To determine the average atomic mass of element M, we need to account for both the relative abundances and the atomic masses of its isotopes. Here’s the step-by-step process to calculate the average atomic mass:
1. List the given relative abundances and atomic masses:
- Relative abundance of isotope 1: [tex]\( 78.99\% \)[/tex]
- Atomic mass of isotope 1: [tex]\( 23.9850 \, \text{amu} \)[/tex]
- Relative abundance of isotope 2: [tex]\( 10.00\% \)[/tex]
- Atomic mass of isotope 2: [tex]\( 24.9858 \, \text{amu} \)[/tex]
- Relative abundance of isotope 3: [tex]\( 11.01\% \)[/tex]
- Atomic mass of isotope 3: [tex]\( 25.9826 \, \text{amu} \)[/tex]
2. Convert the relative abundances from percentages to decimal form by dividing by 100:
- Relative abundance of isotope 1: [tex]\( 0.7899 \)[/tex]
- Relative abundance of isotope 2: [tex]\( 0.1000 \)[/tex]
- Relative abundance of isotope 3: [tex]\( 0.1101 \)[/tex]
3. Multiply each isotope's atomic mass by its decimal relative abundance:
- Contribution of isotope 1: [tex]\( 23.9850 \times 0.7899 \)[/tex]
- Contribution of isotope 2: [tex]\( 24.9858 \times 0.1000 \)[/tex]
- Contribution of isotope 3: [tex]\( 25.9826 \times 0.1101 \)[/tex]
4. Sum these contributions:
- Contribution of isotope 1: [tex]\( 23.9850 \times 0.7899 = 18.9482 \, \text{amu} \)[/tex]
- Contribution of isotope 2: [tex]\( 24.9858 \times 0.1000 = 2.4986 \, \text{amu} \)[/tex]
- Contribution of isotope 3: [tex]\( 25.9826 \times 0.1101 = 2.8582 \, \text{amu} \)[/tex]
- Total = [tex]\( 18.9482 + 2.4986 + 2.8582 = 24.3050 \, \text{amu} \)[/tex]
5. Hence, the average atomic mass of element M is:
[tex]\[
24.3050 \, \text{amu}
\][/tex]
Looking at the given choices:
- 2.86
- 5.36
- 24.30
- 24.98
The correct answer is:
[tex]\[
\boxed{24.30}
\][/tex]
