To determine the average atomic mass of the element given the data table, we need to follow these steps:
1. Identify the masses and abundances:
- 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 to decimals:
- Decimal abundance of isotope 1 ([tex]\(a_1\_dec\)[/tex]): [tex]\( \frac{75.77}{100} \approx 0.7577 \)[/tex]
- Decimal abundance of isotope 2 ([tex]\(a_2\_dec\)[/tex]): [tex]\( \frac{24.23}{100} \approx 0.2423 \)[/tex]
3. Calculate the weighted average atomic mass:
- Use the formula:
[tex]\[
\text{Average Atomic Mass} = (m_1 \times a_1\_dec) + (m_2 \times a_2\_dec)
\][/tex]
- Substitute in the values:
[tex]\[
\text{Average Atomic Mass} = (35.0 \, \text{amu} \times 0.7577) + (37.0 \, \text{amu} \times 0.2423)
\][/tex]
4. Perform the multiplication for each component:
- Component 1: [tex]\( 35.0 \times 0.7577 = 26.52 \)[/tex]
- Component 2: [tex]\( 37.0 \times 0.2423 = 8.97 \)[/tex]
5. Add the results from the two components together to get the average atomic mass:
- Total: [tex]\( 26.52 + 8.97 = 35.49 \)[/tex]
Thus, the average atomic mass of the element is approximately 35.5 amu. The correct choice from the provided options is:
35.5 amu
