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 calculate the percentage of abundance of the isotopes B-10 and B-11 of boron, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = percentage abundance of B-10
- \( 100 - x \) = percentage abundance of B-11

### Step 2: Set Up the Equation for Average Atomic Mass
The average atomic mass of boron is given as 10.80 u. The equation for the average atomic mass based on the abundances of the isotopes can be set up as follows:

\[ \text{Average Atomic Mass} = \frac{(x \cdot 10) + ((100 - x) \cdot 11)}{100} \]

### Step 3: Substitute the Average Atomic Mass
Substituting the average atomic mass into the equation, we have:

\[ 10.80 = \frac{(x \cdot 10) + ((100 - x) \cdot 11)}{100} \]

### Step 4: Clear the Denominator
Multiply both sides of the equation by 100 to eliminate the denominator:

\[ 10.80 \cdot 100 = (x \cdot 10) + ((100 - x) \cdot 11) \]

This simplifies to:

\[ 1080 = 10x + 1100 - 11x \]

### Step 5: Combine Like Terms
Rearranging the equation gives:

\[ 1080 = 1100 - x \]

### Step 6: Solve for \( x \)
Now, isolate \( x \):

\[ x = 1100 - 1080 \]
\[ x = 20 \]

### Step 7: Calculate the Abundance of Each Isotope
Now that we have \( x \):
- The abundance of B-10 is \( 20\% \).
- The abundance of B-11 is \( 100 - x = 100 - 20 = 80\% \).

### Final Answer
- Percentage abundance of B-10 = 20%
- Percentage abundance of B-11 = 80%

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