The behaviour of photoelectrons in the photoelectric effect can be explained by Einsteịn’s photoelectric equation:
\[
h f=W+\frac{1}{2} m v_{\max }^2
\]
\(h=\) Planck’s constant
\(f=\) frequency of incident light wave (photon)
\(W=\) work function
\(m=\) mass of photoelectrons
\(v_{\max }=\) maximum velocity of photoelectrons
Assuming that one photon emits one photoelectron, Einstein’s equation is consistent with the principle of conservation of energy:
\[
E = W +K_{\max }
\]
\(E =\) energy of incident photon
\(W =\) work function
\(K_{\max } =\) maximum kinetic energy of photoelectron
In the graph in Diagram below, gradient of the graph = Planck’s constant, \(h\).
Thus, the maximum kinetic energy of photoelectron increases linearly with the frequency of the incident photon.