Concept:The average atomic mass of an element is the weighted sum of the masses of its constituent isotopes, determined by their relative percentage abundances.
Formula:$$ \text{Avg Mass} = \left( \text{Mass}_1 \times \frac{x}{100} \right) + \left( \text{Mass}_2 \times \frac{100 - x}{100} \right) $$
Solution:- Let the percentage abundance of Boron-10 be \( x\% \).
- Therefore, the percentage abundance of Boron-11 is \( (100 - x)\% \).
- Set up the equation based on the given average mass (10.8):
\( 10.8 = \frac{(10 \times x) + (11 \times (100 - x))}{100} \)
- Multiply by 100: \( 1080 = 10x + 1100 - 11x \).
- Simplify: \( 1080 - 1100 = -x \).
- \( -20 = -x \rightarrow x = 20 \).
- The abundance of the isotope with mass 10 is 20%.
Why other options are incorrect:- 80%: This is the percentage of the heavier Boron-11 isotope. Students commonly misread which isotope the question is asking for.
- 60% & 50%: These do not mathematically satisfy the weighted average of 10.8.
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