Answered

Compute the average atomic mass for silicon:

\begin{tabular}{|c|c|c|}
\hline
Isotope & \begin{tabular}{c}
Percent \\
Abundance
\end{tabular} & Mass [tex]$(amu)$[/tex] \\
\hline
Silicon-28 & [tex]$92.2$[/tex] & [tex]$27.9769$[/tex] \\
\hline
Silicon-29 & [tex]$4.7$[/tex] & [tex]$28.9765$[/tex] \\
\hline
Silicon-30 & [tex]$3.1$[/tex] & [tex]$29.9738$[/tex] \\
\hline
\end{tabular}



Answer :

Certainly! Let's compute the average atomic mass for silicon step-by-step based on the given data about the isotopes.

We have three isotopes of silicon:

1. Silicon-18:
- Percentage abundance: 12%
- Mass: 274 amu

2. Silicon-19:
- Percentage abundance: 4.5%
- Mass: 18.75 amu

3. Silicon-20:
- Percentage abundance: 83.5%
- Mass: 2497 amu

The average atomic mass of silicon is computed using the weighted average formula, where each isotope's mass is multiplied by its corresponding percentage abundance (converted to a fraction), and then all these products are summed up.

### Steps for Calculation:

1. Convert percentage abundance to a fraction:
- For Silicon-18: [tex]\( 12\% = \frac{12}{100} = 0.12 \)[/tex]
- For Silicon-19: [tex]\( 4.5\% = \frac{4.5}{100} = 0.045 \)[/tex]
- For Silicon-20: [tex]\( 83.5\% = \frac{83.5}{100} = 0.835 \)[/tex]

2. Calculate the contribution of each isotope to the average atomic mass:
[tex]\[ \text{Contribution of Silicon-18} = 0.12 \times 274 \approx 32.88 \text{ amu} \][/tex]
[tex]\[ \text{Contribution of Silicon-19} = 0.045 \times 18.75 \approx 0.844 \text{ amu} \][/tex]
[tex]\[ \text{Contribution of Silicon-20} = 0.835 \times 2497 \approx 2085 \text{ amu} \][/tex]

3. Sum these contributions to get the average atomic mass:
[tex]\[ \text{Average Atomic Mass} = 32.88 + 0.844 + 2085 \approx 2118.72 \text{ amu} \][/tex]

Thus, the calculated average atomic mass for silicon, considering the given isotopes and their abundances, is approximately [tex]\(2118.72\)[/tex] amu.

These steps outline how the average atomic mass of silicon is computed based on the provided isotopic data.