How does the photoelectric effect (gold leaf experiment) demonstrate the particle nature of light?

A certain amount of energy is required to eject an electron from a metal surface. The gold leaf experiment shows that only light above a certain threshold frequency is able to eject electrons. If the frequency of the light incident on the metal surface is even slightly below this threshold frequency, then no electrons will be ejected; no matter how intense the light source is. This seems counterintuitive as we know that light intensity is proportional to power, and hence proportional to energy. This can be explained by looking at light as stream of particles, (called a photons). A photon's energy is proportional the its frequency, E = hf (where h is planks constant = 6.63 x 10^-34 Js). One photon interacts with one electron. So for an electron to be ejected by a photon; the photon's energy must be greater than or equal to that required to eject the electron. This energy divided by planks constant is the threshold frequency. So if the frequency of a photon is below the threshold frequency, it's photons will not have enough energy to eject an electron, so no electrons will be ejected no matter how many of these photons are fired at it. The number of photons is proportional to intensity; hence intensity will have no effect on the emission of electrons.