JEE Main 2024 — Electrostatics Question with Solution

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $$\mathrm{S}$$ having surface charge density $$+\sigma$$. The electron at $$t=0$$ is at a distance of $$1\mathrm{m}$$ from $$S$$ and has a speed of $$1\mathrm{m}/\mathrm{s}$$. The maximum value of $$\sigma$$ if the electron strikes $$S$$ at $$t=1\mathrm{s}$$ is $$\alpha \left[\frac{m{ϵ}_0}{e}\right]\frac{C}{m^2}$$, the value of $$\alpha$$ is ___________.