To find the average atomic mass of element [tex]\( M \)[/tex], we need to use the relative abundances and atomic masses of its isotopes. We will calculate the weighted average of the atomic masses based on their relative abundances.
Here are the steps to solve the problem:
1. List the given data:
- Relative abundances: 78.99%, 10.00%, and 11.01%.
- Atomic masses: 23.9850 amu, 24.9858 amu, and 25.9826 amu.
2. Convert the relative abundances from percentages to decimal form:
- The relative abundance for the first isotope: [tex]\( 78.99 / 100 = 0.7899 \)[/tex]
- The relative abundance for the second isotope: [tex]\( 10.00 / 100 = 0.1000 \)[/tex]
- The relative abundance for the third isotope: [tex]\( 11.01 / 100 = 0.1101 \)[/tex]
3. Multiply each atomic mass by its corresponding relative abundance:
- Contribution from the first isotope: [tex]\( 23.9850 \times 0.7899 \)[/tex]
- Contribution from the second isotope: [tex]\( 24.9858 \times 0.1000 \)[/tex]
- Contribution from the third isotope: [tex]\( 25.9826 \times 0.1101 \)[/tex]
4. Calculate each multiplication:
- [tex]\( 23.9850 \times 0.7899 = 18.9485015 \)[/tex]
- [tex]\( 24.9858 \times 0.1000 = 2.49858 \)[/tex]
- [tex]\( 25.9826 \times 0.1101 = 2.85793426 \)[/tex]
5. Add the contributions together:
- [tex]\( 18.9485015 + 2.49858 + 2.85793426 = 24.30501576 \)[/tex]
6. Round the final result to an appropriate number of significant figures if necessary:
- The final result is [tex]\( 24.30501576 \)[/tex] amu, which we can round to [tex]\( 24.30 \)[/tex] amu as it matches the precision of the given data.
Thus, the average atomic mass of element [tex]\( M \)[/tex] is [tex]\( \boxed{24.30} \)[/tex] amu.
