NEET Physics: Mean free path Practice Questions

Correct answer: D — λ∝ v₍avg) / (collision frequency)

The mean free path is fundamentally determined by how far the molecules travel (related to velocity) and the rate at which they interact (collision frequency). A long path requires high velocity and low collision rate.

Correct answer: D — The density of the gas

The mean free path is inversely proportional to the square of the molecular density (n²), which is directly related to the density of the gas. Lower density means molecules are farther apart, leading to a longer mean free path.

Correct answer: C — The density of the gas (number density).

The mean free path depends on how frequently molecules encounter one another, which is governed by their density (number density, n). While temperature affects the velocity (and thus collision rate), the fundamental mean free path length is directly tied to the density of the system.

Correct answer: A — A dilute gas

A large mean free path indicates that molecules travel long distances before colliding, which is characteristic of a very low density or a dilute gas.

Correct answer: B — Larger molecules occupy a greater volume, increasing collision frequency per unit volume.

When molecules are larger (larger molecular diameter, d), they occupy more space. For a fixed density, this larger size increases the frequency of collisions, effectively reducing the average distance between those collisions, thus decreasing the mean free path.

Correct answer: C — the volume occupied by the gas

The mean free path is determined by the density of molecules and their relative motion. In a fixed volume, if the molecular speed is constant, the mean free path is directly related to the volume available for molecular travel.

Correct answer: B — It is halved

The mean free path is inversely related to the square root of the molecular mass (when other parameters are held constant). Therefore, doubling the molecular mass will reduce the mean free path. (More precisely, λ∝ 1/√M).

Correct answer: A — The average molecular speed

Since mean free path is inversely related to the average molecular speed, and for a fixed temperature, the average molecular speed is directly related to the kinetic energy, the mean free path is inversely related to the average molecular speed.

Correct answer: D — The average distance traveled by a molecule between successive collisions

The mean free path (λ) is the average distance that a molecule travels in a gas before it undergoes a collision with another molecule.

Correct answer: B — It decreases

When the density of a gas increases (meaning molecules are packed closer together), the frequency of collisions increases, and consequently, the average distance traveled between collisions (the mean free path) decreases.

Correct answer: B — It decreases proportionally

Increasing the pressure means the molecules are closer together, leading to a higher frequency of collisions. Consequently, the average distance traveled between collisions (mean free path) decreases.

Correct answer: A — The gas tends towards a continuum state

When the mean free path is very small compared to the container dimensions, it indicates that molecules are constantly interacting, behaving like a continuous medium, which is the basis for the continuum approximation in gases.

Correct answer: B — It represents the average distance a molecule travels before colliding with another molecule.

The mean free path is fundamentally the average distance traveled by a molecule during its motion between collisions with other molecules.

Correct answer: C — λ is inversely proportional to n

The mean free path (λ) is inversely proportional to the number density (n) of the gas because a higher density means molecules are closer together, leading to more frequent collisions and thus a shorter average distance traveled between collisions. Mathematically, λ∝ 1/n (or more accurately, related to 1/(√2 πd² n) where n is the concentration).