To calculate the average atomic mass of iodine, we need to consider the mass and relative abundance of each isotope. The average atomic mass is a weighted average of the isotopic masses, where each weight corresponds to the relative abundance of the isotope.
Here are the given isotopes and their respective abundances:
- Isotope [tex]\( ^{127}I \)[/tex] has an isotopic mass of 127 and an abundance of 80.00%.
- Isotope [tex]\( ^{126}I \)[/tex] has an isotopic mass of 126 and an abundance of 17.00%.
- Isotope [tex]\( ^{128}I \)[/tex] has an isotopic mass of 128 and an abundance of 3.00%.
### Step-by-Step Calculation:
1. Convert Percent Abundances to Fractions:
- Abundance of [tex]\( ^{127}I \)[/tex]: [tex]\( \frac{80.00}{100} = 0.80 \)[/tex]
- Abundance of [tex]\( ^{126}I \)[/tex]: [tex]\( \frac{17.00}{100} = 0.17 \)[/tex]
- Abundance of [tex]\( ^{128}I \)[/tex]: [tex]\( \frac{3.00}{100} = 0.03 \)[/tex]
2. Multiply Each Isotope’s Mass by Its Fractional Abundance:
- Contribution of [tex]\( ^{127}I \)[/tex]: [tex]\( 127 \times 0.80 = 101.60 \)[/tex]
- Contribution of [tex]\( ^{126}I \)[/tex]: [tex]\( 126 \times 0.17 = 21.42 \)[/tex]
- Contribution of [tex]\( ^{128}I \)[/tex]: [tex]\( 128 \times 0.03 = 3.84 \)[/tex]
3. Sum the Contributions to Find the Average Atomic Mass:
- Average atomic mass = [tex]\( 101.60 + 21.42 + 3.84 = 126.86 \)[/tex]
Therefore, the average atomic mass of iodine is approximately [tex]\( 126.860 \)[/tex] (rounded to three decimal places).
