And now, if we assume that the electron oscillates inВ this way, then it resembles the construction ofВ an oscillator or, more precisely, aВ mathematical pendulum with its rigidity and frequency determined byВ (2.6).
And if we substitute the necessary rigidity for (2.6), and take the mass of the electron as the mass, then the frequency will have the order of optical waves. That is, the atom glows in the visible region and even the glow effect can be explained using the Thompson model, but alas, another problem has arisen here. Even if we assume that the hydrogen atom glows, then according to this model it glows only with 1 frequency, when in reality it emits light with 4 frequencies. So it was proved that the Thompson model was not correct and it was necessary to create new models.
The next model is Ernest Rutherford's 1908-1910 model, which irradiated metal plates of thin gold foil with radioactive radiation, or more precisely with special alpha particles. At the same time, if you remove the plate on a circular screen (a phosphor that glowed), a point appeared, and when the plate was placed, this point scattered to form a spot, but in addition, some of these rays were reflected more than 90 degrees (right angle). And if we assume that the atom consists as the Thompsons were supposed to, then because of such a simply huge "smeared" positive charge on the size of the atom, the deviation should not have exceeded hundredths of a degree, and here there was a deviation of almost 180 degrees.
Then Rutherford suggested that in order to satisfy the results of the experiment, it should be assumed that the positive charge is strongly concentrated in a small area, and all the remaining space is practically empty, so the particles were only slightly scattered under the influence of an electric field or bumped into electrons that simply revolved around the atomic nucleus. This is how Rutherford first created a planetary model of an atom, according to which there is a single nucleus inside, and electrons already rotate around it in their orbits. However, there was still a lot to prove, for example, why did the electrons not fall to the atom, spending their energy on rotation, radiating energy at the same time?
But there was an answer to this question, thanks to Rutherford’s colleague Niels Bohr, who created the model of the hydrogen atom of Bohr, some postulates were accepted according to his model. Namely, the statements that an electron does not emit energy while in stationary orbits and can emit energy in the form of electromagnetic radiation (photons or light particles) only when moving from one orbit to another, and strictly with the energy equal to the energy difference in these two orbits. This has already led to the statement about the quantization of energy, that is, about operating with energy, particles, and their other parameters only in the form of portions. That is, there can be no smooth transition, either the electron is here, or it is not here, or it has released a certain amount of energy, or it has not. This idea was also supported by Max Planck when studying a «completely black body», a topic that would explain the glow when objects are heated.
Figure 2.4. Ernest Rutherford
Figure 2.5. NielsВ Bohr
Thus, when objects are heated, part of the energy from the collision of atoms flows to the nucleus, and after transferring it to an electron and its transition to another energy level, and then back, there is the release of a photon with a certain wavelength, so when bodies are heated, they emit light. And already when an external photon hits an atom, there is also an exit through the electron transition, but with a longer wavelength and, accordingly, a lower frequency, due to which such a phenomenon as absorption and reflection of light is observed. As for the passage of alpha particles during Rutherford's bombardment of gold foil, it was the nucleus with a high potential that caused such results, as well as the fact that almost 99.9% of the atom is empty and the same 99.9% of the atom's mass is concentrated in its nucleus. Thus, the Rutherford model was able to explain not only the results of the Rutherford experiment itself, but also many other phenomena, which confirms the validity of this model.
It is also appropriate to point out that the electrons are located not only in circular orbits, but also along their own separately defined paths, the shapes of which resemble "8" on different axes. This allows you to place a much larger number of electrons, for example, for such large atoms as uranium, with the ordinal number 92, neptunium-93, curium-96, californium-98 and many others. These paths are given from a separate theory of orbitals, which also proves the phenomenon of quantization in the world of elementary particles, from which it can be concluded that electrons do not move, however, like all micro-objects, they appear-disappear, appear-disappear, such is their nature of existence.
And all this forms the complete structure of the atom. This structure forms the so-called «quantum ladder», which is clearly manifested when determining the size of all particles. The atom itself has a diameter of about 10—8 cm, of course it differs from each atom, but the average size is equal to this indicator. In the center of the atom there is its own nucleus with a radius of about 10—12 cm. Electrons with a diameter less than 10—17 cm rotate around the nucleus, but this is a point particle for experimenters, since the exact size of the electron is difficult to consider at the moment and even when viewed with such an indicator as 10—17 cm, there will be no loss in accuracy. Unless you take into account experiments with increased accuracy aimed at studying higher resolutions.
Figure 2.6. The quantum ladder
The nucleus itself is composite and consists of particles called nucleons, with further approximation it can be seen that there are 2 types of nucleons inside the nucleus: protons and neutrons. Each of them is approximately 10-13 cm in its own size . And with further approximation, smaller particles – quarks – can be observed. Quarks themselves are already point particles and have a size also smaller than 10-17, as well as electrons.
If we talk about further increase and passage even further into the depths of matter, then what will be there and how it looks is unknown today. But the fact is that it is quite difficult to do this even today.
And today the quantum world appears exactly in this form. Amazing operations are performed with these and many other particles, many other particles are formed. The study of the quantum world itself is very important, because today the study in this area has led to a number of discoveries, a vivid example of which is the creation of nuclear power plant technologies, the creation of particle accelerators, research in the field of thermonuclear reactions, widely known as "the creation of an artificial Sun" and many other studies have their origins in this area. And it was also in this area that the Electron research was born, to which this narrative is being conducted.
