An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t = 0$ is at a distance of $1\text{ m}$ from $S$ and has a speed of $1\text{ m/s}$. The maximum value of $\sigma$ if the electron strikes $S$ at $t = 1\text{s}$ is $\alpha\left[\frac{m\epsilon_0}{e}\right]\frac{\text{C}}{\text{m}^2}$, the value of $\alpha$ is ________.
