Final answer:
To calculate the relative abundance of boron-10 (B-10) and boron-11 (B-11), use the average atomic mass of boron (10.80 amu) and solve the equation that sets it equal to a weighted average of the isotopes' masses. Solve for the abundance of one isotope and subtract from 100% to find the other.
Step-by-step explanation:
The question is asking to calculate the relative abundance of each isotope of boron given that the average atomic mass is 10.80 amu. To find the relative abundance of boron-10 (B-10) and boron-11 (B-11), we set up the equation based on the weighted average of their masses:
average atomic mass = (% abundance of B-10) × (mass of B-10) + (% abundance of B-11) × (mass of B-11)
Since the question does not provide specific abundances, we let x represent the abundance of B-10, and thus (1-x) will be the abundance of B-11 because the total abundance must equal 100%. Now we write the equation as follows:
10.80 amu = (x) × 10.0129 amu + (1-x) × 11.00931 amu
We then solve for x to find the percentage abundance for B-10, and subtract that from 100% to find the percentage abundance for B-11. Once we have both values, we have determined the relative abundance of the isotopes.
Please note: The example assumes the isotopes have the masses of exactly 10 and 11 amu for simplification, whereas actual isotopic masses are typically more precise (e.g., 10.0129 amu for B-10).
To verify the answer, one could consult the Periodic Table of the Elements which should confirm the average atomic mass of boron (boron average mass).