Question #43768

A rigid vacuum phototube of total mass $M$ is located in deep space (a gravity-free region). Inside the tube, a planar cathode with work function $\Phi$ and a parallel planar anode are separated by a distance $d$. A highly intense laser beam of frequency $\nu$ (where $h\nu > \Phi$), uniform intensity $I$, and cross-sectional area $A$ is incident normally on the perfectly reflecting outer surface of the anode end of the tube. The radiation pressure from the laser accelerates the entire phototube along the axis perpendicular to the electrodes. If $m$ and $-e$ are the mass and charge of an electron respectively, and $c$ is the speed of light, what is the exact stopping potential $V_s$ required to just prevent the most energetic photoelectrons from reaching the anode? (Assume the mass of the emitted electrons is negligible compared to $M$).