Answer
$\Delta V=11.38 V\approx 11.4 V$
Work Step by Step
Initial speed of an electron = 0
Final speed of an electron = $2\times 10^{6} m/s$
By the conservation of energy;
Loss in energy = Gain in energy
$q \Delta V=\frac{1}{2}m_{e}v_{e}^{2}-0$
$\Delta V =\frac{\frac{1}{2}m_{e}v_{e}^{2}}{q}$
$q \Delta V=\frac{1}{2}\times 9.11\times 10^{-31}\times (2\times 10^{6} )^{2}$
$\Delta V=\frac{\frac{1}{2}\times 9.11\times 10^{-31}\times (2\times 10^{6} )^{2}}{1.6 \times 10^{-19}}$
$\Delta V=11.38 V\approx 11.4 V$