Question #43649

A metal surface with a work function $W = 4.0 \text{ eV}$ is irradiated by a high-intensity laser of frequency $\omega$ and intensity $I$. The electric field of the laser is given by $E(t) = E_0 \sin(\omega t)$, where $I = \frac{1}{2} \epsilon_0 c E_0^2$. In this high-intensity regime, the electron undergoes forced oscillations before emission. The time-averaged kinetic energy of this oscillation, $U_p$, effectively increases the binding energy of the electron, such that the new effective work function becomes $W_{eff} = W + U_p$. If the energy of a single photon is $\hbar \omega = 1.5 \text{ eV}$, multi-photon absorption is required for photoemission. Determine the threshold intensity $I_{th}$ above which a minimum of $4$ photons must be simultaneously absorbed to emit a photoelectron. (Assume the initial drift velocity of the electron is zero, $m$ is the mass of the electron, and $e$ is the elementary charge).