Answer
\[\underline{\text{29}\text{.96 amu}}\] and \[\underline{\text{3}\text{.13}\,\text{percent}\,}\]
Work Step by Step
Calculate the Si-28 fraction as follows:
\[\begin{align}
& \text{Fraction Si-}28=\frac{92.2}{100} \\
& =0.922
\end{align}\]
Calculate the Si-29 fraction as follows:
\[\begin{align}
& \text{Fraction Si-}29=\frac{4.67}{100} \\
& =0.0467
\end{align}\]
Calculate the Si-30 natural abundance as follows:
\[\begin{align}
& \text{Natural abundance}=100\,\text{percent}\,-\left( \text{Natural abundance Si-}28+\text{Natural abundance Si-}29 \right) \\
& =100\,\text{percent}\,-\left( 92.2\,\text{percent}\,+4.67\,\text{percent}\, \right) \\
& =3.13\,\text{percent}\,
\end{align}\]
Calculate the Si-30 fraction as follows:
\[\begin{align}
& \text{Fraction isotope Si-}30=\frac{3.13}{100} \\
& =0.0313
\end{align}\]
Calculate the atomic mass of the element as follows:
\[\begin{align}
& \text{Atomic mass}=\left( \text{fraction of Si-}28\times \text{mass of Si-}28 \right)+ \\
& \left( \text{fraction of Si-}29\times \text{mass of Si-}29 \right)+ \\
& \left( \text{fraction of Si-}30\times \text{mass of Si-}30 \right) \\
& \text{28}\text{.09 amu}=\left( 0.922\times 27.9769\text{ amu} \right)+\left( 0.0467\times 28.9765\text{ amu} \right)+\left( 0.0313\times \text{mass of Si-}30 \right)
\end{align}\]
Rearrange the above expression as follows:
\[\begin{align}
& \left( 0.0313\times \text{mass of Si-}30 \right)=0.93763768\text{ amu} \\
& \text{mass of Si-}30=29.96\text{ amu}
\end{align}\]
The mass of Si-30 is \[\underline{\text{29}\text{.96 amu}}\] and the natural abundance is \[\underline{\text{3}\text{.13}\,\text{percent}\,}\].
