Quants

QUANTUM THEORY
THE NEW GREAT IDEA

In 1887 Hertz discovered the phenomena of the emission of the negatively charged particles of metal under the influence of light. The particles as it got later shown are the 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 the A electrode is incidenced by a beam of monochromatic light causing the emission of electrons which then incidence the B electrode then the current flows. Using the classic, physical laws one could expect that when increasing the intensity of the light (and so the energy of a light beam) incidencing the electrode, the knocked out electrons should be of higher energy (the light beam should give them more energy). But no such phenomena happens. With the increase of the light intensity increases only the number of knocked out electrons.

The diagram for the experimentialsystem for studying the photoelectric effect

    The experiments showed also that when increasing the frequency of the light incidencing the electrode the kinetic energy of the electrons is the thing that increases. That energy is proportional to the frequency. It was also noticed that there is some frequency limit under which the electrons are not emitted from the cathode at all. The frequency was called the treshold one. Its value is on the kind of the chemical element of which the electrode was made depended. But the dependence between the increase of the kinetic energy and the light frequency is the same for every chemical element.
    Those experimental facts were in contrary with the classic electromagnetic theories. In 1905 Albert Einstein gave the solution. He assumed that electromagnetic radiation energy occurs not in the perpetual form but in the form of the not continuous packets of waves - the quantum called the photons. The energy of photons increases with the increase of radiation frequency. According to the theory the energy of the photon is equal h*v, where v is the frequency of radiation, h is the Planck constant.
    The light incidencing the electrode and consisting of photons of given energy knocks the electrons out. The electrons of metal just absorb the photons and take its all energy. So when the intensity of light increases, increases the number of photons of the given energy. They knock out the greater number of electrons giving each of them the same energy by the smaller intensity of light. Whereas when the light frequency increases then the energy of photons increases too. The photons absorbed by the electrons give them more energy than before.
    Using the energy conservation law Einstein formulated:

(1)

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

(2)

The kinetic energy of the kicked out electron is given by the formula:

(3)

where m is the mass of the electron, b is its velocity. The energy can be also calculated from this formula:

(4)

where e is the charge of the electron, V is the retardation potential that is - the potential needed to be applied to the electrodes to achieve the situation of the whole range of the knocked out electrons coming back-the current doesn't flow. Putting the (2) and (4) into the(1) we achieve:

(5)

According to the achieved formula the graph of V from the radiation frequency is linear. The slope of the straight line is the constant h/e. Because W depends on the metal of which the electrode is made so the graphs of the V from niu

for different metals are the straight lines of the same angle of inclination but of different abscissa of the roots. The graphs are in a very good accordance with the experimental data. Having that data one can calculate the value of the h.
The theory said that radiation is emitted or absorbed under the form of quantum. Energy of a quantum is connected with frequency of radiation according with formula (2).
Thanks to this new theory many experimental facts were explained, and Niels Bohr used this theory to make new model of atom.