Question

the natural abundance for boron isotopes is 19.9% ^10 B and 80.1% ^11B. calculate boron's atomic mass.

Answer 1

To calculate the atomic mass of boron based on its isotopes and their natural abundances, we can use the following formula:

\[
\text{Atomic mass} = \left( \text{abundance of } ^{10}\text{B} \times \text{mass of } ^{10}\text{B} \right) + \left( \text{abundance of } ^{11}\text{B} \times \text{mass of } ^{11}\text{B} \right)
\]

Given:
- Abundance of \(^{10}\text{B} = 19.9\% = 0.199\)
- Abundance of \(^{11}\text{B} = 80.1\% = 0.801\)
- Mass of \(^{10}\text{B} \approx 10.012937\) u
- Mass of \(^{11}\text{B} \approx 11.009305\) u

Now, we can substitute the values:

\[
\text{Atomic mass} = (0.199 \times 10.012937) + (0.801 \times 11.009305)
\]

Calculating each part:

1. For \(^{10}\text{B}\):

\[
0.199 \times 10.012937 \approx 1.993
\]

2. For \(^{11}\text{B}\):

\[
0.801 \times 11.009305 \approx 8.817
\]

Now, adding these two results together:

\[
\text{Atomic mass} \approx 1.993 + 8.817 \approx 10.81 \text{ u}
\]

Therefore, the atomic mass of boron is approximately **10.81 u**.