why the classical theory fails to support the observed cut-off frequency?

Question

why the classical theory fails to support the observed cut-off frequency?

Answer 1

Classical physics says that the energy in light is ‘spread out’, so to speak, over the electromagnetic wave. When the light wave hits an electron and is absorbed, it should eject an electron. However, classical theory predicts that, one, it should take time for the electron to absorb the energy from the light since it is spread out, and two, electrons should be ejected from the atom at any frequency of light.

We know from quantum theory that these predictions are incorrect in addition to its explanation of the nature of light. Although light can behave as a wave, it can also behave as a particle, as it would in this case….photoelectric effect. Additionally, the energy in light is quantized into ‘packets’ of energy. When light strikes an electron, it is the entire photon which is absorbed by the electron all at once, there is no time delay and the electron must absorb all of the energy or none at all. Since the photon’s carry a very specific amount of energy (proportional to their frequency, E = hv) the electrons will only be ejected when they absorb photon’s with energies greater than or equal to the minimum amount of energy needed to eject them, which corresponds to a minimum frequency of light needed to eject photons.

Keeping the intensity of the light constant and increasing the frequency of the light, electrons are ejected from the atom with a greater and greater energy but the number remains the same. Keeping the frequency constant and increasing the intensity, a greater and greater number of electrons are ejected, but their energies stay the same. Below a certain frequency, no matter the intensity of the light, no electrons are ejected because, at this frequency and lower, the photons do not carry sufficient energy to overcome the work function of the material in order to eject an electron.