To find the average atomic mass of an element given the masses of its isotopes and their respective abundances, you need to compute a weighted average. This method involves multiplying each isotope's mass by its relative abundance (expressed as a fraction), and then summing the results. Here is the step-by-step solution:
1. List the given data:
- Masses (amu): [tex]\(24.0, 25.0, 26.0\)[/tex]
- Abundances (%): [tex]\(78.99, 10.0, 11.01\)[/tex]
2. Convert the abundances from percentage to fraction:
- [tex]\(78.99\% = 0.7899\)[/tex]
- [tex]\(10.0\% = 0.10\)[/tex]
- [tex]\(11.01\% = 0.1101\)[/tex]
3. Multiply each mass by its corresponding fractional abundance:
- Mass 24.0 amu with abundance 0.7899: [tex]\(24.0 \times 0.7899 = 18.9576\)[/tex]
- Mass 25.0 amu with abundance 0.10: [tex]\(25.0 \times 0.10 = 2.5\)[/tex]
- Mass 26.0 amu with abundance 0.1101: [tex]\(26.0 \times 0.1101 = 2.8626\)[/tex]
4. Sum the products:
- [tex]\(18.9576 + 2.5 + 2.8626 = 24.3202\)[/tex]
5. Conclusion:
The average atomic mass of the element is [tex]\(24.3202\)[/tex] amu, which is closest to the option [tex]\(24.3 \, \text{amu}\)[/tex].
So, the average atomic mass of the element is [tex]\(24.3\)[/tex] amu.
