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 find the atomic mass of athenium, we need to calculate the weighted average of the masses of its isotopes. The weighted average takes into account both the mass of each isotope and its relative abundance. Here’s the step-by-step process:
Step 1: List the isotopes and their abundances
- Isotope 1: Mass = 26.0 amu, Abundance = 2.50% or 0.0250
- Isotope 2: Mass = 27.0 amu, Abundance = 75.0% or 0.750
- Isotope 3: Mass = 28.0 amu, Abundance = 22.5% or 0.225
Step 2: Calculate the contribution of each isotope to the atomic mass
The contribution of each isotope to the atomic mass is found by multiplying the mass of the isotope by its fractional abundance.
- For Isotope 1:
[
26.0 \, \text{amu} \times 0.0250 = 0.65 \, \text{amu}
] - For Isotope 2:
[
27.0 \, \text{amu} \times 0.750 = 20.25 \, \text{amu}
] - For Isotope 3:
[
28.0 \, \text{amu} \times 0.225 = 6.30 \, \text{amu}
]
Step 3: Add the contributions to find the total atomic mass
Now, sum the contributions of each isotope to get the total atomic mass:
[
0.65 + 20.25 + 6.30 = 27.20 \, \text{amu}
]
Step 4: Conclusion
The atomic mass of athenium is 27.2 amu.
Thus, the correct answer is D) 27.2 amu.
Explanation
The atomic mass of an element is the weighted average mass of all its isotopes, accounting for both their individual masses and their relative abundances. Since 75% of athenium atoms have a mass of 27.0 amu, this isotope contributes the most to the atomic mass. Although the other two isotopes (with masses of 26.0 amu and 28.0 amu) also contribute, their lower abundances mean they have less influence on the final value. By calculating the weighted average, we find that the atomic mass of athenium is closest to 27.2 amu.
