To find the average atomic mass of element [tex]\( M \)[/tex], we will follow these steps:
1. Convert Relative Abundances to Fractions:
The relative abundances need to be converted from percentages to fractions.
[tex]\[
\text{Fraction for isotope 1} = \frac{78.99}{100} = 0.7899
\][/tex]
[tex]\[
\text{Fraction for isotope 2} = \frac{10.00}{100} = 0.1
\][/tex]
[tex]\[
\text{Fraction for isotope 3} = \frac{11.01}{100} = 0.1101
\][/tex]
2. Multiply Each Atomic Mass by its Corresponding Fractional Abundance:
Next, multiply the atomic mass of each isotope by its fractional abundance.
[tex]\[
\text{Contribution of isotope 1} = 23.9850 \times 0.7899 = 18.9500515
\][/tex]
[tex]\[
\text{Contribution of isotope 2} = 24.9858 \times 0.1 = 2.49858
\][/tex]
[tex]\[
\text{Contribution of isotope 3} = 25.9826 \times 0.1101 = 2.8563842599999998
\][/tex]
3. Add These Values to Get the Average Atomic Mass:
Finally, add the contributions from all isotopes to get the average atomic mass.
[tex]\[
\text{Average atomic mass} = 18.9500515 + 2.49858 + 2.8563842599999998 = 24.305015759999998
\][/tex]
Therefore, the average atomic mass of element [tex]\( M \)[/tex] is approximately [tex]\( 24.30 \)[/tex] amu. So, the correct answer is:
[tex]\[
\boxed{24.30}
\][/tex]
