Atomic weight of chlorine is 35.5 . It has two isotopes of atomic weight 35 and 37 . What is the percentage of the heavier isotope in the sample ?

Options

A. 5
B. 10
C. 25
D. 20

Answer

To find the percentage of the heavier isotope of chlorine (atomic weight 37) in a sample, we can follow these steps:

### Step 1: Define Variables
Let:
- \( x \) = percentage of the lighter isotope (atomic weight 35)
- \( 100 - x \) = percentage of the heavier isotope (atomic weight 37)

### Step 2: Set Up the Equation
The average atomic weight of chlorine is given as 35.5. The average atomic weight can be calculated using the formula:
\[ \text{Average Atomic Weight} = \left( \text{Atomic Weight of Isotope 1} \times \frac{\text{Percentage of Isotope 1}}{100} \right) + \left( \text{Atomic Weight of Isotope 2} \times \frac{\text{Percentage of Isotope 2}}{100} \right) \]
Substituting the known values:
\[ 35.5 = \left( 35 \times \frac{x}{100} \right) + \left( 37 \times \frac{100 - x}{100} \right) \]

### Step 3: Simplify the Equation
Multiply through by 100 to eliminate the denominator:
\[ 3550 = 35x + 37(100 - x) \]
Expanding the equation:
\[ 3550 = 35x + 3700 - 37x \]
Combine like terms:
\[ 3550 = 3700 - 2x \]

### Step 4: Solve for \( x \)
Rearranging gives:
\[ 2x = 3700 - 3550 \]
\[ 2x = 150 \]
\[ x = 75 \]

### Step 5: Find the Percentage of the Heavier Isotope
Now, we can find the percentage of the heavier isotope:
\[ \text{Percentage of heavier isotope} = 100 - x = 100 - 75 = 25 \]

### Conclusion
The percentage of the heavier isotope (atomic weight 37) in the sample is **25%**.

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