On excited state of orbital electron

V.6 No 1	5
On excited state of orbital electron

We see alike thing in mathematical modelling of photon as a quantum of energy radiated, as the supporters of quantum hypothesis think, by an orbital electron due to its excitation. But we can show it visually on the mathematical and phenomenological explanation of the Compton effect.

As is known, “the Compton effect is the scattering of electromagnetic radiation on a free either weakly bound electron, where a separate photon resulting from the elastic collision with an electron transfers to it a part of its energy” [11, p. 431].

The conventional diagram of this scattering is shown in Fig. 2 [9, p. 394].

Fig. 2. Conventional diagram of photon’s interaction with a slow electron to calculate the Compton effect

Basing on this scheme, “applying the laws of energy and momentum conservation, i.e. calculating this collision as an impact of elastic spheres, we yield two equations. From the law of energy conservation we have

where m₀c^² is the mass of rest of the electron. Denoting shortly the mass of moving electron as m, rewrite (25) as follows:

The law of momentum conservation gives

[9, p. 394].

Let us draw our attention to the modelling equations (26) and (27). It follows from this last that the electron was at rest before collision. But in this case, in accordance with classical mechanics, the angle between the photon’s and electron’s motion after collision can appear only if non-central collision. While we remember, the photon is identified with the transverse EM wave and transfers the energy just of the EM wave. But transverse EM wave interacts with the charged particles as shown in Fig. 3.

Fig. 3. Interaction of transverse EM wave with the charged particle

If the EM wave interacts as shown in Fig. 2, it basically will not be transverse. To understand the meaning of physical process that really puts the change of X-radiation frequency into dependence on the scattering angle , we have to address to the experimental scheme. We see from it that the effect was seen not in scattering of X-rays on slow electrons but in scattering on graphite consisting of atoms. Thus, it interacted with the resonance system at the radiation frequency close to the frequency of electron orbitals. This is especially well-seen in Fig. 4 taken from G.E. Pustovalov [14, p. 184].

Fig. 4. The electron’s radiation in the Compton effect after G.E. Pustovalov [14, p. 184]

In this case, noting a complex pattern of the atom’s resonance system, we actually can expect the effect that Compton observed. Comparing the pattern of EM field - electron interaction with the kinematic scheme shown in Fig. 4, we see that factually the electron’s inclined radiation is caused not by the conservation law but because the electron’s motion was superimposed with the motion acquired from the electric component of the external electric field, as shown in Fig. 5.

Fig. 5. Kinematic scheme of electron’s emission under affection of an external EM field

The atom’s radiation is caused here by the redistribution of electrons in the ionised atom and its direction will be close to that experimentally registered.

Thus, in the very statement of problem in the quantum-mechanical interpretation we also see a full disregard of physical meaning of process for sake of outward likeness of the result.

So we showed on particular examples how the founders of quantum mechanics freely interpreted the ways of cognition of physical processes. Naturally, this did not add progress in understanding the meaning of atom’s interaction with an external field. “To my mind, the conception of wave mechanics (in this case Mandelschtam means quantum mechanics - Authors) reflects much correctly, it showed itself rather fruitful. But it seems to me, a number of basic concepts with which wave mechanics operates is treated in the main interpretations quite briefly, insufficiently clear and not always convinsingly. Moreover, I am not sure that these concepts have been established enough, that they are so clear and sharp as the main concepts of classical physics are. And I think, this is not occasionally.

The circumstance that vagueness and reticence in the foundations of wave mechanics originate not from a bad description of some or other textbook is seen at least because these main issues are under debates up to now, and by such people that we do not know anyone greater among physicists. Up to last years there was not a full agreement among greatest authorities. It is worthy to recall the exchange of opinions that took place few years ago on the completeness of wave mechanics in which such researchers as Einstein, Bohr, Schroedinger and others expressed opposite opinions” [10, p. 326].