If the ratio of the rates of diffusion of two gases A and B is 4:1 the
ratio of their density is

Options

A. `1:16`
B. `1:4`
C. `1:2`
D. `1:8`

Explanation

To solve the problem, we will use Graham's law of effusion and the relationship between the rates of diffusion and the densities of the gases.

### Step-by-Step Solution:

1. **Understanding the Given Information**:
We are given that the ratio of the rates of diffusion of two gases A and B is 4:1. This can be expressed mathematically as:
\[ \frac{R_A}{R_B} = \frac{4}{1} \]

2. **Applying Graham's Law**:
According to Graham's law, the rate of diffusion of a gas is inversely proportional to the square root of its density. This can be expressed as:
\[ \frac{R_A}{R_B} = \sqrt{\frac{d_B}{d_A}} \]
where \(d_A\) and \(d_B\) are the densities of gases A and B, respectively.

3. **Setting Up the Equation**:
From the information given, we can substitute the known ratio into Graham's law:
\[ \frac{4}{1} = \sqrt{\frac{d_B}{d_A}} \]

4. **Squaring Both Sides**:
To eliminate the square root, we square both sides of the equation:
\[ \left(\frac{4}{1}\right)^2 = \frac{d_B}{d_A} \]
This simplifies to:
\[ \frac{16}{1} = \frac{d_B}{d_A} \]

5. **Finding the Ratio of Densities**:
We can express the ratio of densities \(d_A\) to \(d_B\) by taking the reciprocal of the previous equation:
\[ \frac{d_A}{d_B} = \frac{1}{16} \]

6. **Final Ratio**:
Therefore, the ratio of the densities of gases A and B is:
\[ d_A : d_B = 1 : 16 \]

### Conclusion:
The ratio of the densities of gases A and B is \(1:16\).