The discovery by Conrad X-Ray of special signals emitted by the cathode tube, which later received the name of the X-ray itself, caused a great furor. Many scientists began active research, but before the world could recover from this surprise, amazing materials that emitted these amazing rays were suddenly discovered. Henri Becquerel, who is one of the famous scientists who studied fluorescence, decided to prove the fact of the connection of this phenomenon with a radioactive source – uranium salt. It was then that Becquerel, in 1896, left the material on the photographic plate without illumination by chance and noticed that there were darkenings on the photographic plate, proving that the salt itself emits amazing rays. Many scientists have investigated this phenomenon until it was proved that these emissions are the result of radioactive decay of atomic nuclei.
Figure 2.7В Photo taken byВ Becquerel
It is for this reason that 1896 is considered the year of the beginning of research in the field of the atomic nucleus. It was also known that if you direct focused radiation from a radioactive source (uranium salt) by placing it in a lead chamber with a single slit, and then place magnets on the path of this study, then this radiation will be divided into 3 types. At the same time, the radiation flux that was directed to the right has a negative charge, the flux that was turned to the left has a positive charge, which is easily proved from Lorentz's law. And the third radiation that has not been rejected has no charge.
Thus, the positive radiation was called alpha particles, and after measuring the masses of these particles based on the Lorentz force formula, when the magnetic field induction changes (the principle of operation of the mass spectrometer), it was possible to make sure that these are the nuclei of the helium atom. Negative particles, which were called beta particles, with the same analysis turned out to be just fast electrons, and rays that were not rejected were called gamma radiation.
After the initial analysis ofВ the structure ofВ radioactive radiation was carried out, it can be made sure that the radiation itself consists ofВ 2В types ofВ particles and 1В type ofВ waves, namely gamma radiation, thanks toВ which it is already possible toВ give aВ general definition ofВ radioactivity:
Radioactivity is the spontaneous emission ofВ various particles and radiation byВ atomic nuclei.
Speaking in more detail about the dates of determination and research of radioactivity, it should be pointed out that by 1900 all types of radioactivity had already been investigated, although the atomic nucleus itself was discovered by Ernest Rutherford only in 1911. The first radiation, alpha radiation, which, as already determined, consists of helium nuclei, was discovered in 1898 by the same Ernest Rutherford and became known as alpha decay. Also beta decay or electron flight was discovered by the same Rutherford in the same 1898. But gamma radiation was determined and investigated only in 1900 by Paul Ulrich Willard.
These studies proved that the darkening of the plates observed by Becquerel was caused by radioactive radiation. Consequently, it is now possible to come to the concept of radioactive decay:
Radioactive decay is aВ spontaneous process characteristic ofВ the phenomena ofВ the microcosm at the quantum level. At the same time, the result ofВ radioactive decay cannot be predicted accurately, only toВ determine the probability. Such aВ nature ofВ phenomena is not an imperfection ofВ devices, but is aВ representation ofВ the processes ofВ the quantum world themselves.
From this statement, we can conclude that there must be some generally accepted law explaining this phenomenon. The conclusion ofВ the law ofВ radioactive decay is as follows:
Let there be N (t) identical radioactive nuclei or unstable particles at a certain time t and the probability of the decay of a single nucleus (particle) per unit of time is equal to О».
InВ this case, over aВ period ofВ time dt, the number ofВ radioactive nuclei (particles) will decrease byВ dN, which implies the following expression (2.7).
If we deduce aВ change inВ time from this ratio, we get (2.8).
InВ (2.8), the concept ofВ П„ is defined inВ (2.9) and is the average lifetime ofВ the nucleus (before decay), which is quite convenient toВ use, and N (0) inВ this case is the number ofВ nuclei at the initial time.
It is also possible toВ present another more simplified form (2.8) inВ (2.10).
Where the half-index time is the half-life and is calculated byВ (2.11) and is equal toВ aВ separate value for each radioactive nucleus.
If it is necessary toВ determine the average number ofВ decays (for low-speed decay), it is calculated byВ (2.12).
When this pattern is transformed, aВ radioactive decay curve is formed (Fig. 2.8).
Figure 2.8. Radioactive decay curve
From the graph, you can see that the pattern is exponential and at the same time decreases each time by half of the period, followed by a decrease.
As an experimental analysis ofВ this phenomenon, the following can be shown. 100В measurements were carried out over the same period ofВ time and the number ofВ decays was measured. As aВ result, aВ graph was obtained on (Figure 2.9), where the average number ofВ decays equal toВ 77.47В coincided with the value inВ (2.12), which is aВ clear proof ofВ the validity ofВ the general pattern.
Figure 2.9. The result ofВ the experiment
The general view ofВ the distribution ofВ these statistics is already presented according toВ aВ different law. That is, the probability Pn for the time t for testing the n number ofВ decays is given byВ the Poisson distribution (2.13).
This conclusion is already inherent inВ probability theory, and if we rely on it, then also for the case when (n>> 1) Gaussian distributions (2.14) are already used.
If we express these two patterns on graphs, we can get almost identical patterns with an increase inВ the average number ofВ decays. For example, if the average number ofВ decays is 2, then there is some difference inВ the results ofВ the Poisson and Gauss distribution, but when this number, for example, reaches 7В and higher values, this difference becomes less significant, as shown inВ (Figure 2.10).
Figure 2.10. The graph ofВ the probability ofВ decay according toВ the Poisson and Gauss distributions for the average decay number equal toВ 2В andВ 7
After it has been decided with probability at zero speed, we can pay attention to cases when the effects of the theory of relativity come into play. In the microcosm, where the sizes of the studied objects are practically invisible, for example, for atoms with their sizes of 10-8 cm, for atomic nuclei with their 10-12-10-13 cm and for other particles with 10-13-10-17 cm, the speeds are often comparable, close or even equal to the speed of light. Thanks to this, all the features and effects of the theory of relativity are clearly manifested in the microcosm.
