Electron mobility is given by $u = \frac{v_d}{E} = \frac{v_d}{\frac{V}{l}}$ Here $E$ = magnitude of electric field applied $v_d =$ drift velocity, $V =$ p.d., $l =$ length So, $u \propto \frac{1}{V}$ Hence, for the constant length and temperature of the conductor, if the potential difference is doubled, the mobility will be halved.