AIIMS 2019 Physics Molecular Collisions MCQ Question

To determine the time of relaxation for an O₂ molecule, we can use the formula for the mean free time (τ) between collisions, which is given by τ = 1/(√2 * n * σ * v), where n is the number density, σ is the collision cross-section, and v is the average speed of the molecules. Given the radius of the O₂ molecule as 40 Å (4 × 10⁻⁹ m), the collision cross-section (σ) can be approximated as πr², leading to a value that, when combined with the density and average speed at the given temperature (27°C or 300 K), results in a relaxation time on the order of 10⁻¹² seconds.

Options A (10⁻¹⁰ sec), C (10⁻¹⁴ sec), and D (10⁻⁸ sec) are incorrect as they do not align with the calculated mean free time for gas molecules under the specified conditions, which is significantly shorter than 10⁻¹⁰ sec and longer than 10⁻¹⁴ sec.