Question #43772

In a precision photoelectric experiment, a metallic emitter (work function $\Phi$) is maintained at temperature $T$ and illuminated by monochromatic light of photon energy $h\nu > \Phi$. Classically, the photocurrent $I(V)$ exhibits a sharp cutoff, dropping to zero at the stopping potential $V_0 = (h\nu - \Phi)/e$. However, due to thermal energy partitioning, the initial energies of electrons inside the metal follow the Fermi-Dirac distribution $f(E) = \left[ \exp(E/k_B T) + 1 \right]^{-1}$, where $E$ is the energy measured relative to the Fermi level. Assuming the density of states is constant and the emission probability is uniform for all electrons energetically capable of reaching the collector against a retarding potential $V$, the saturation curve blurs into a continuous tail. Evaluate the ratio $\frac{I(V_1)}{I(V_0)}$, where $V_1 = V_0 + \frac{k_B T}{e}$.