The mean free path in ideal gas A is half the mean free path in ideal gas B. The molecular diameter in A is twice that in B. If the number densities are nₐ and nᵦ, identify the correct relation.
Options

Question

The mean free path in ideal gas A is half the mean free path in ideal gas B. The molecular diameter in A is twice that in B. If the number densities are nₐ and nᵦ, identify the correct relation.

G1 Physics · Accepted Answer

Step 1: Mean free path for spherical molecules is λ = 1/(√2 πd²n). Step 2: Hence λₐ/λᵦ = (dᵦ² nᵦ)/(dₐ² nₐ). Step 3: With dₐ = 2dᵦ, λₐ/λᵦ = nᵦ/(4nₐ). Step 4: Given λₐ/λᵦ = 1/2, so 1/2 = nᵦ/(4nₐ). Final answer: nₐ = nᵦ/2 (Option D).