To find the average atomic mass of element [tex]\( M \)[/tex], we first need to consider the atomic masses and relative abundances of its isotopes. The isotopes' data is provided in the table:
| Relative abundance (%) | Atomic mass (amu) |
|------------------------|-------------------|
| 78.99 | 23.9850 |
| 10.00 | 24.9858 |
| 11.01 | 25.9826 |
Here is the step-by-step process:
1. Convert the relative abundances from percentages to fractions:
[tex]\[
\text{Fractional abundance of isotope 1} = \frac{78.99}{100} = 0.7899
\][/tex]
[tex]\[
\text{Fractional abundance of isotope 2} = \frac{10.00}{100} = 0.10
\][/tex]
[tex]\[
\text{Fractional abundance of isotope 3} = \frac{11.01}{100} = 0.1101
\][/tex]
2. Use the formula for average atomic mass:
[tex]\[
\text{Average atomic mass} = (\text{fractional abundance of isotope 1} \times \text{atomic mass of isotope 1}) + (\text{fractional abundance of isotope 2} \times \text{atomic mass of isotope 2}) + (\text{fractional abundance of isotope 3} \times \text{atomic mass of isotope 3})
\][/tex]
3. Substitute the given values into the formula:
[tex]\[
\text{Average atomic mass} = (0.7899 \times 23.9850) + (0.10 \times 24.9858) + (0.1101 \times 25.9826)
\][/tex]
4. Compute each term:
[tex]\[
0.7899 \times 23.9850 = 18.945915
\][/tex]
[tex]\[
0.10 \times 24.9858 = 2.49858
\][/tex]
[tex]\[
0.1101 \times 25.9826 = 2.86052026
\][/tex]
5. Sum these values to get the average atomic mass:
[tex]\[
\text{Average atomic mass} = 18.945915 + 2.49858 + 2.86052026 = 24.30501576
\][/tex]
Therefore, the average atomic mass of element [tex]\( M \)[/tex] is approximately [tex]\( 24.30 \)[/tex] amu.
Hence, the correct answer is:
[tex]\[ \boxed{24.30} \][/tex]
