Chemistry

Question Analysis
This question involves calculating the percent abundance of a specific isotope (B-11) using the element’s average atomic mass and the masses of its two isotopes.
The main focus is on setting up and solving a linear algebraic equation for isotope abundances (a core skill for two-isotope problems).

Key Concept Explanation
For an element with two isotopes:
Let = percent abundance of isotope 1 (in %), so the percent abundance of isotope 2 = .
Convert percentages to decimals (divide by 100) for calculation: isotope 1 = , isotope 2 = .
Average atomic mass = (mass of isotope 1 × decimal abundance₁) + (mass of isotope 2 × decimal abundance₂).

Step-by-Step Solution
1. Define variables:
Let = percent abundance of B-10 (in %), so decimal abundance = .
Percent abundance of B-11 = , decimal abundance = .
2. Set up the average atomic mass equation:

3. Simplify and solve for :
Multiply both sides by 100 to eliminate denominators: