Answer
\[\underline{\text{207 amu}}\]
Work Step by Step
Calculate the abundance of Pb-208 as follows:
\[\begin{align}
& \text{Abundance of Pb-}208=\frac{100\,\text{percent}}{100\,\text{percent}+48.9\,\text{percent}+41.1\,\text{percent}}\times 100\,\text{percent} \\
& =52.63\,\text{percent}
\end{align}\]
Calculate the abundance of Pb-206 as follows:
\[\begin{align}
& \text{Abundance of Pb-}206=\frac{48.9\,\text{percent}}{100\,\text{percent}+48.9\,\text{percent}+41.1\,\text{percent}}\times 100\,\text{percent} \\
& =25.74\,\text{percent}
\end{align}\]
Calculate the abundance of Pb-207 as follows:
\[\begin{align}
& \text{Abundance of Pb-}207=\frac{41.1\,\text{percent}}{100\,\text{percent}+48.9\,\text{percent}+41.1\,\text{percent}}\times 100\,\text{percent} \\
& =21.63\,\text{percent}
\end{align}\]
Calculate the fraction of Pb-208 as follows:
\[\begin{align}
& \text{Fraction of isotope Pb-}208=\frac{52.63}{100} \\
& =0.5263
\end{align}\]
Calculate the fraction of Pb-206 as follows:
\[\begin{align}
& \text{Fraction of isotope Pb-}206=\frac{25.74}{100} \\
& =0.2574
\end{align}\]
Calculate the fraction of Pb-207 as follows:
\[\begin{align}
& \text{Fraction of isotope Pb-}207=\frac{21.63}{100} \\
& =0.2163
\end{align}\]
Calculate the atomic mass of the element as follows:
\[\begin{align}
& \text{Atomic mass}=\left( \text{Fraction of Pb-}208\times \text{Mass of Pb-}208 \right)+ \\
& \left( \text{Fraction of Pb-}206\times \text{Mass of Pb-}206 \right)+ \\
& \left( \text{Fraction of Pb-}207\times \text{Mass of Pb-}207 \right) \\
& =\left( 0.5263\times 208\text{ amu} \right)+\left( 0.2574\times 206\text{ amu} \right) \\
& +\left( 0.2163\times 207\text{ amu} \right) \\
& =109.47\text{ amu}+53.02\text{ amu}+44.77\text{ amu} \\
& =207.26\text{ amu}
\end{align}\]
The atomic mass of lead is \[\underline{\text{207 amu}}\].
