To determine the average atomic mass of element M, we need to calculate the weighted average of the atomic masses, considering their relative abundances. Here’s a step-by-step process to solve the problem:
1. List the given relative abundances and atomic masses:
- 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. Convert the relative abundances into decimal form:
- Isotope 1: 78.99% = 0.7899
- Isotope 2: 10.00% = 0.1000
- Isotope 3: 11.01% = 0.1101
3. Multiply each atomic mass by its corresponding relative abundance (in decimal form):
- Contribution of Isotope 1 to average atomic mass:
[tex]\[
23.9850 \, \text{amu} \times 0.7899 \approx 18.950415 \, \text{amu}
\][/tex]
- Contribution of Isotope 2 to average atomic mass:
[tex]\[
24.9858 \, \text{amu} \times 0.1000 \approx 2.49858 \, \text{amu}
\][/tex]
- Contribution of Isotope 3 to average atomic mass:
[tex]\[
25.9826 \, \text{amu} \times 0.1101 \approx 2.85502076 \, \text{amu}
\][/tex]
4. Sum the contributions from all isotopes to find the average atomic mass:
[tex]\[
18.950415 + 2.49858 + 2.85502076 \approx 24.30501576 \, \text{amu}
\][/tex]
5. Round the result to a reasonable number of decimal places. Considering that atomic masses are often presented to three or four significant figures, the average atomic mass can be rounded to four decimal places:
[tex]\[
24.3050 \, \text{amu}
\][/tex]
After evaluating the options:
- 2.86
- 5.36
- 24.30
- 24.98
The answer closest to our calculation is 24.30 amu.
Thus, the average atomic mass of element M is approximately 24.30 amu.
