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.
