Question

We are shining a red light on a totally different metal, and are ejecting photo electrons with a small KE of 1.5 eV. We are going to make predictions about what happens when we shine light of a greater intensity red light on the same sample. Identify what classical (wave) theory of light incorrectly predicts we would observe. Contrast that with the result which the Quantum Model correctly predicts. I am looking for several solid details.

Answer 1

Concept required - The photoelectric effect is an effect by which an electric current is produced when a light of suitable energy is incident on a material with suitable threshold frequency

Solution -

The classical theory of photoelectric effect says that Intensity of a wave is the energy incident on a unit area, and that the energy of the wave is proportional to the square of wave amplitude

Now there are 3 observations of PE effect that couldn't be explained using the classical theory- these predictions are -

1. This theory predicts that the ejaculation of electrons is dependent on the intensity of light and not on the threshold frequency. Hence this theory cant explain for the existence of threshold frequency
2. Classical theory says that the electrons require some time to absorb energy before they could escape form the material. But in PE effect no delay is found , and the electron emission is immediate
3. This theory says that the light of higher intensity would affect the kinetic energy of the released electron. But it cant predict why max kinetic energy is dependent on the frequency

This was the result given by the photoelectric effect. Now coming to the Quantum theory, which correctly explains the PE effect,

Using Planck's theory of Quantization where symbols have their usual meaning. Now the Kinetic energy is given by , as per Einstein - ( phi is the work function). So this explains the fact that the kinetic energy is depending on the frequency of incident radiation.

Now for the frequency such that   , KE is 0 , hence no photo-emission is possible. This explains the concept of threshold frequency , below which the photo- emission is not possible

Now the work function depends upon metal , hence varies in substances. Also the radiation from quantum concept is associated with the number of photons on unit area in unit time .Thus greater intensity means a greater number of photons being incident on the surface. Thus a higher number of photons means larger photo-emission- and consequently, larger current. Hence the current increases with the number of photons incident, or in other words, the intensity of the light

So in this way, the Quantum theory contrasts with the classical theory which couldn't explain the above 3 observation