Explain mobility of electrons. The resistivity of Cu is 1.72 x 10-8 ohm-m. Calculate the mobility of electrons in Cu given that number of electrons per unit volume is 10.41 x 1028 m-3.

Mobility (μ): When an electric field E is applied, free electrons acquire a drift velocity \(v_d\) proportional to E. Mobility is the drift velocity per unit electric field:

\[ \mu=\frac{v_d}{E}\quad[\text{m}^2/\text{V s}] \]

It shows how easily carriers move through the material, and it falls as temperature rises because lattice scattering increases. Since \(J=nev_d=ne\mu E\), the conductivity is \(\sigma=ne\mu\).

Given: \(\rho=1.72\times10^{-8}\) Ω m, \(n=10.41\times10^{28}\) m\(^{-3}\), \(e=1.6\times10^{-19}\) C.

\[ \mu=\frac{\sigma}{ne}=\frac{1}{\rho ne}=\frac{1}{1.72\times10^{-8}\times10.41\times10^{28}\times1.6\times10^{-19}}=\frac{1}{2.865\times10^{2}} \]

\(\mu\approx3.49\times10^{-3}\) m²/V s

(\(\sigma=5.81\times10^7\) S/m.)