Question

silicon is the second most abundant element in the earth’s crust. it is used in the electronics industry to manufacture transistors, and in the construction industry to produce concrete and cement. the graph below shows the relative abundance of the naturally occurring silicon isotopes. based on the graph, what would be the estimated mass of silicon? si - 29 4.68% si - 30 3.09% si - 28 92.22%

Explanation:

Step1: Recall the formula for average atomic mass

The average atomic mass ($A_{r}$) of an element with isotopes is calculated as $A_{r}=\sum_{i} (m_{i}\times p_{i})$, where $m_{i}$ is the mass - number of the isotope and $p_{i}$ is the relative abundance of the isotope (expressed as a decimal).
For silicon, we have three isotopes: Si - 28 with $p_1 = 0.9222$, Si - 29 with $p_2=0.0468$, and Si - 30 with $p_3 = 0.0309$. The mass - numbers of the isotopes are $m_1 = 28$, $m_2=29$, and $m_3 = 30$.

Step2: Calculate the contribution of each isotope

The contribution of Si - 28 to the average atomic mass is $m_1\times p_1=28\times0.9222 = 25.8216$.
The contribution of Si - 29 to the average atomic mass is $m_2\times p_2=29\times0.0468 = 1.3572$.
The contribution of Si - 30 to the average atomic mass is $m_3\times p_3=30\times0.0309 = 0.927$.

Step3: Sum up the contributions

$A_{r}=25.8216 + 1.3572+0.927=28.1058\approx28.1$ amu.

Answer:

28.1 amu