Photoelectric Effect and Wave Theory of Light
It is generally argued that the photoelectric effect provides evidence for the particle nature of light as the photoelectrons are almost released instantaneously when the light hits the detector. This argument is based on the classical wave theory of light and the assumption that a light wave has an energy flux c.E2/4π where E is the electric field amplitude of the wave and c the speed of light. Using this expression, the energy absorbed by an atom would indeed be so small that it would take about one second for sunlight to release any photoelectrons, contrary to what is observed and hence suggesting that the wave model of light could not explain the photoeffect. However, this conclusion is based on the flawed assumption that the above expression can be assigned to the 'energy flux' of the electromagnetic wave and in fact that such a physical quantity exists in the first place for electromagnetic waves. The point is that this expression is a result from classical electrostatics describing the potential energy of a capacitor (i.e. the work that is needed to charge the capacitor). However, even here it is wrong to interpret this as energy stored in the electric field, because kinetic and potential energies of the particles fully describe the system and there is no room for a separate field energy, neither in electrostatics nor in electrodynamics. Additionally of course, there is no explanation as to how this assumed electromagnetic wave 'energy' should be converted to the kinetic energy of the released photoelectrons.
In the following it is shown that a consistent semi-classical treatment of the interaction process between an atomic electron and an electromagnetic wave does indeed yield ionization times that may be short enough to explain the observations. On the other hand, it is shown that the particle model would in fact not enable any photoelectric effect at all as the collisional energy transfer would be much too small.
Classical wave theory cannot explain the first 3 observations of photoelectric effect.
1. Existence of the threshold frequency
Since energy of the wave is dependent on the square of its amplitude, the classical wave theory predicts that if sufficiently intense light is used, the electrons would absorb enough energy to escape. There should not be any threshold frequency.
2. Almost immediate emission of photoelectrons
Based on classical wave theory, electrons require a period of time before sufficient energy is absorbed for it to escape from the metal. Accordingly, a dim light after some delay would transfer sufficient energy to the electrons for ejection, whereas a very bright light would eject electrons after a short while. However, this did not happen in photoelectric effect.
3. The independence of kinetic energy of photoelectron on intensity and the dependence on frequency
According to classical wave theory, if light of higher intensity is used, the kinetic energy of an ejected electron can be increased. This is because the greater the intensity, the larger the energy of the light wave striking the metal surface, so electrons are ejected with greater kinetic energy. However, it cannot explain why maximum kinetic energy is dependent on the frequency and independent of intensity.