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Question #42588

Difficulty: 8/10 | 🟢 Free

The Question

A vessel contains a mixture of two ideal gases, A and B, with molecular masses $m_A = m$ and $m_B = 2m$ , maintained at a constant temperature $T$ . The number densities of both gases are equal ( $n_A = n_B = n$ ). Assuming the collision diameters of both molecules are identical ( $d_A = d_B = d$ ), what is the ratio of the collision frequency per unit volume between unlike molecules ( $Z_{AB}$ ) to that between like molecules of gas A ( $Z_{AA}$ )?

Options

A.
$\sqrt{3}$
B.
$\frac{\sqrt{3}}{2}$
C.
$\frac{2}{\sqrt{3}}$
D.
$\sqrt{2}$

Check Your Answer

Correct Answer

Step-by-Step Solution

Explanation

How the Examiner Thinks

Variable_Constraint

Develop pure symbolic logic skills by mastering algebraic constraints without relying on numerical data.

Concepts Behind This Question

Pressure-Kinetic Energy Relation|Reduced Mass Effect|Integration

Why This Question Is Tricky

Common Mistakes

This question tests the application of the reduced mass effect in kinetic theory and the binary collision constraint.

Students commonly fall into two traps: (1) using the arithmetic mean mass or the mass of a single particle instead of the reduced mass $\mu = \frac{m_1 m_2}{m_1 + m_2}$ for calculating the relative velocity between unlike molecules, and (2) forgetting the $1/2$ factor in the collision frequency of identical particles, which is strictly required to prevent double-counting collisions in a single-component gas.

Quick Facts About This Question

Question Information

Subject	Physics
Chapter	Kinetic Theory - Class 11 Part 2
Concept	Pressure-Kinetic Energy Relation
Difficulty	8
Cognitive Load	7
Target Solve Time	160 sec
Access	Free