| Parameter name | Meaning |
| Article topic: | ALPHA DECAY |
| Rubric (thematic category) | Radio |
Decay condition. Alpha decay is characteristic of heavy nuclei, in which a growth A a decrease in binding energy per nucleon is observed. In this region of mass numbers, a decrease in the number of nucleons in the nucleus leads to the formation of a more tightly bound nucleus. At the same time, the gain in energy with a decrease A one is much less than the binding energy of one nucleon in the nucleus; therefore, the emission of a proton or neutron, which has a binding energy equal to zero outside the nucleus, is impossible. The emission of the 4 Ne nucleus turns out to be energetically favorable, since the specific binding energy of a nucleon in a given nucleus is about 7.1 MeV. Alpha decay is possible if the total binding energy of the product nucleus and the alpha particle is greater than the binding energy of the original nucleus. Or in mass units:
M(A,Z)>M(A-4, Z-2) + M α (3.12)
An increase in the binding energy of nucleons means a decrease in the rest energy precisely by the amount of energy released during alpha decay E α. For this reason, if we imagine the alpha particle as a whole within the product nucleus, then it should occupy a level with positive energy equal to E α(Fig. 3.5).
Rice. 3.5. Diagram of the energy level of an alpha particle in a heavy nucleus
When an alpha particle leaves the nucleus, this energy is released in free form, as the kinetic energy of the decay products: the alpha particle and the new nucleus. The kinetic energy is distributed between these decay products in inverse proportion to their masses and, since the mass of the alpha particle is much less than the mass of the newly formed nucleus, almost all of the decay energy is carried away by the alpha particle.. Τᴀᴋᴎᴍ ᴏϬᴩᴀᴈᴏᴍ, with great accuracy E α is the kinetic energy of the alpha particle after decay.
At the same time, the release of energy is prevented by the Coulomb potential barrier U k(see Figure 3.5), the probability of passage of which by an alpha particle is small and falls very quickly with decreasing E α. For this reason, relation (3.12) is not a sufficient condition for alpha decay.
The height of the Coulomb barrier for a charged particle penetrating into or leaving the nucleus increases in proportion to its charge. For this reason, the Coulomb barrier constitutes an even greater obstacle to the escape of other tightly bound light nuclei from a heavy nucleus, such as 12 C or 16 O. The average binding energy of a nucleon in these nuclei is even higher than in the nucleus 4 Not, in connection with this, in a number of cases, the emission of a nucleus 16 O instead of sequentially emitting four alpha particles, it would be energetically more favorable. In this case, the emission of nuclei heavier than the nucleus 4 Not, not visible.
Explanation of the collapse. The mechanism of alpha decay is explained by quantum mechanics, because within the framework of classical physics this process is impossible. Only a particle with wave properties can appear outside the potential well when E α . Moreover, it turns out that only a potential barrier of infinite width, with a probability equal to one, limits the presence of a particle within the potential well. If the width of the barrier is finite, then the probability of moving beyond the potential barrier is fundamentally always different from zero. True, this probability quickly decreases with increasing width and height of the barrier. The apparatus of quantum mechanics leads to the following expression for the barrier transparency or probability ω for a particle to be outside the potential barrier when colliding with its wall:
(3.13)
If we imagine an alpha particle inside a spherical potential well with a radius R, moving at speed v α, then the frequency of impacts on the pit walls will be v α/R, and then the probability of an alpha particle leaving the nucleus per unit time, or the decay constant, will be equal to the product of the number of attempts per unit time times the probability of passing the barrier in one collision with the wall:
, (3.14)
where is some indefinite coefficient, since provisions were accepted that were far from the truth: the alpha particle does not move freely in the nucleus, and in general there are no alpha particles in the composition of nuclei. It is formed from four nucleons during alpha decay. The value has the meaning of the probability of the formation of an alpha particle in the nucleus, the frequency of collisions of which with the walls of the potential well is equal to v α/R.
Comparison with experience. Based on dependence (3.14), many phenomena observed during alpha decay can be explained. The half-life of alpha-active nuclei is longer, the lower the energy E α emitted during the decay of alpha particles. Moreover, if the half-lives vary from fractions of a microsecond to many billions of years, then the range of change E α very small and approximately 4-9 MeV for nuclei with mass numbers A>200. Regular dependence of half-life on E α was discovered long ago in experiments with natural α-active radionuclides and is described by the relation:
(3.15)
where and are constants that differ slightly for different radioactive families.
