Iodine is 80% 127I, 17% 126I, and 3% 128I. Calculate the average atomic mass of Iodine.
The Correct Answer and Explanation is:
To calculate the average atomic mass of iodine, we consider the masses and relative abundances of its isotopes. The formula for average atomic mass is:
[
\text{Average atomic mass} = (\text{mass of isotope 1} \times \text{fractional abundance 1}) + (\text{mass of isotope 2} \times \text{fractional abundance 2}) + (\text{mass of isotope 3} \times \text{fractional abundance 3})
]
Given Data:
- ( ^{127}\text{I} ): 80% (0.80 fractional abundance), mass = 127 u
- ( ^{126}\text{I} ): 17% (0.17 fractional abundance), mass = 126 u
- ( ^{128}\text{I} ): 3% (0.03 fractional abundance), mass = 128 u
Calculation:
[
\text{Average atomic mass} = (127 \times 0.80) + (126 \times 0.17) + (128 \times 0.03)
]
Step 1: Calculate contributions of each isotope.
- Contribution of ( ^{127}\text{I} ): ( 127 \times 0.80 = 101.6 )
- Contribution of ( ^{126}\text{I} ): ( 126 \times 0.17 = 21.42 )
- Contribution of ( ^{128}\text{I} ): ( 128 \times 0.03 = 3.84 )
Step 2: Add contributions.
[
\text{Average atomic mass} = 101.6 + 21.42 + 3.84 = 126.86 \, \text{u}
]
Explanation:
The average atomic mass of an element reflects the weighted average of the masses of all its naturally occurring isotopes, based on their relative abundances. Each isotope contributes to the average based on how commonly it occurs in nature. Here, ( ^{127}\text{I} ) is the most abundant isotope, so it contributes the most to the average mass, while ( ^{126}\text{I} ) and ( ^{128}\text{I} ) contribute less due to their lower abundances. This weighted approach ensures the calculated value reflects the actual mass of iodine atoms as found in nature. The result, 126.86 u, closely matches iodine’s tabulated atomic mass.