To calculate the average atomic mass of iodine, we can use the formula:
\[ \text{Average Atomic Mass} = \sum (\text{fraction} \times \text{isotope mass}) \]
where the fractions are the decimal representations of the percentages of each isotope.
Let's break it down for each isotope:
-
Isotope \(^{127}\text{I}\):
- Percentage: 80%
- Fraction: \(0.80\)
- Atomic mass: \(127 , \text{amu}\)
- Contribution: \(0.80 \times 127 = 101.6 , \text{amu}\)
-
Isotope \(^{126}\text{I}\):
- Percentage: 17%
- Fraction: \(0.17\)
- Atomic mass: \(126 , \text{amu}\)
- Contribution: \(0.17 \times 126 = 21.42 , \text{amu}\)
-
Isotope \(^{128}\text{I}\):
- Percentage: 3%
- Fraction: \(0.03\)
- Atomic mass: \(128 , \text{amu}\)
- Contribution: \(0.03 \times 128 = 3.84 , \text{amu}\)
Now, we can add together all of the contributions:
\[ \text{Average Atomic Mass} = 101.6 + 21.42 + 3.84 = 126.86 , \text{amu} \]
Thus, the average atomic mass of iodine is approximately \( \mathbf{126.86} , \text{amu} \).