THE NEW INTERPRETATION OF PHOTOEFFECT

 

Ph.M. Kanarev

 

The Kuban State Agrarian University, Department of Theoretical Mechanics

13, Kalinin Street, 350044 Krasnodar, Russia

E-mail: kanphil@mail.kuban.ru

 

Abstract: It has been disclosed that the equation suggested by A. Einstein for the interpretation of photoeffect is a mathematical model of the law of formation of the atom and ion spectra discovered in 1993. 

Key words: energy, photon, electron, bond

INTRODUCTION 

 

It is known that the most acceptable interpretation of experimental dependencies of photoeffect has been suggested by A. Einstein in 1905, and he got the Nobel prize for it [1], [2], [3]. He made it in the absence of the law of formation of the atom and ion spectra. Now this law has been discovered, and we can check correctness of its interpretation and the possibility of deeper understanding of photoeffect [4], [5], [6], [7].

 

THEORETICAL PART

 

The mathematical model suggested by A. Einstein for the interpretation of experimental dependencies of photoeffect has the following form [3]

 ,                                                                          (1)

 

where  is kinetic energy of the photoelectron emitted by the photocathode;  is energy of the photon, but it is not explained in the papers, of which photon exactly [1], [2], [3], is the photoelectron exit work is a constant, which does not depend on frequency [1], [2], [3]. The main experimental dependencies of photeffect are given in Fig. 1 [2].

 

 

Fig. 1. Dependence of photocurrent on light intensity: a) at its constant frequency; b) at different frequency

 

Photocurrent takes place in the photocathode-collector circuit. If the photocathode is exposed to monochromatic light  (Fig. 1, a), the value of potential – retarding the photoelectrons emitted by the photocathode does not depend on light intensity. Light intensity increase increases photocurrent and does not exert influence on the retarding potential value and, consequently, on kinetic energy of the photoelectrons. If frequency of light, which strikes upon the photocathode, is increased, the value of the negative potential – retarding the photoelectrons is increased (Fig. 1, b).

As the value of the retarding negative potential – is determined by kinetic energy  of the electrons emitted by the photocathode under the influence of light illumination, it results from the dependence shown in Fig. 1,b that kinetic energy  of the photoelectrons emitted by them is increased with the increase of frequency of the photons exposing the photocathode.

Let us try to find a connection of Einstein’s equation (1) with the mathematical model of the law of formation of the atom and ion spectra (2). We have already shown that the mathematical model, which describes the spectra of the multi-electron atoms and ions, has the following form [4], [10], [12]:

 

,                                                         (2)

 

where  is energy of the photon absorbed or emitted by the electron;  is ionization energy of the electron; E₁ is energy of the bond of the electron with the atomic nucleus, which corresponds to its first energy level;  is the main quantum number.

The correlation (2) appears from experimental spectroscopy, that’s why it is a mathematical model of the law of formation of the atom and ion spectra. Einstein’s equation (1) describes similar process of photon absorption by the electrons. It affords ground for supposition of identity of  the equations (1) and (2) and uniformity of their interpretation. It appears from the given equations

.                                                                                (3)

 

It means that if the electron loses bond with the atomic nucleus, its kinetic energy  is equal to energy  of the absorbed photon. Then

.                                                                 (4)

 

It appears from this that  energy value in Einstein’s equation (1) is ionization energy  of the electron emitted by the photocathode material. It appears from the equations (1) and (2) that

 

.                                                              (5)

 

The new clarification: photoelectron exit work  is equal to binding energy of electron  when it is on a definite energy level in the atom or the molecule.

Experimental investigations of photoeffect are carried out usually with the photocathodes made of alkali metals [1]. For example, it is known that the work of the photoelectron exit from the lithium photocathode is equal to =2.4 eV [1]. Ionization energy of this electron is equal to =5.392 eV, and its binding energy with the nucleus corresponding to the first energy level is equal to =14.05 eV [4]. If we take it into account and use the mathematical model of the law of formation of the atom and ion spectra (2), we’ll get a theoretical spectrum of this electron  (theor.), which coincides completely with the experimental spectrum (exp.) (Table 1). Formula (5) gives an opportunity to calculate binding energies  of this electron with the atomic nucleus  (according to Einstein, the exit work), which correspond to all () energy levels of this electron [4].

