Q.For light of a fixed frequency above the threshold frequency, explain how the photoelectric current varies as the intensity of the incident light is increased, and state what this tells us about the number of photoelectrons emitted per second.

Saturation current counts the total number of photoelectrons emitted per second, which is set by how many photons strike the metal per second — i.e. the intensity of light, not its frequency.

In the photoelectric effect, when the collector plate is made sufficiently positive, ALL photoelectrons ejected from the metal surface are collected, and the photocurrent reaches a maximum, constant value called the saturation current — increasing the collector voltage further does not increase it any more.

The NUMBER of photoelectrons ejected per second is proportional to the number of photons incident per second, which is exactly what light INTENSITY measures (energy delivered per unit area per unit time). A higher intensity beam (at the same frequency) delivers more photons per second, ejecting more photoelectrons per second, and hence a higher saturation current.

Frequency and work function instead determine the maximum KINETIC ENERGY of the photoelectrons (via Einstein's equation) and the stopping potential needed to halt them — not the magnitude of the saturation current.

Einstein's photoelectric equation rearranged in terms of stopping potential is linear in frequency with slope h/e.

Einstein's photoelectric equation is $h\nu = \phi_0 + eV_0$, where $V_0$ is the stopping potential and $\phi_0$ the work function. Rearranging for $V_0$:

$V_0 = \dfrac{h}{e}\nu - \dfrac{\phi_0}{e}$

This is a straight line when $V_0$ is plotted against $\nu$, with slope $h/e$ and intercept $-\phi_0/e$. The slope is the same for every metal (since $h$ and $e$ are universal constants); only the intercept (work function) changes with the metal.

The stopping potential is the potential that just stops the fastest photoelectrons, found by equating eV0 to their maximum kinetic energy.

The stopping potential V0 is defined by the condition that the retarding field decelerates even the most energetic photoelectrons (of maximum speed v) to rest just before they reach the collector: work done against the field equals the electron's kinetic energy,

eV0 = (1/2)mv² ⟹ V0 = mv²/(2e)