The isotopes of chlorine with mass numbers 35 and 37 exist in the ratio of

Options

A. `1:1`
B. `2:1`
C. `3:1`
D. `3:2`

Explanation

To find the ratio of the isotopes of chlorine with mass numbers 35 and 37, we can follow these steps:

### Step-by-Step Solution:

1. **Define Variables**:
Let the fraction of chlorine-35 be \( x \) and the fraction of chlorine-37 be \( 1 - x \).

2. **Set Up the Equation**:
The average atomic mass of chlorine is given as 35.5. We can set up the equation based on the contributions of each isotope to the average atomic mass:
\[ 35x + 37(1 - x) = 35.5 \]

3. **Expand the Equation**:
Expanding the equation gives:
\[ 35x + 37 - 37x = 35.5 \]

4. **Combine Like Terms**:
Combine the terms involving \( x \):
\[ -2x + 37 = 35.5 \]

5. **Isolate \( x \)**:
Subtract 37 from both sides:
\[ -2x = 35.5 - 37 \]
\[ -2x = -1.5 \]

6. **Solve for \( x \)**:
Divide both sides by -2:
\[ x = \frac{1.5}{2} = \frac{3}{4} \]

7. **Find the Fraction of Chlorine-37**:
Now, calculate the fraction of chlorine-37:
\[ 1 - x = 1 - \frac{3}{4} = \frac{1}{4} \]

8. **Determine the Ratio**:
The ratio of chlorine-35 to chlorine-37 is:
\[ \frac{x}{1 - x} = \frac{\frac{3}{4}}{\frac{1}{4}} = \frac{3}{1} \]

9. **Final Answer**:
Therefore, the ratio of the isotopes of chlorine with mass numbers 35 and 37 is:
\[ 3 : 1 \]