The mean free path λ for a gas, with molecular diameter d and number density n, can be expressed as:
Options

Question

The mean free path λ for a gas, with molecular diameter d and number density n, can be expressed as:

G1 Physics · Accepted Answer

Step 1: For dilute gas of hard spherical molecules, the collision cross-section is σ = πd², where d is molecular diameter. Step 2: Collision frequency accounting for relative molecular velocities is z = √2 nσv̄. Step 3: Mean free path = average speed/collision frequency: λ = v̄/z = 1/(√2 nσ). Step 4: Substitute σ = πd²: λ = 1/(√2 πnd²). Final answer: (A).