To determine the average atomic mass of element [tex]\( M \)[/tex] given the relative abundances and atomic masses of its isotopes, follow these steps:
1. List the given data:
- Relative abundances ([tex]\( \% \)[/tex]) of the isotopes:
- Isotope 1: [tex]\( 78.99\% \)[/tex]
- Isotope 2: [tex]\( 10.00\% \)[/tex]
- Isotope 3: [tex]\( 11.01\% \)[/tex]
- Atomic masses ([tex]\( \text{amu} \)[/tex]) of the isotopes:
- Isotope 1: [tex]\( 23.9850 \text{ amu} \)[/tex]
- Isotope 2: [tex]\( 24.9858 \text{ amu} \)[/tex]
- Isotope 3: [tex]\( 25.9826 \text{ amu} \)[/tex]
2. Convert the relative abundances to fractions:
- Isotope 1: [tex]\( \frac{78.99}{100} = 0.7899 \)[/tex]
- Isotope 2: [tex]\( \frac{10.00}{100} = 0.1000 \)[/tex]
- Isotope 3: [tex]\( \frac{11.01}{100} = 0.1101 \)[/tex]
3. Multiply each atomic mass by its respective fractional abundance:
- Contribution of Isotope 1: [tex]\( 0.7899 \times 23.9850 = 18.9521815 \)[/tex]
- Contribution of Isotope 2: [tex]\( 0.1000 \times 24.9858 = 2.49858 \)[/tex]
- Contribution of Isotope 3: [tex]\( 0.1101 \times 25.9826 = 2.85425426 \)[/tex]
4. Sum these contributions to get the weighted average atomic mass:
[tex]\[
\text{Average atomic mass} = 18.9521815 + 2.49858 + 2.85425426 = 24.30501576
\][/tex]
Therefore, the average atomic mass of element [tex]\( M \)[/tex] is:
[tex]\[
\boxed{24.30 \, \text{amu}}
\][/tex]
