Question #43625

A photocell with a sensitive area $A$ is illuminated by a monochromatic light source of wavelength $\lambda$. The intensity of the incident light varies with time $t$ as $I(t) = I_0 \sin^2(\omega t)$, where $I_0$ is the peak intensity and $\omega$ is a positive constant. The photocell is connected in series with an initially uncharged capacitor of capacitance $C$ and an ideal DC voltage source $V_0$. The voltage $V_0$ is sufficiently large to ensure that all emitted photoelectrons are instantaneously swept to the anode, maintaining a saturation current at all times. If the quantum efficiency of the photocell is $\eta$ (defined as the number of photoelectrons emitted per incident photon) and the work function of the cathode material is $\Phi < \frac{hc}{\lambda}$, what is the total charge accumulated on the capacitor from $t = 0$ to $t = \frac{2\pi}{\omega}$? (Here $h$ is Planck's constant, $c$ is the speed of light, and $e$ is the elementary charge).