Introduction:
The rate of diffusion of a gas is determined by its molecular mass and the temperature. Diffusion is the process by which gas molecules move from an area of high concentration to an area of low concentration. In this case, we are comparing the diffusion rates of helium and methane under identical conditions of pressure and temperature.

Explanation:
The rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, we can express this relationship as:

Rate of diffusion ∝ 1/√(Molar mass)

Step 1: Calculate the molar mass of helium and methane:
The molar mass of helium (He) is approximately 4 g/mol.
The molar mass of methane (CH4) can be calculated as follows:
1 atom of carbon (C) = 12.01 g/mol
4 atoms of hydrogen (H) = (4 x 1.01) g/mol
Total molar mass of methane = 12.01 + (4 x 1.01) = 16.05 g/mol

Step 2: Calculate the ratio of the molar masses:
Ratio of molar masses = Molar mass of helium / Molar mass of methane
= 4 g/mol / 16.05 g/mol
= 0.2492

Step 3: Calculate the ratio of the rates of diffusion:
Using the relationship mentioned earlier, we can write:
Rate of diffusion of helium / Rate of diffusion of methane = √(Molar mass of methane / Molar mass of helium)
= √(16.05 g/mol / 4 g/mol)
= √4.0125
= 2

Therefore, the ratio of the rate of diffusion of helium to methane under identical conditions of pressure and temperature is 2 (option B).

Conclusion:
The ratio of the rate of diffusion of helium and methane under identical conditions of pressure and temperature is 2. This is because the rate of diffusion is inversely proportional to the square root of the molar mass, and helium has a molar mass of 4 g/mol while methane has a molar mass of 16.05 g/mol.

Graham's law states that the rate of diffusion  or of effusion of a gas is inversely proportional to the square root of its molecular weight.... so after putting the value u will get B is correct