Silicon is widely used in the semiconductor industry. Its...

Silicon is widely used in the semiconductor industry. Its isotopes and abundances are: $\mathrm{Si}-28$ $\begin{array}{ll}27.977 \mathrm{amu} & 92.34 \%\end{array}$ $\begin{array}{lll}\mathrm{Si}-29 & 28.977 \mathrm{amu} & 4.70 \% \\ \mathrm{Si}-30 & 29.974 \mathrm{amu} & 2.96 \%\end{array}$ What is the average atomic mass of silicon?

Silicon is widely used in the semiconductor industry. Its isotopes and abundances are:
$\mathrm{Si}-28$
$\begin{array}{ll}27.977 \mathrm{amu} & 92.34 \%\end{array}$
$\begin{array}{lll}\mathrm{Si}-29 & 28.977 \mathrm{amu} & 4.70 \% \\ \mathrm{Si}-30 & 29.974 \mathrm{amu} & 2.96 \%\end{array}$
What is the average atomic mass of silicon?

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Key Concepts

Average Atomic Mass

The average atomic mass of an element is the mean mass of its atoms, taking into account the relative abundances of its isotopes. It is not simply an arithmetic mean but a weighted average that provides a more accurate depiction of the element's mass as it naturally occurs. This value is essential in chemical calculations and helps predict the behavior of elements in reactions.

Isotopes

Isotopes refer to different forms of the same element that contain the same number of protons but different numbers of neutrons. This variation in neutron count gives each isotope a slightly different atomic mass while retaining identical chemical properties. Understanding isotopes is crucial in many scientific fields as the differences in their masses lead to varied physical properties and contribute to averaged values such as atomic mass.

Weighted Average Calculation

The weighted average calculation is a method used to determine a single representative value (such as the average atomic mass) from a set of values that have different levels of occurrence. For isotopes, this involves multiplying the mass of each isotope by its relative abundance (as a fraction) and then summing these products. This process yields an average value that accurately reflects the overall distribution of the isotopes.

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