An element A exist in two isotopic forms `A^15` and `A^16` . If the average atomic mass of A was found to be 15.24, then the % relative abundance of `A^15` will be

Options

A. 0.1
B. 0.2
C. 0.4
D. 0.76

Answer

To find the percentage relative abundance of the isotopic form \( A^{15} \) given the average atomic mass of element A is 15.24, we can use the following steps:

### Step 1: Define Variables
Let:
- \( x \) = percentage relative abundance of \( A^{15} \)
- \( 100 - x \) = percentage relative abundance of \( A^{16} \)

### Step 2: Set Up the Equation for Average Atomic Mass
The average atomic mass can be calculated using the formula:
\[ \text{Average Atomic Mass} = \frac{(x \cdot 15) + ((100 - x) \cdot 16)}{100} \]
Given that the average atomic mass is 15.24, we can set up the equation:
\[ 15.24 = \frac{(x \cdot 15) + ((100 - x) \cdot 16)}{100} \]

### Step 3: Clear the Denominator
Multiply both sides of the equation by 100 to eliminate the fraction:
\[ 15.24 \cdot 100 = (x \cdot 15) + ((100 - x) \cdot 16) \]
\[ 1524 = 15x + 1600 - 16x \]

### Step 4: Simplify the Equation
Combine like terms:
\[ 1524 = 1600 - x \]
Rearranging gives:
\[ x = 1600 - 1524 \]
\[ x = 76 \]

### Step 5: Calculate Percentage Relative Abundance
Since \( x \) represents the percentage relative abundance of \( A^{15} \):
\[ \text{Percentage of } A^{15} = 76\% \]

### Final Answer
The percentage relative abundance of \( A^{15} \) is **76%**.

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