Boron has two stable isotopes, `.^(10)B(19%)` and `.^(11)B(81%)`. The atomic mass that should appear for boron in the periodic table is

Options

A. 10.8
B. 10.2
C. 11.2
D. 10

Explanation

To calculate the atomic mass of boron based on its isotopes and their abundances, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Isotopes and Their Abundances**:
- Boron has two stable isotopes:
- Isotope 1: \( ^{10}B \) with an atomic mass of 10 and an abundance of 19%
- Isotope 2: \( ^{11}B \) with an atomic mass of 11 and an abundance of 81%

2. **Convert Percentages to Decimal Form**:
- The abundance of \( ^{10}B \) in decimal form is \( 19\% = 0.19 \).
- The abundance of \( ^{11}B \) in decimal form is \( 81\% = 0.81 \).

3. **Use the Formula for Average Atomic Mass**:
- The average atomic mass (or relative atomic mass) can be calculated using the formula:
\[ \text{Average Atomic Mass} = \frac{(a_1 \cdot x_1) + (a_2 \cdot x_2)}{100} \]
- Where \( a_1 \) and \( a_2 \) are the atomic masses of the isotopes, and \( x_1 \) and \( x_2 \) are their respective abundances.

4. **Substitute the Values into the Formula**:
- For boron:
\[ \text{Average Atomic Mass} = \frac{(10 \cdot 19) + (11 \cdot 81)}{100} \]

5. **Calculate Each Component**:
- Calculate \( 10 \cdot 19 = 190 \).
- Calculate \( 11 \cdot 81 = 891 \).

6. **Add the Results**:
- Add the two results: \( 190 + 891 = 1081 \).

7. **Divide by 100**:
- Finally, divide by 100 to get the average atomic mass:
\[ \text{Average Atomic Mass} = \frac{1081}{100} = 10.81 \text{ AMU} \]

8. **Conclusion**:
- The atomic mass that should appear for boron in the periodic table is **10.81 AMU**.