There is evidence that light behaves like a wave - it can undergo reflection, refraction, diffraction and interference. Light, however, is not limited to this wave behaviour. At smaller scales, light behaves like a particle. The photoelectric effect is one phenomenon that helps us to explain this particulate theory. When a photon strikes a metallic surface, it can dislodge an electron:
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Some of its energy goes into removing the electron and the remaining energy becomes the kinetic energy of that electron:
$$ \begin{equation}\begin{aligned} E_{photon}&=\phi+E_k\\ hf&=\phi+E_k\\ \end{aligned}\end{equation} $$ where $h$ is Planck’s constant ($6.63\times 10^{-34}Js$) and $f$ is the frequency of the incident light. The energy, $\phi$, required to dislodge the electron is called the work function.
The right frequency
In order for the electron to be dislodged, the frequency of the light must exceed the threshold frequency. We can write the work function in terms of Planck’s constant and this frequency: $$ \begin{equation}\begin{aligned} \phi=hf_0\\ \end{aligned}\end{equation} $$
The energy of the photon is thus: $$ \begin{equation}\begin{aligned} hf&=hf_0+\frac12 mv^2\\ \end{aligned}\end{equation} $$
We can also express this in terms of wavelength, $\lambda$. Recall that for light, $$f=\frac{c}{\lambda}$$ where $c$ is the speed of light ($3\times 10^8 ms^{-1}$). We thus get:
$$ \begin{equation}\begin{aligned} \frac{hc}{\lambda}&=\frac{hc}{\lambda_0}+\frac12 mv^2\\ \end{aligned}\end{equation} $$ This $\lambda_0$ value is referred to as the cut-off wavelength and is the maximum wavelength that the light can have in order to dislodge the electron. When the light’s frequency exceeds the $f_0$, its wavelength will be less than $\lambda_0$.