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 use the weighted average formula based on the relative abundances and masses of its naturally occurring isotopes:
[
\text{Atomic Mass} = (\% \text{ abundance of isotope 1} \times \text{ mass of isotope 1}) + (\% \text{ abundance of isotope 2} \times \text{ mass of isotope 2}) + (\% \text{ abundance of isotope 3} \times \text{ mass of isotope 3})
]
Given Data:
- Isotope 1: 2.50% (0.0250 fraction) with a mass of 26.0 amu
- Isotope 2: 75.0% (0.750 fraction) with a mass of 27.0 amu
- Isotope 3: 22.5% (0.225 fraction) with a mass of 28.0 amu
Step-by-Step Calculation:
[
\text{Atomic Mass} = (0.0250 \times 26.0) + (0.750 \times 27.0) + (0.225 \times 28.0)
]
[
= (0.650) + (20.25) + (6.30)
]
[
= 27.2 \text{ amu}
]
Answer:
The atomic mass of athenium is 27.2 amu, which corresponds to option D.
Explanation:
The atomic mass of an element is the weighted average of the masses of its isotopes, based on their natural abundances. Since 75% of athenium atoms have a mass of 27.0 amu, this isotope has the highest contribution to the average atomic mass. The other isotopes (26.0 amu at 2.5% and 28.0 amu at 22.5%) contribute less but still influence the final value.
Since the majority of the atoms have a mass of 27.0 amu, the final atomic mass is close to this value but slightly higher due to the contribution of the heavier 28.0 amu isotope. The presence of the 26.0 amu isotope pulls the average down slightly but not enough to offset the heavier isotope.
Thus, the correct answer is 27.2 amu (D).
