Why do different metals have different threshold frequencies?

Different metals have different threshold frequencies because they possess unique electronic work functions. The work function represents the minimum amount of energy required to remove the most loosely bound electron from the surface of a specific metal.1

Because each metal holds its electrons with varying degrees of tightness, the energy required to eject them differs from one material to another. In the context of the photoelectric effect, the threshold frequency (${\nu }_0$) is defined as the specific frequency of incident light at which electron ejection becomes barely possible. This value is determined by the ratio of the metal's work function ($\psi$) to Planck’s constant ($h$), expressed by the equation:12

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

Consequently, since the work function is a characteristic property of each metal, the threshold frequency must also vary accordingly. Metals that hold their electrons more tightly have higher work functions and thus require higher threshold frequencies to trigger the photoelectric effect.21