Question

The mobility of free electrons (charge = $e$, mass = $m$ and relaxation time = $\tau$ .) in a metal is proportional to

• A. $\frac{e}{m}\tau$
• B. $\frac{m}{e}\tau$
• C. $\frac{e}{m\tau }$
• D. $\frac{m}{e\tau }$

Answer 1

Answer: (A)

$\frac{e}{m}\tau$

Answer 2

Drift velocity per unit electric field is called mobility of electron,
ie, $\mu=\frac{v_{d}}{E}=\frac{E}{\rho n e E}$
Now, $\rho=\frac{m}{n e^{2} \tau}$
$\therefore s \mu=\frac{n e^{2} \tau}{m n e}=\frac{e \tau}{m}$