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NEET PHYSICSEasy

The mean free path for a gas, with molecular diameter dd and number density nn, can be expressed as:

A

12nπd2\frac{1}{\sqrt{2}n\pi d^2}

B

12n2πd2\frac{1}{\sqrt{2}n^2\pi d^2}

C

12n2π2d2\frac{1}{\sqrt{2}n^2\pi^2 d^2}

D

12nπd\frac{1}{\sqrt{2}n\pi d}

Step-by-Step Solution

  1. Definition: The mean free path (λ\lambda) is the average distance a gas molecule travels between successive collisions.
  2. Derivation Concept: Consider a molecule of diameter dd moving with average speed vv. It sweeps out a cylinder of volume πd2vΔt\pi d^2 v \Delta t in time Δt\Delta t. The number of collisions is determined by the number density nn. To account for the motion of all other molecules, a relative velocity factor of 2\sqrt{2} is introduced.
  3. Formula: The standard expression derived in the Kinetic Theory of Gases is λ=12nπd2\lambda = \frac{1}{\sqrt{2}n\pi d^2}.
  4. Analysis of Options: Option A matches the standard formula. The other options have incorrect powers of nn or dd.
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