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 \(\( ^{127}I \)\) has an isotopic mass of 127 and an abundance of 80.00%.
- Isotope \(\( ^{126}I \)\) has an isotopic mass of 126 and an abundance of 17.00%.
- Isotope \(\( ^{128}I \)\) has an isotopic mass of 128 and an abundance of 3.00%.
### Step-by-Step Calculation:
1. Convert Percent Abundances to Fractions:
- Abundance of \(\( ^{127}I \)\): \(\( \frac{80.00}{100} = 0.80 \)\)
- Abundance of \(\( ^{126}I \)\): \(\( \frac{17.00}{100} = 0.17 \)\)
- Abundance of \(\( ^{128}I \)\): \(\( \frac{3.00}{100} = 0.03 \)\)
2. Multiply Each Isotope’s Mass by Its Fractional Abundance:
- Contribution of \(\( ^{127}I \)\): \(\( 127 \times 0.80 = 101.60 \)\)
- Contribution of \(\( ^{126}I \)\): \(\( 126 \times 0.17 = 21.42 \)\)
- Contribution of \(\( ^{128}I \)\): \(\( 128 \times 0.03 = 3.84 \)\)
3. Sum the Contributions to Find the Average Atomic Mass:
- Average atomic mass = \(\( 101.60 + 21.42 + 3.84 = 126.86 \)\)
Therefore, the average atomic mass of iodine is approximately \(\( 126.860 \)\) (rounded to three decimal places).
