Work function, \(W\) is the minimum energy required to emit photoelectrons from a metal surface.
\[
W=h f_0
\]
\(h =\) Planck’s constant,
\(f_0\) threshold frequency
Threshold frequency, \(f_0\) is the minimum frequency required to emit photoelectrons from a metal surface.
The value of threshold frequency (and thus work function) for different metal surfaces is unique as shown in the graph in Diagram below.
Einstein’s photoelectric equation can also be expressed as
\[
h f=h f_0+\frac{1}{2} m v_{\max }^2
\]
Thus, if the frequency of the incoming photon is just equal to the threshold frequency of the metal surface \(\left(f=f_0\right)\), then \(\frac{1}{2} m v_{\max }^2=0\).
The photoelectrons emitted will have zero kinetic energy.
This means that the energy of the photon is just enough to release the electrons to the metal surface.