The time of fall ($t$) for a charged particle starting from rest in a uniform electric field is derived from the kinematic equation $h = \frac{1}{2}at^2$, where $a$ is the acceleration. The acceleration due to the electric field is $a = \frac{F}{m} = \frac{qE}{m}$. Substituting this into the time equation gives $t = \sqrt{\frac{2h}{a}} = \sqrt{\frac{2hm}{qE}}$.

For a given distance $h$ and electric field $E$, and since the magnitude of charge $q$ is the same for both electron and proton ($e$), the time of fall is proportional to the square root of the mass ($t \propto \sqrt{m}$). Since the mass of an electron ($m_e \approx 9.11 \times 10^{-31}$ kg) is significantly smaller than the mass of a proton ($m_p \approx 1.67 \times 10^{-27}$ kg), the time of fall for the electron will be smaller.