The average atomic mass of an element A is 16.2 u. There are two isotopes `""_(8)^(16) A` and `""_(8)^(18)A` of an element. What will be the percentage of these two isotopes in element A ?

Options

A. 90%,10%
B. 10%,90%
C. 20%,80%
D. 80%,20%

Explanation

To find the percentage of the two isotopes of element A, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the percentage of isotope \( \text{A}_{8}^{16} \) be \( X \). Consequently, the percentage of isotope \( \text{A}_{8}^{18} \) will be \( 100 - X \).

2. **Set Up the Average Atomic Mass Equation**:
The average atomic mass (AAM) can be calculated using the formula:
\[ \text{AAM} = \frac{(X \cdot 16) + ((100 - X) \cdot 18)}{100} \]
We know the average atomic mass is given as 16.2 u. Therefore, we can set up the equation:
\[ \frac{(X \cdot 16) + ((100 - X) \cdot 18)}{100} = 16.2 \]

3. **Multiply Through by 100**:
To eliminate the fraction, multiply both sides of the equation by 100:
\[ (X \cdot 16) + ((100 - X) \cdot 18) = 1620 \]

4. **Expand the Equation**:
Expand the left side:
\[ 16X + 1800 - 18X = 1620 \]

5. **Combine Like Terms**:
Combine the terms involving \( X \):
\[ -2X + 1800 = 1620 \]

6. **Isolate \( X \)**:
Subtract 1800 from both sides:
\[ -2X = 1620 - 1800 \]
\[ -2X = -180 \]
Divide by -2:
\[ X = 90 \]

7. **Calculate the Percentage of Each Isotope**:
- The percentage of isotope \( \text{A}_{8}^{16} \) is \( X = 90\% \).
- The percentage of isotope \( \text{A}_{8}^{18} \) is \( 100 - X = 100 - 90 = 10\% \).

### Final Result:
- The percentage of isotope \( \text{A}_{8}^{16} \) is **90%**.
- The percentage of isotope \( \text{A}_{8}^{18} \) is **10%**.