A cylindrical conductor of length \(2 \, \text{m}\) and area of cross-section \(0.2 \, \text{mm}^2\) carries an electric current of \(1.6 \, \text{A}\) when its ends are connected to a \(2 \, \text{V}\) battery. Mobility of electrons in the conductor is \( \alpha \times 10^{-3} \, \text{m}^2\text{/V s}. \) The value of \( \alpha \) is ______________.
(Electron concentration \(= 5 \times 10^{28} \, \text{m}^{-3}\), electron charge \(= 1.6 \times 10^{-19} \, \text{C}\))