Question #43758

In a photoelectric experiment, an emitter plate at $x=0$ is illuminated by light of frequency $f$. The work function of the emitter is $\Phi$ (where $hf > \Phi$). A collector plate is located at $x=d$. Consider an electron emitted at $t=0$ with the maximum possible kinetic energy, traveling directly along the $x$-axis towards the collector. The potential difference $V(t) = V_{\text{collector}} - V_{\text{emitter}}$ is initially zero. At a time $t_0 = \frac{d}{3} \sqrt{\frac{m}{2(hf - \Phi)}}$ (where $m$ is the mass of the electron), the potential difference is instantaneously switched to a constant positive value $V_0$, and remains $V_0$ thereafter. Assuming the electric field between the plates is always spatially uniform, what is the kinetic energy of this electron at the instant it reaches the collector?