The relation between relaxation time, mean free path, collision time and drift velocity— pitfalls and a proposal for an approach illustrating the essentials

The collisionmodel is frequently introduced to describe electronic conductivity in solids. Depending on the chosen approach, the introduction of the collision time can lead to erroneous results for the average velocity of the electrons, which enters the expression for the electrical conductivity. In other textbooks, correct results are obtained by erroneous arguments. In this contribution we propose a more detailed presentation involving the proper consideration of the underlying collision statistics. The paper addresses instructors teaching elementary solid state physics at the university level and graduate students aiming at gaining increased insight into the subtleties associated with the collision model.