Three naturally occurring isotopes exist for the hypothetical element athenium. 2.50% of athenium atoms have a relative mass of 26.0 amu, 75.0% of athenium atoms have a relative mass of 27.0 amu, and 22.5% of athenium atoms have a relative mass of 28.0 amu. What is the atomic mass of athenium?
A) 26.8 amu
B) 27.0 amu
C) 28.0 amu
D) 27.2 amu
The correct answer and explanation is :
To determine the atomic mass of the hypothetical element athenium, we need to calculate the weighted average of its isotopes’ masses, considering their relative abundances. The formula for this calculation is:
Atomic Mass = (Fraction of Isotope 1 × Mass of Isotope 1) + (Fraction of Isotope 2 × Mass of Isotope 2) + (Fraction of Isotope 3 × Mass of Isotope 3)
Given data:
- Isotope 1: 2.50% abundance with a mass of 26.0 amu
- Isotope 2: 75.0% abundance with a mass of 27.0 amu
- Isotope 3: 22.5% abundance with a mass of 28.0 amu
First, convert the percentage abundances to decimal fractions:
- 2.50% → 0.025
- 75.0% → 0.750
- 22.5% → 0.225
Now, apply the formula:
Atomic Mass = (0.025 × 26.0 amu) + (0.750 × 27.0 amu) + (0.225 × 28.0 amu)
Calculating each term:
- 0.025 × 26.0 amu = 0.65 amu
- 0.750 × 27.0 amu = 20.25 amu
- 0.225 × 28.0 amu = 6.30 amu
Summing these values:
0.65 amu + 20.25 amu + 6.30 amu = 27.2 amu
Therefore, the atomic mass of athenium is 27.2 amu.
Answer: D) 27.2 amu
This method of calculating the atomic mass is standard in chemistry, where the atomic mass of an element is defined as the weighted average mass of its naturally occurring isotopes, reflecting both their masses and relative abundances.