Question #41994

In a non-linear model of the photoelectric effect, the intense incident light modifies the surface properties of a metal. The maximum kinetic energy $K$ of the emitted photoelectrons is given by the relation: $K = h\nu - \Phi_0 \exp\left(-\frac{I \lambda}{\alpha \nu}\right)$ where $h$ is Planck's constant, $\nu$ is the frequency of the incident light, $\lambda$ is its wavelength in vacuum, $I$ is the intensity of the incident light, $\Phi_0$ is the baseline work function of the material, and $\alpha$ is a positive constant. Assuming the equation is dimensionally consistent, what is the dimensional formula of the constant $\alpha$, and what is the theoretical threshold frequency $\nu_{th}$ in the limit of extremely high light intensity ($I \to \infty$)?