant.

Thus $M/N_\mathrm{A}$ gives you a calculation for mass of an atom for the specific element.

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The average mass of a single element is its atomic mass on the periodic table (measured in $\pu{u}$, the unified atomic mass unit). One $\pu{u}$ equals about $\pu{1.661E-27 kg}$.

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