Boron has two isotopes, B-10 and B-11. The average atomic mass of boron is found to be 10.80u. Calculate the percentage of abundance of these isotopes.

Answer

To solve the problem of calculating the percentage of abundance of the isotopes B-10 and B-11 given the average atomic mass of boron as 10.80 u, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables:**
Let the percentage abundance of B-10 be \( X \) percent. Consequently, the percentage abundance of B-11 will be \( 100 - X \) percent.

2. **Set Up the Equation:**
The average atomic mass of boron can be expressed as a weighted average of the masses of its isotopes:
\[ \text{Average Atomic Mass} = \frac{(X \times 10) + ((100 - X) \times 11)}{100} \]
Given that the average atomic mass is 10.80 u, we can set up the equation:
\[ 10.80 = \frac{(X \times 10) + ((100 - X) \times 11)}{100} \]

3. **Clear the Denominator:**
Multiply both sides of the equation by 100 to eliminate the fraction:
\[ 1080 = 10X + (100 - X) \times 11 \]

4. **Expand the Equation:**
Distributing the terms on the right-hand side:
\[ 1080 = 10X + 1100 - 11X \]

5. **Combine Like Terms:**
Rearranging the equation gives:
\[ 1080 = 1100 - X \]
Now, isolate \( X \):
\[ X = 1100 - 1080 \]
\[ X = 20 \]

6. **Calculate Abundances:**
Now that we have \( X \):
- Percentage abundance of B-10: \( 20\% \)
- Percentage abundance of B-11: \( 100 - X = 100 - 20 = 80\% \)

### Final Answer:
- The percentage of abundance of B-10 is **20%**.
- The percentage of abundance of B-11 is **80%**.