In a conductor, the mobility of electrons is 2 × 10−4 m2V−1s−1. The average collision time for electrons in the conductor would be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 11.38 × 10−16 s
Mobility is the drift speed per unit electric field. Since the drift speed is \( v_d = eE\tau/m \), mobility is linked to the average collision time \( \tau \) by
\( \displaystyle \mu = \frac{v_d}{E} = \frac{e\tau}{m} \)
\( \displaystyle \tau = \frac{\mu m}{e} \)
Taking \( m = 9.1\times10^{-31}\,\mathrm{kg} \) and \( e = 1.6\times10^{-19}\,\mathrm{C} \):
\( \displaystyle \tau = \frac{2\times10^{-4}\,\mathrm{m^{2}\,V^{-1}\,s^{-1}} \times 9.1\times10^{-31}\,\mathrm{kg}}{1.6\times10^{-19}\,\mathrm{C}} \)
\( \displaystyle \tau = 1.1375\times10^{-15}\,\mathrm{s} \approx 11.38\times10^{-16}\,\mathrm{s} \)