Question

silicon has three stable isotopes: si - 28, si - 29, and si - 30. the following table lists the percent abundance of each isotope.

isotope % abundance
si - 28 92.2
si - 29 4.7
si - 30 3.1

using the data above, what is the average atomic mass of silicon? ignore significant figures and report your answer to three decimal places.

Explanation:

Step1: Calculate contribution of Si - 28

The contribution of an isotope to the average atomic mass is given by \( \text{Isotope mass}\times\text{% abundance (in decimal)} \). For Si - 28, mass \( m_{28}=28\), and abundance \( a_{28}=0.922\). The contribution \( C_{28}=28\times0.922 = 25.816\)

Step2: Calculate contribution of Si - 29

For Si - 29, mass \( m_{29}=29\), and abundance \( a_{29}=0.047\). The contribution \( C_{29}=29\times0.047=1.363\)

Step3: Calculate contribution of Si - 30

For Si - 30, mass \( m_{30}=30\), and abundance \( a_{30}=0.031\). The contribution \( C_{30}=30\times0.031 = 0.93\)

Step4: Calculate average atomic mass

The average atomic mass \( M\) of silicon is the sum of the contributions of all isotopes. So, \( M=C_{28}+C_{29}+C_{30}\)

$$
LATEXBLOCK0
$$

Answer:

\(28.109\)