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:
- For \(^{10}\text{B}\):
\[ 0.199 \times 10.012937 \approx 1.993 \]
- 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.