Unizor - Physics4Teens - Energy - Light as Quants

Notes to a video lecture on http://www.unizor.com

Quants of Light

By the end of 19th century the electrons, as carriers of electricity, were discovered by Sir Joseph Thomson in 1897, and many scientists experimented with electricity.

At that time the wave theory of light was dominant. It could explain most of experimental facts and was shared by most physicists.
However, there were some new interesting experimental facts that could not be easily explained in the framework of the classical wave theory of light as oscillation of electromagnetic field.

The photoelectric effect was one of such experimental facts that physicists could not fit into classical wave theory.

Consider a simple electrical experiment when two poles, positive and negative, positioned close to each other, are gradually charged. After a charge reaches certain value, a spark between these poles causes the discharge of electricity.

The electric charge was attributed to electrons with a negatively charged pole having more electrons than in an electrically neutral state and a positively charged one having less electrons than in an electrically neutral state.
The electric spark was the flow of excess electrons from a negative pole to a positive one, thus bringing them both to an electrically neutral state.

It was observed that, if the negative pole is lit by light, the discharge occurs earlier, with less amount of charge accumulated in the poles.
This was so-called photoelectric effect.

The experimental characteristics of the photoelectric effect were:
(a) if photoelectric effect is observed with specific frequency of the light, the number of electrons leaving the negative pole in a unit of time is proportional to intensity of the light;
(b) the speed of photo-electrons and, therefore, their kinetic energy do not depend on intensity of light, but on its frequency; higher intensity light produces more electrons, but their speed remains the same, while higher frequency light produces faster photo-electrons;
(c) for each material, used as a negative pole, there is minimal frequency of light necessary to initiate the photoelectric effect; high intensity or prolong time exposure to light of a lesser frequency do not produce photoelectric effect.

The explanation coming to mind within a framework of the wave theory of light would be as follows.
Light is oscillations of the electromagnetic field. Electrons, accumulated during the charging process, are vibrating more intensely as a result of the oscillations of the electromagnetic field of the light, whose energy is transformed to electrons, so photo-electrons leave the negative pole easier, thus facilitating an earlier discharge.

This would be a great explanation if not for a couple of contradictory facts.
The first contradiction is the property (b) of the photoelectric effect. According to the classical wave theory, the speed of photo-electrons must be dependent on the intensity of the light (amplitude of electromagnetic waves), which was not observed. And the (c) property is also unexplainable by classical wave theory, because, again, within a framework of the classical wave theory for any frequency we can find an intensity of light sufficient to "knock" out the electrons from the negative pole or keep the light of lesser intensity long enough time to transfer to electrons sufficient amount of energy to fly off the surface of the pole, which was not observed.

The explanation of these phenomena came with introduction of quants of light - a hypothesis offered by Planck and used by Einstein to explain the properties of photoelectric effect.

According to the explanation of photoelectric effect offered by Einstein, light propagates in space not as a continuous stream of waves of electromagnetic oscillations, but in small indivisible packets (quants of light or photons), separated in space and traveling along the same path, thus resurrecting the corpuscular theory, but without rejecting the electromagnetic origin of light.

The energy of each photon proportionally depends on the frequency of oscillation of electromagnetic field that carries the light, not on intensity of light, with intensity of light being just a measure of the number of photons passing through a point in space in a unit of time.

The energy of light is absorbed by electrons also in these photons. To break away the electron needs certain minimal energy.
If the energy of a single photon is sufficient to overcome the atomic forces that keep the electron inside the negative pole, this electron becomes a photo-electron and flies away to a positive pole.
If the energy of a photon is less than this minimal amount necessary to overcome the atomic forces, this energy is dissipated as heat, and no photo-electrons are produced.

Within the framework of this new quantum theory of light all the characteristics of the photoelectric effect can find their explanation.
Let's analyze them.

(a) If photoelectric effect is observed with specific frequency of the light, the number of electrons leaving the negative pole in a unit of time is proportional to intensity of the light;
Explanation: each photon has sufficient amount of energy to "knock" out an electron, and intensity is the number of such photons per unit of time.

(b) The speed of photo-electrons and, therefore, their kinetic energy do not depend on intensity of light, but on its frequency; higher intensity light produces more electrons, but their speed remains the same, while higher frequency light produces faster photo-electrons;
Explanation: speed of electrons and, therefore, their kinetic energy depend on the energy of a photon that "knocked" these electrons out, which, in turn, is proportional to the frequency of light, while intensity of light (the number of photons per unit of time) affects the number of photo-electrons produced by light, not their individual energy.

(c) For each material, used as a negative pole, there is minimal frequency of light necessary to initiate the photoelectric effect; high intensity or prolong time exposure to light of a lesser frequency do not produce photoelectric effect.
Explanation: the energy, needed by an electron to break away from atomic forces that keep it inside the material, obviously depend on the material; as soon as the light frequency is sufficient for one photon to carry that amount of energy, the photoelectric effect can start; photons of lesser level of frequency cannot "knock" out the electrons from the surrounding material, and the energy of the light is just dissipated as heat.