Boron, which has an average atomic mass of 10.81 amu, has two stable isotopes: boron-10 and boron-11. Boron-10 has an atomic mass of 10.0129 amu and a natural abundance of 19.78%. What is the atomic mass of boron-11?
The Correct Answer and Explanation is :
To calculate the atomic mass of boron-11, we use the concept of the weighted average atomic mass based on the natural abundances of the isotopes.
Given:
- The atomic mass of boron-10 (B-10) is 10.0129 amu, and its natural abundance is 19.78% (or 0.1978 in decimal form).
- The average atomic mass of boron is 10.81 amu.
- The remaining natural abundance of boron must be the abundance of boron-11 (B-11). Since the total abundance must add up to 100%, the natural abundance of boron-11 is 100% – 19.78% = 80.22% (or 0.8022 in decimal form).
Let’s define the atomic mass of boron-11 as ( x ). The weighted average atomic mass formula for boron is:
[
\text{Average Atomic Mass} = ( \text{atomic mass of B-10} \times \text{abundance of B-10} ) + ( \text{atomic mass of B-11} \times \text{abundance of B-11} )
]
Substituting the known values:
[
10.81 = (10.0129 \times 0.1978) + (x \times 0.8022)
]
First, calculate the contribution from boron-10:
[
10.0129 \times 0.1978 = 1.9801
]
Now substitute into the equation:
[
10.81 = 1.9801 + (x \times 0.8022)
]
Next, isolate ( x ):
[
10.81 – 1.9801 = x \times 0.8022
]
[
8.8299 = x \times 0.8022
]
Finally, solve for ( x ):
[
x = \frac{8.8299}{0.8022} \approx 11.01
]
Thus, the atomic mass of boron-11 is approximately 11.01 amu.
Explanation:
The average atomic mass of an element is the weighted sum of the masses of its isotopes, with each mass multiplied by the fraction of the element’s occurrence in nature. Boron-10 and boron-11 have different atomic masses and natural abundances. By setting up the equation based on these quantities, we can solve for the unknown atomic mass of boron-11. This calculation demonstrates how isotope abundance and mass contribute to an element’s average atomic mass, providing an essential understanding of atomic structure and properties.