Assertion: A lighter gas diffuses more rapidly than heavier gas.
Reason: At a given temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density.

Options

A. If both (`A`) and (`R`) are correct and (`R`) is the correct explanation of (`A`).
B. If both (`A`) and (`R`) are correct, but (`R`) is not the correct explanation of (`A`).
C. If (`A`) is correct, but (`R`) is incorrect.
D. If (`A`) is incorrect, but (`R`) is correct.

Explanation

To solve the assertion and reason question, we will analyze both the assertion and the reason step by step.

### Step 1: Understand the Assertion
The assertion states: "A lighter gas diffuses more rapidly than a heavier gas."

- **Explanation**: This statement is based on the principles of gas diffusion. Lighter gases, which have lower molar masses, tend to move faster than heavier gases, which have higher molar masses.

### Step 2: Understand the Reason
The reason states: "At a given temperature and pressure, the rate of diffusion of a gas is inversely proportional to the square root of its density."

- **Explanation**: This is a reference to Graham's Law of Effusion and Diffusion, which states that the rate of diffusion (or effusion) of a gas is inversely proportional to the square root of its molar mass (or density). Mathematically, it can be expressed as:

\[ \frac{r_1}{r_2} = \sqrt{\frac{d_2}{d_1}} \]

where \( r_1 \) and \( r_2 \) are the rates of diffusion of gases 1 and 2, and \( d_1 \) and \( d_2 \) are their respective densities.

### Step 3: Apply Graham's Law
Using Graham's Law, if we let gas 1 be the lighter gas and gas 2 be the heavier gas, we can say:

- Since the density of the lighter gas (d1) is less than that of the heavier gas (d2), we have \( d_1 < d_2 \).
- Therefore, the rate of diffusion of the lighter gas (r1) will be greater than that of the heavier gas (r2).

### Step 4: Conclusion
Both the assertion and the reason are correct, and the reason provides a valid explanation for the assertion.

### Final Answer
- **Assertion**: Correct
- **Reason**: Correct
- **Explanation**: The reason is the correct explanation for the assertion.