Solid-state physics – mean free path relation If v denotes the average electron speed between collisions and t_c is the mean time between collisions, then the mean free path λ is given by λ = v * t_c. Is this statement correct?

Introduction:
Transport in metals and semiconductors is often modeled using the Drude or semiclassical framework. Mean free path λ indicates the average distance a charge carrier travels between successive scattering events, crucial for mobility, conductivity, and nanoscale device analysis.

Given Data / Assumptions:

• Average carrier speed v between collisions is well defined (e.g., drift-averaged or thermal-averaged appropriate to the model).
• Mean free time between collisions t_c is defined.
• Steady-state conditions with many scattering events.

Concept / Approach:

By definition, mean free path equals mean speed times the mean time between scattering events: λ = v * t_c. In a purely drift picture, v would be the average velocity; in thermal motion, a thermal speed can be used for order-of-magnitude estimates. The identity captures the intuitive notion that faster carriers or longer times between collisions yield longer paths between collisions.

Step-by-Step Solution:

Verification / Alternative check:

Drude conductivity σ = n * e^2 * t_c / m relates to mobility µ = e * t_c / m; combining with typical thermal speeds allows cross-checks of λ scales in metals and semiconductors.

Why Other Options Are Wrong:

λ = v / t_c has wrong dimensions; restricting to 0 K or to holes only is unjustified.

Common Pitfalls:

Confusing drift velocity with thermal velocity; misusing instantaneous velocity instead of an appropriate average.

Final Answer:

True