Why is there a threshold frequency for photoelectric emission from a metal?

In the photoelectric effect, a threshold frequency exists because a minimum amount of energy, known as the work function, is required to liberate an electron from the surface of a metal.12

According to the quantum theory of radiation, light is absorbed in discrete packets of energy called photons, each with an energy defined by $E=h\nu$, where $h$ is Planck’s constant and $\nu$ is the frequency of the light. For an electron to be ejected, the energy of an individual incident photon must be greater than or equal to the work function of the specific metal.123

If the frequency of the light is below this threshold—defined as ${\nu }_0=\psi /h$ (where $\psi$ is the work function)—the individual photons lack the necessary energy to overcome the binding forces holding the electron to the metal, regardless of how intense the light is. Consequently, no photoelectric emission occurs below this frequency.124