To find the average atomic weight of the element, we use the formula for the weighted average, taking into account the abundance and atomic weight of each isotope:

$\text{Average Atomic Weight} = \left( \frac{\text{Abundance}_1}{100} \times \text{Atomic Weight}_1 \right) + \left( \frac{\text{Abundance}_2}{100} \times \text{Atomic Weight}_2 \right) + \left( \frac{\text{Abundance}_3}{100} \times \text{Atomic Weight}_3 \right)$

Given:

• Abundance of isotope 1: $92.21\%$
• Atomic weight of isotope 1: $27.97693 \, \text{amu}$
• Abundance of isotope 2: $4.70\%$
• Atomic weight of isotope 2: $28.97649 \, \text{amu}$
• Abundance of isotope 3: $(100\% - 92.21\% - 4.70\%) = 3.09\%$
• Atomic weight of isotope 3: $29.97376 \, \text{amu}$

Substitute these values into the formula:

$\text{Average Atomic Weight} = \left( \frac{92.21}{100} \times 27.97693 \right) + \left( \frac{4.70}{100} \times 28.97649 \right) + \left( \frac{3.09}{100} \times 29.97376 \right)$

Now, calculate each term:

$\frac{92.21}{100} \times 27.97693 = 25.79318$ $\frac{4.70}{100} \times 28.97649 = 1.36289$ $\frac{3.09}{100} \times 29.97376 = 0.92620$

Adding these together:

$\text{Average Atomic Weight} = 25.79318 + 1.36289 + 0.92620 = 28.08227 \, \text{amu}$

Thus, the average atomic weight of the element is approximately 28.082 amu.

Would you like further details or have any questions? Here are 5 related questions you might want to explore:

1. What is the significance of isotopes in determining atomic weight?
2. How do isotopes affect the chemical behavior of an element?
3. Can the percentage abundance of isotopes vary in nature?
4. How are atomic weights measured experimentally?
5. What is the relationship between atomic weight and molar mass?

Tip: When calculating weighted averages, make sure the percentages add up to 100% to avoid calculation errors.