An electron of mass me, initially at rest, moves through a certain distance in a uniform electric field in time t₁. A proton of mass mp, also initially at rest, takes time t₂ to move through an equal distance in this uniform electric field. Neglecting the effect of gravity, the ratio $\frac{t_2}{t_1}$ is equal to

$\left(\frac{m_p}{m_e}\right)^{1 / 2}$

Acceleration in uniform electric field

$a=\frac{q E}{m}$

If t is time for a distance d,

$d=\frac{1}{2}\left(\frac{q E}{m}\right) t^2$

or t = $\sqrt{\frac{2 d m}{q E}}$