Physics Q2 – NEET-UG 2026

Home Physics ThermodynamicsQuestion #538

The mean free path of molecules in an ideal gas A is half that of another ideal gas B. The diameter of the spherical molecules of gas A is twice the diameter of the molecules of B. If number densities of the gases A and B are

n_{A}

and

n_{B}

, respectively, then the correct option is :

Clue 1 of 3: Mean Free Path Concept

The mean free path of gas molecules is the average distance a molecule travels between successive collisions.

🥷

Ninja Strategy•Proportionality Analysis and Elimination

Recognize that $λ \propto 1 / (d^{2} n)$ . Since $d_{A} = 2 d_{B}$ , the diameter effect alone makes $λ_{A} = λ_{B} / 4$ . To increase $λ_{A}$ from $λ_{B} / 4$ to $λ_{B} / 2$ , $n_{A}$ must be smaller than $n_{B}$ . Then, test the remaining options by substituting them into the proportionality.

🧠 Full Solution Path

Step 1: Recall the Mean Free Path Formula✦ Active

The mean free path ( $λ$ ) of molecules in an ideal gas is given by the formula:

λ = \frac{1}{\sqrt{2} π d^{2} n}

Where $d$ is the diameter of the molecules and $n$ is the number density of the gas. From this, we can see that $λ \propto \frac{1}{d^{2} n}$ .

Step 2: Set up the Ratio for Gases A and B○ Expand

Given the relationships for gas A and gas B:

1. Mean free path: $λ_{A} = \frac{1}{2} λ_{B}$

2. Molecular diameter: $d_{A} = 2 d_{B}$

Using the proportionality, we can write the ratio of mean free paths:

\frac{λ_{A}}{λ_{B}} = \frac{d_{B}^{2} n_{B}}{d_{A}^{2} n_{A}}

💡 Teacher's Secret Hint

Ensure you correctly invert the terms for $d$ and $n$ when setting up the ratio due to inverse proportionality.

Step 3: Substitute Values and Solve for

n_{A}

○ Expand

Substitute the given conditions into the ratio equation:

\frac{\frac{1}{2} λ_{B}}{λ_{B}} = \frac{d_{B}^{2} n_{B}}{(2 d_{B})^{2} n_{A}}

Simplify the equation:

\frac{1}{2} = \frac{d_{B}^{2} n_{B}}{4 d_{B}^{2} n_{A}}

\frac{1}{2} = \frac{n_{B}}{4 n_{A}}

Cross-multiply to solve for $n_{A}$ :

4 n_{A} = 2 n_{B}

n_{A} = \frac{2}{4} n_{B}

n_{A} = \frac{1}{2} n_{B}

This matches option (4).

💡 Teacher's Secret Hint

Double-check your algebraic simplification, especially when squaring the diameter term.

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Physics Question 2 – NEET-UG 2026

Clue 1 of 3: Mean Free Path Concept

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