To determine the average atomic mass of the element based on the given data, we utilize a weighted average calculation. Here's the step-by-step process:
1. Identify the given data:
- Mass of isotope 1 ([tex]\( m_1 \)[/tex]) = 35.0 amu
- Abundance of isotope 1 ([tex]\( a_1 \)[/tex]) = 75.77%
- Mass of isotope 2 ([tex]\( m_2 \)[/tex]) = 37.0 amu
- Abundance of isotope 2 ([tex]\( a_2 \)[/tex]) = 24.23%
2. Convert the percentage abundances into decimal form:
[tex]\[
\text{Abundance of isotope 1} = \frac{75.77}{100} = 0.7577
\][/tex]
[tex]\[
\text{Abundance of isotope 2} = \frac{24.23}{100} = 0.2423
\][/tex]
3. Calculate the contribution of each isotope to the average atomic mass:
- Contribution of isotope 1 = [tex]\( m_1 \times a_1 \)[/tex]
- Contribution of isotope 2 = [tex]\( m_2 \times a_2 \)[/tex]
4. Perform the calculations:
[tex]\[
\text{Contribution of isotope 1} = 35.0 \times 0.7577 = 26.5195
\][/tex]
[tex]\[
\text{Contribution of isotope 2} = 37.0 \times 0.2423 = 8.9651
\][/tex]
5. Sum the contributions to get the average atomic mass:
[tex]\[
\text{Average Atomic Mass} = 26.5195 + 8.9651 = 35.4846
\][/tex]
Thus, the average atomic mass of the element is 35.4846 amu. This value is closest to 35.5 amu among the given options. Therefore, the answer is:
35.5 amu.
