Wave theory sufficiently explains the reflection, refraction, diffraction and interference of light. It, however, fails to explain the photoelectric effect.
Intensity of the light
This is the power transmitted to unit cross sectional area of the material containing the electrons. Classical Physics would posit that light with a sufficient intensity (brightness) will be able to dislodge the electrons.
However, it does not matter how intense the light is, if it does not possess the correct frequency, the electrons will never be ejected from the metal. Intensity increases the number of electrons that are ejected (provided that the threshold frequency is exceeded). A greater photoelectric current results from a higher intensity.
Energy buildup over time
Classical Physics would predict that regardless of the wavelength of the incident light, the energy transmitted by the photons should eventually be sufficient to dislodge the electrons.
Think of it as the light wave should “heat up” the electrons over time and eventually dislodge them.
The opposite is true. The time of exposure of the metal to the light does not matter - unless the light has the correct wavelength, the electrons will remain intact.
1) Light with low intensity and $f>f_0$ will dislodge electrons
- False
- True
2) Light with high intensity and $f<f_0$ will dislodge electrons
- True
- False
3) Light with low intensity and $f<f_0$ will dislodge electrons
- False
- True
4) Light with high intensity and $f>f_0$ will dislodge electrons
- False
- True
The particulate theory
With the view that light consists of particles called photons, we can say that each photon has a certain amount of energy and that energy is not dependent on the intensity of the light but rather its frequency: $$ \begin{equation}\begin{aligned} E_{photon}=hf\\ \end{aligned}\end{equation} $$
In the photoelectric effect, exactly one photon interacts with an electron and only if the frequency of this photon is sufficient then will its energy be enough to cause the electron to be ejected: $$ \begin{equation}\begin{aligned} hf\geq hf_0\\ \end{aligned}\end{equation} $$
All of the energy of the photon is transferred instantly to the electron, with the excess energy becoming the kinetic energy of the electron: $$ \begin{equation}\begin{aligned} hf&=\phi+E_k\\ E_k&=hf-\phi\\ \frac12mv^2&=hf-hf_0\\ \end{aligned}\end{equation} $$
This theory was introduced by Albert Einstein.