Atomic weight of ` Ne` is ` 20.2 Ne` is a mixuture of ` Ne^(20)` and ` Ne^(22)`. Relative abunduance fo heavior isotope is :

Options

A. ` 90`
B. `20`
C. `40`
D. `10`

Explanation

To find the relative abundance of the heavier isotope \( Ne^{22} \) in a mixture of \( Ne^{20} \) and \( Ne^{22} \) given that the average atomic weight of neon is 20.2, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = relative abundance of \( Ne^{20} \)
- \( 1 - x \) = relative abundance of \( Ne^{22} \)

### Step 2: Set Up the Equation
The average atomic weight can be expressed as:
\[ \text{Average Atomic Weight} = (x \cdot 20) + ((1 - x) \cdot 22) \]
Given that the average atomic weight of neon is 20.2, we can set up the equation:
\[ 20.2 = 20x + 22(1 - x) \]

### Step 3: Simplify the Equation
Now, simplify the equation:
\[ 20.2 = 20x + 22 - 22x \]
Combine like terms:
\[ 20.2 = 22 - 2x \]

### Step 4: Solve for \( x \)
Rearranging gives:
\[ 2x = 22 - 20.2 \]
\[ 2x = 1.8 \]
\[ x = \frac{1.8}{2} = 0.9 \]

### Step 5: Calculate the Relative Abundance of \( Ne^{22} \)
Since \( x \) is the abundance of \( Ne^{20} \), the abundance of \( Ne^{22} \) is:
\[ 1 - x = 1 - 0.9 = 0.1 \]
To express this as a percentage:
\[ \text{Relative abundance of } Ne^{22} = 0.1 \times 100\% = 10\% \]

### Final Answer
The relative abundance of the heavier isotope \( Ne^{22} \) is **10%**.

---