Diffusion:
Diffusion is the process by which particles move from an area of higher concentration to an area of lower concentration. It occurs due to the random motion of particles.

Graham's Law of Diffusion:
Graham's law of diffusion states that the rate of diffusion of a gas is inversely proportional to the square root of its molar mass. Mathematically, it can be represented as:

Rate1 / Rate2 = √(Molar mass2 / Molar mass1)

Where Rate1 and Rate2 are the rates of diffusion of gases 1 and 2, and Molar mass1 and Molar mass2 are the molar masses of gases 1 and 2, respectively.

Ratio of the Rate of Diffusion:
In this question, we are given that the pressure and temperature are identical for helium and methane. Therefore, the only factor that affects the rate of diffusion is the molar mass.

Let's consider the ratio of the rate of diffusion of helium (Rate1) to the rate of diffusion of methane (Rate2):

Rate1 / Rate2 = √(Molar mass2 / Molar mass1)

Since the molar mass of helium is less than the molar mass of methane, the ratio of the molar masses (Molar mass2 / Molar mass1) will be greater than 1.

Therefore, the square root of the ratio of the molar masses (√(Molar mass2 / Molar mass1)) will also be greater than 1.

Hence, the ratio of the rate of diffusion of helium to the rate of diffusion of methane will be greater than 1.

Answer:
The correct answer is option 'B' - 2. The ratio of the rate of diffusion of helium to the rate of diffusion of methane under identical conditions of pressure and temperature is 2.