The ratio of rate of diffusion for two gases is 1 : 2 if their molecular masses :-

Options

A. `16.1`
B. `1:16`
C. `1:4`
D. `4:1`

Explanation

To solve the problem of finding the molecular masses of two gases given their rate of diffusion ratio, we can follow these steps:

### Step-by-Step Solution:

1. **Understand Graham's Law of Effusion/Diffusion**:
Graham's Law states that the rate of diffusion of a gas is inversely proportional to the square root of its molecular mass. Mathematically, it can be expressed as:
\[ \frac{R_1}{R_2} = \sqrt{\frac{M_2}{M_1}} \]
where \( R_1 \) and \( R_2 \) are the rates of diffusion of gas 1 and gas 2, and \( M_1 \) and \( M_2 \) are their respective molecular masses.

2. **Set Up the Given Ratio**:
According to the problem, the ratio of the rates of diffusion is given as:
\[ \frac{R_1}{R_2} = \frac{1}{2} \]

3. **Substitute the Given Values into Graham's Law**:
Substitute the values into the equation from Graham's Law:
\[ \frac{1}{2} = \sqrt{\frac{M_2}{M_1}} \]

4. **Square Both Sides**:
To eliminate the square root, square both sides of the equation:
\[ \left(\frac{1}{2}\right)^2 = \frac{M_2}{M_1} \]
This simplifies to:
\[ \frac{1}{4} = \frac{M_2}{M_1} \]

5. **Express the Molecular Masses in Ratio**:
From the equation \(\frac{M_2}{M_1} = \frac{1}{4}\), we can express the ratio of the molecular masses:
\[ M_2 : M_1 = 1 : 4 \]

6. **Reverse the Ratio**:
To find the ratio of \(M_1\) to \(M_2\):
\[ M_1 : M_2 = 4 : 1 \]

7. **Conclusion**:
The molecular masses of the two gases are in the ratio of \(4 : 1\).

### Final Answer:
The ratio of the molecular masses \(M_1 : M_2\) is \(4 : 1\).

---