To determine the average atomic mass of element \( M \), we will use the weighted average formula, which considers both the relative abundance and the atomic mass of each isotope. Here are the steps involved:
1. List the given data:
- Isotope 1: Relative abundance = \( 78.99\% \), Atomic mass = \( 23.9850 \) amu
- Isotope 2: Relative abundance = \( 10.00\% \), Atomic mass = \( 24.9858 \) amu
- Isotope 3: Relative abundance = \( 11.01\% \), Atomic mass = \( 25.9826 \) amu
2. Calculate the weighted contribution of each isotope:
- Isotope 1 contribution = \( 0.7899 \times 23.9850 \)
- Isotope 2 contribution = \( 0.1000 \times 24.9858 \)
- Isotope 3 contribution = \( 0.1101 \times 25.9826 \)
3. Sum the contributions to get the total weighted atomic mass:
- Total weighted atomic mass = \( (0.7899 \times 23.9850) + (0.1000 \times 24.9858) + (0.1101 \times 25.9826) \)
4. Divide the total weighted atomic mass by \( 100 \) to find the average atomic mass:
- Average atomic mass = \(\frac{ (0.7899 \times 23.9850) + (0.1000 \times 24.9858) + (0.1101 \times 25.9826) }{100}\)
Performing these calculations, we find that the average atomic mass of element \( M \) is approximately:
\( 24.30 \)
Thus, the correct choice from the given options is:
24.30
