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 in a sample, we can follow these steps:

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

### Step 2: Set up the equation based on average atomic weight
The average atomic weight of chlorine is given as 35.5. We can express this as:
\[ \text{Average Atomic Weight} = \frac{(35 \times (100 - x)) + (37 \times x)}{100} \]
Setting this equal to 35.5 gives us:
\[ 35.5 = \frac{(35 \times (100 - x)) + (37 \times x)}{100} \]

### Step 3: Multiply through by 100 to eliminate the denominator
\[ 3550 = 35 \times (100 - x) + 37x \]

### Step 4: Expand the equation
\[ 3550 = 3500 - 35x + 37x \]
\[ 3550 = 3500 + 2x \]

### Step 5: Rearrange to solve for \( x \)
Subtract 3500 from both sides:
\[ 50 = 2x \]
Now, divide by 2:
\[ x = 25 \]

### Step 6: Calculate the percentage of the lighter isotope
Since \( x \) is the percentage of the heavier isotope (Cl-37), the percentage of the lighter isotope (Cl-35) is:
\[ 100 - x = 100 - 25 = 75 \]

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

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