Ratio of the rate of diffusion of He to `H_(2)` at `0^(@)C` is same in the case :

Options

A. (a) When temperature is changed to `100^(@)C`
B. (b) When O2 and CH4 are taken instead of He and `H_(2)`
C. (c) When volume of the flask is doubled
D. (d) All the above are correct

Explanation

To solve the question regarding the ratio of the rate of diffusion of helium (He) to hydrogen (H₂) at 0°C, we will use Graham's law of diffusion, which states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass.

### Step-by-Step Solution:

1. **Identify the Molar Masses:**
- Molar mass of helium (He) = 4 g/mol
- Molar mass of hydrogen (H₂) = 2 g/mol

2. **Apply Graham's Law of Diffusion:**
Graham's law states that:
\[ \frac{R_1}{R_2} = \sqrt{\frac{M_2}{M_1}} \]
where \( R_1 \) and \( R_2 \) are the rates of diffusion of the two gases, and \( M_1 \) and \( M_2 \) are their molar masses.

3. **Substitute the Values:**
Here, \( M_1 \) is the molar mass of hydrogen (2 g/mol) and \( M_2 \) is the molar mass of helium (4 g/mol). Therefore, we can write:
\[ \frac{R_{He}}{R_{H_2}} = \sqrt{\frac{M_{H_2}}{M_{He}}} = \sqrt{\frac{2}{4}} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}} \]

4. **Conclusion:**
The ratio of the rate of diffusion of helium to hydrogen at 0°C is \( \frac{1}{\sqrt{2}} \).

5. **Evaluate the Options:**
- **Option A:** Changing the temperature to 100°C does not affect the ratio since Graham's law is independent of temperature.
- **Option B:** The ratio remains the same when comparing other gases (O₂ and CH₄) since the relationship holds true for any two gases.
- **Option C:** Doubling the volume of the flask does not affect the rate of diffusion, as it is dependent on the properties of the gases, not the volume.
- **Option D:** Since all previous options are correct, this option is also correct.

Thus, the final answer is that the ratio of the rate of diffusion of He to H₂ remains the same in all cases mentioned.