lodine has three isotopes: 1271, 1261, and 1281. 1271 has a percent abundance of 80.00%, 126 has a relative abundance of 17.00%, and 1281 has a relative abundance of 3.00%. Calculate the average atomic mass of iodine.
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).