 

Table 1. Spectrum of the first electron of the lithium atom

 

It is known that the like atoms are united in a molecule with the covalent bond, and binding energies between valence electrons correspond to fractional quantum numbers  [4]. It allows us to determine what is a photoelectron emission source: atoms or molecules of the photocathode material. If we substitute =2.4 eV and =14.05 eV in the formula (5), we’ll find =2.4. As value  is a fractional number, it means that the lithium molecules, not atoms are the source of the photoelectrons (Table 1) [4].

For a photoelectron of the sodium photocathode, we have: =5.139 eV, =13.086 eV and =2.1 eV [1], [4]. If we use the mathematical model of the law of formation of the atom and ion spectra (2), we’ll get a sodium photoelectron spectrum (Table 2) [4].

 

 

Table 2. Spectrum of the 1st electron of the sodium atom

 

 

Value  determined with the help of the formula (5) is equal to =2.5. It appears from this that the sodium molecules, not atoms are the source of the photoelectrons of the sodium photocathode.

The mathematical model of the law of formation of the atom and ion spectra (2) shows that it has no orbital component of electron energy. It appears from this that the electron has no orbital motion in the atom. The molecules are formed by means of a combination of the unlike magnetic poles of their valence atomic electrons, which are connected with the nuclear protons by means of the magnetic poles as well [4], [8].

The analysis of the law of formation of the atom and ion spectra (2) as well as the spectrum calculation results (Table 1 and 2) show that binding energy  of the electron with the atomic nucleus and, consequently, binding energy of valence electrons of two atoms with each other is changed step by step (5). It appears from this that kinetic energy of the photoelectrons  and value of retarding potential – (Fig. 1, b) should be changed step by step as well. The photoelectrons can absorb only the photons, which correspond to their binding energies in the molecules of the given substance. The greater binding energy between the electrons in the molecules, the greater photon energy is required for the break of this bond and the greater kinetic energy the photoelectrons being released will acquire, and the greater potential will be required for their retardation on the way to the collector. Let us pay attention to the fact that the given logical chain originates from the mathematical model of the law of formation of the atom and ion spectra (2) and is present in Einstein’s equation implicitly (1).

Current is present in the circuit due to the fact that the photoelectrons emitted by the photocathode material molecules are substituted by free electrons. They should emit the photons, which energy is equal to binding energy of the electrons in the molecules, but light striking the photocathode does not allow us to see this emission.

 

CONCLUSION

 

Mathematical Einstein’s equation describing experimental regularities of photoeffect has deeper physical sense. When the components of this equation are interpreted correctly, it becomes the mathematical model of the law of formation of the atom and ion spectra discovered by us in 1993 and published in the papers [9], [10], [11], [12], [4].

 

REFERENCES

 

1. Shpolsky E.V.. Atomic Physics. Volume 1. M.: 1963. 575 pages.

2. R. Sprole. Modern Physics. Quantum Physics of Atoms of Solid Body and Nuclei. M.: Nauka, 1974. 591 pages

3. Vikhman E.. Quantum Physics. M.: Nauka, 1977.

4. Kanarev Ph. M.. The Foundation of Physchemistry of Microworld. Krasnodar 2002. 320 pag. (In Russian and in English)

 5. Kanarev Ph. M.. Modelling the Photon and Analyzing  Its Electromagnetic and Physical Nature.  Journal of Theoretics. Vol. 4 – 1. http://www.journaloftheoretics.com

  6. Kanarev Ph.M.   Model for the Free Electron. Galilean Electrodynamics. Volumes 13, Special  Issues 1. Spring 2002. pag. 15-18.

  7. Kanarev Ph.M.  Model of the Electron. «Apeiron» V. 7, no. 3-4, 2000. Pag. 184-193.  http://redshift.vif.com

  8.  Kanarev Ph.M.  Electrons in Atoms.  Journal of Theoretics. Vol. 4 –4. http://www.journaloftheoretics.com

  9. Kanarev Ph.M.. Analysis of Fundamental Problems of Modern Physics. Krasnodar. 1993. 255 pages.

 10. Kanarev Ph. M.. The Analytical Theory of  Spectroscopy. Krasnodar, 1993. 88 pag. (In English).      

 11. Kanarev  Ph.M.  On The Way to The Physics of The XXI Century. Krasnodar. 1995. Pag. 269. (In English).

 12. Kanarev Ph.M.. Law of Formation of the Spectra of the Atoms and Ions. Proceedings of the international conference “Problems of space, time, gravitation”. St.-Petersburg. Publishing house “Polytechnic”, 1997, pp. 30-37.