Briefly tell what is meant by the drift velocity and mobility of a free electron.

Drift velocity is the average velocity of free charge carriers, such as electrons, when they are subjected to an external electric field inside a conducting medium like a metal. The drift velocity depends on the strength of the applied electric field, the charge and the mass of the electron, and the interaction between the electron and the lattice of the conducting medium. The drift velocity can be calculated using the formula: \(v_d = \frac{I}{nAe}\) where \(v_d\) is the drift velocity, \(I\) is the current, \(n\) is the number density of charge carriers (electrons), \(A\) is the cross-sectional area of the conductor, and \(e\) is the elementary charge.

Mobility is a property that characterizes how easily electrons can move in response to an electric field. Mathematically, it's defined as the ratio of the drift velocity of the charged particle to the strength of the electric field acting on it. The mobility of an electron can be represented as: \(\mu = \frac{v_d}{E}\) where \(\mu\) is the mobility, \(v_d\) is the drift velocity, and \(E\) is the electric field.

There is a direct relationship between drift velocity and mobility. As introduced earlier, mobility can be expressed as the ratio of drift velocity to the electric field: \(\mu = \frac{v_d}{E}\) By rearranging the formula and solving for drift velocity, we can find that: \(v_d = \mu E\) This equation shows that the drift velocity is directly proportional to the mobility of a free electron in an electric field. Higher mobility indicates that the electron can move more easily in response to the electric field, resulting in a higher drift velocity. The mobility of an electron depends on factors such as the nature of the medium (conductor, insulator or semiconductor), temperature, and impurity levels present in the material.