In 1887 Hertz discovered the emission of negatively charged particles from metal under the influence of light. Later the particles turned out to be electrons. The phenomena called the photoelectric effect became a new subject of researches for many scientists. For the researches they used the system shown on the picture.

When a beam of monochromatic light falls on the first electrode then some electrons are emitted and next fall on the second electrode so the current flows. The effect could be explained easily using classic Maxwell equations. Light is an electromagnetic wave and like all such waves it transfers energy. Light can also give that energy away to particles, in this case to electrons knocking them out of the metal. So there would be nothing special about that phenomenon if the classic Maxwell theory gave the right view of its course. But it didn't.

To begin with, according to the classic theory the higher intensity of light illuminating the electrode, the more electrons emitted. Also the maximal velocity of an electron should rise. That all should happen according to the classic theory which says that the energy of an electromagnetic wave is connected with its amplitude. And amplitude is directly proportional to wave intensity.
On the other hand maximal kinetic energy (maximal velocity) of electrons shouldn't be conditioned by frequency of the falling wave.

But the classic theory failed.

For the experiments showed that when the frequency of light falling on the electrode increased, the kinetic energy of electrons increased too. In fact the energy was proportional to the frequency of that light. Violet light (whose frequency is higher) brought electrons up to much higher speed than red light did (whose frequency is lower). It was also noticed that there was some frequency limit beneath which electrons were not at all emitted from the cathode. The frequency was called the threshold one. Its value depends on the kind of the chemical element of which the electrode was made. But the dependence between the increase of the kinetic energy and the light frequency is the same for all chemical elements. On the other hand it turned out that the increasing intensity of the falling light didn't induce the increase of the velocity of the emitted electrons.

In 1905 Albert Einstein presented a new theory about how the photoelectric effect proceeded. He assumed that the electromagnetic radiation energy occurs not in the perpetual form but in the form of not continuous packets of waves - the quantum called the photons. The energy of photons increases with the increase of radiation frequency:

       (1)

Light falling on the electrode, and consisting of photons having some energy, knocks the electrons out. The electrons of metal just absorb the photons and take all their energy. So when light intensity increases, the number of photons having proper energy increases too. They knock out a greater number of electrons giving each of them the same energy by the smaller intensity of light. Whereas when light frequency increases, the energy of photons increases too. Yet the photons absorbed by the electrons give them more energy than before. (They give them higher speed.)

Using the energy conservation law Einstein formulated:

       (2)

where: E_k is the maximal energy of an emitted photon, F is the energy of a photon, W is the work needed for knocking out an electron from the electrode (the emission work characteristic for each metal). As you probably remember:

       (3)

So:

     (4)

Maximal kinetic energy of an electron can be measured: We apply some voltage between the electrodes. The voltage slows down electrons. The slower electrons don't reach the electrode but those having the highest energy still do. Careful increasing of the voltage leads to such point where no electron reaches the electrode (current doesn't flow through the circuit). Voltage at which it happens is called the stopping voltage V. So the maximal energy of an electron (e charge) can be determined by using the formula:

       (5)

Placing formulas (3), and (5) into the formula (2) results in:

       (6)

Due to the formula, we achieved, the diagram of V to radiation frequency dependence is linear. The slope of the line is determined by a constant h/e. Because W depends on the kind of metal that constitutes an electrode, then diagrams of V to n for different metals are straight lines of the same angle of inclination but of different abscissa of the roots. Studying the slopes and knowing the e value one can determine the exact value of h.

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As it was shown here, the theory which Einstein offered, explained the experiment very well. Quantum physics began to exist.

 The Compton effect