Drude model for conductivity

$\vec v_\text{D} = eE \tau / m_e$

$\vec J = ne \vec v_\text{D}$

Ohm’s theorem in

$\vec J = \sigma \vec E$

⇒ $\sigma = ne^2\tau / m_e$

The resistivity $\rho$ is inverse of conductivity $\sigma$ : $\rho = 1 / \sigma$

The definition of mobility $\mu$ is given by (constitutive relation $v_D = \mu E$ )

$\mu \equiv v_D / E$

Conductivity $\sigma$ in terms of mobility $\mu$ is therefore

$\sigma = ne\mu$

⇒ $\mu = e\tau / m_e$