Question #82015

Students often memorize the collision frequency formula $Z = \sqrt{2} n \sigma v_{avg}$ for a single gas without understanding its statistical mechanics origin.

The $\sqrt{2}$ factor arises because the mean relative speed $\langle v_{rel} \rangle = \sqrt{2} v_{avg}$ is a specific case of the general relative velocity distribution using reduced mass $\mu = m/2$ for identical particles.

When faced with a gas mixture, students fall into traps: they either blindly apply the $\sqrt{2}$ factor (Option C), or incorrectly assume scalar addition/subtraction of mean speeds like $v_0 \pm v_0/2$ (Options B and D).

This question tests the fundamental understanding that relative velocity in a 3D Maxwellian gas must be treated as the difference of two random vectors, requiring the reduced mass $\mu = \frac{m_A m_B}{m_A + m_B}$ to correctly compute the mean relative speed magnitude.