To determine the average atomic mass of element [tex]\( M \)[/tex] based on the given isotopes and their relative abundances, we follow these steps:
1. Convert the Relative Abundances to Decimals:
The given relative abundances are in percentages and need to be converted to decimals.
[tex]\[
78.99\% = 0.7899, \quad 10.00\% = 0.1000, \quad 11.01\% = 0.1101
\][/tex]
2. Calculate the Weighted Average Atomic Mass:
The average atomic mass is calculated by multiplying the decimal abundance of each isotope by its corresponding atomic mass and summing up these products.
Using the given values:
- For the isotope with an atomic mass of 23.9850 amu:
[tex]\[
0.7899 \times 23.9850 = 18.9505115
\][/tex]
- For the isotope with an atomic mass of 24.9858 amu:
[tex]\[
0.1000 \times 24.9858 = 2.49858
\][/tex]
- For the isotope with an atomic mass of 25.9826 amu:
[tex]\[
0.1101 \times 25.9826 = 2.85592426
\][/tex]
3. Sum the Products:
Adding these values together gives the average atomic mass:
[tex]\[
18.9505115 + 2.49858 + 2.85592426 = 24.30501576
\][/tex]
So, the average atomic mass of element [tex]\( M \)[/tex] is approximately [tex]\( 24.30 \)[/tex] amu. Therefore, the correct answer is:
[tex]\[
\boxed{24.30}
\][/tex]
