How can the work function of a metal be calculated from its threshold frequency?

The work function of a metal, denoted by the Greek letter $\psi$ (or sometimes $\varphi$), represents the minimum energy required to eject an electron from the surface of a material.123

In the context of the photoelectric effect, the threshold frequency (${\nu }_0$) is defined as the minimum frequency of incident radiation at which electron emission is just barely possible. The relationship between the work function and the threshold frequency is expressed by the following equation:3

$$\psi =h{\nu }_0$$

In this formula:
* $\psi$ is the photoelectric work function of the metal surface.3
* $h$ is Planck’s constant, a universal constant that relates the energy of a photon to its frequency.24
* ${\nu }_0$ is the threshold frequency of the incident radiation.3

Essentially, because a photon must possess at least enough energy to overcome the binding energy of the electron to eject it, the work function is exactly equal to the energy of a photon at the threshold frequency.23