This expression is commonly called the Geiger-Nattall law and represents the power law dependence of the decay constant λ from E α with a very high rate. Such a strong addiction λ from E α directly follows from the mechanism of alpha particle passage through a potential barrier. Transparency of the barrier, and therefore the decay constant λ depend on the area integral R 1 -R exponentially and rapidly increases with growth E α. When E α approaches 9 MeV, the lifetime with respect to alpha decay is small fractions of a second, ᴛ.ᴇ. At an alpha particle energy of 9 MeV, alpha decay occurs almost instantly. I wonder what the meaning is E α still significantly less than the height of the Coulomb barrier U k, which for heavy nuclei for a doubly charged point particle is approximately 30 MeV. The barrier for a finite size alpha particle is somewhat lower and should be estimated at 20-25 MeV. However, the passage of the Coulomb potential barrier by an alpha particle is very efficient if its energy is not lower than a third of the barrier height.
The transparency of the Coulomb barrier also depends on the charge of the nucleus, because The height of the Coulomb barrier depends on this charge. Alpha decay is observed among nuclei with mass numbers A>200 and in the region A~150. It is clear that the Coulomb barrier at A~150 the probability of alpha decay is noticeably lower for the same E α much bigger.
Although theoretically, at any energy of an alpha particle there is a possibility of penetration through the barrier, there are limitations in the ability to experimentally determine this process. It is not possible to determine the alpha decay of nuclei with a half-life greater than 10 17 – 10 18 years. Corresponding minimum value E α higher for heavier nuclei and is 4 MeV for nuclei with A>200 and about 2 MeV for nuclei with A~150. Consequently, the fulfillment of relation (3.12) does not necessarily indicate the instability of the nucleus with respect to alpha decay. It turns out that relation (3.12) is valid for all nuclei with mass numbers greater than 140, but in the region A>140 contains about one third of all naturally occurring stable nuclides.
Limits of stability. Radioactive families. The limits of stability of heavy nuclei with respect to alpha decay can be explained using the nuclear shell model. Nuclei that have only closed proton or neutron shells are especially tightly bound. For this reason, although the binding energy per nucleon for medium and heavy nuclei decreases with increasing A, this decrease always slows down when approaching A to the magic number and accelerates after passing A through the magic number of protons or neutrons. As a result, energy E α turns out to be significantly lower than the minimum value at which alpha decay is observed for magic nuclei, or the mass number of the nucleus is less than the mass number of the magic nucleus. On the contrary, energy E α increases abruptly for nuclei with mass numbers exceeding the values A magic nuclei, and exceeds the minimum practical stability in terms of alpha decay.
In the field of mass numbers A~150 alpha-active are nuclides whose nuclei contain two or more neutrons more than the magic number 82. Some of these nuclides have half-lives much longer than the geological age of the Earth and, therefore, are presented in their natural form - nuclides 144 Nd, 147 Sm, 149 Sm, 152 Gd. Others were produced by nuclear reactions. The latter have a lack of neutrons compared to stable nuclides of the corresponding mass numbers, and for these nuclides β + decay usually competes with alpha decay. The heaviest stable nuclide is 209 Bi, the nucleus of which contains a magic number of neutrons of 126. The element leading to bismuth, lead, has a magic number of protons of 82, and 208 Pb is a doubly magic nuclide. All heavier nuclei are radioactive.
Since the product nucleus is enriched in neutrons as a result of alpha decay, several alpha decays are followed by beta decay. The latter does not change the number of nucleons in the nucleus; therefore, any nucleus with mass number A>209 can become stable only after a certain number of alpha decays. Since the number of nucleons during alpha decay decreases by 4 units at once, the existence of four independent decay chains is possible, each with its own final product. Three of them are present in nature and are called natural radioactive families. Natural families end their decay with the formation of one of the isotopes of lead, the final product of the fourth family being the nuclide 209 Bi(see table 3.1).
The existence of natural radioactive families is due to three long-lived alpha-active nuclides - 232 Th, 235 U, 238 U, having half-lives comparable to the geological age of the Earth (5.10 9 years). The longest-lived representative of the extinct fourth family is the nuclide 237 Np– isotope of the transuranium element neptunium.
Table 3.1. Radioactive families
Today, by bombarding heavy nuclei with neutrons and light nuclei, a lot of nuclides have been obtained, which are isotopes of transuranium elements (Z>92). All of them are unstable and belong to one of four families.
The sequence of decays in natural families is shown in Fig. 3.6. In cases where the probabilities of alpha decay and beta decay are comparable, forks are formed that correspond to the decay of nuclei with the emission of either alpha or beta particles. In this case, the final decomposition product remains unchanged.
Rice. 3.6. Decay patterns in natural families.
The names given are assigned to radionuclides during the initial study of natural decay chains.
ALPHA DECAY - concept and types. Classification and features of the category "ALPHA DECAY" 2017, 2018.
1.3. Alpha decays, beta decays and gamma emissions of radioactive nuclei
Alpha decay is the spontaneous emission of alpha particles, representing the nuclei of a helium atom, by a radioactive nucleus. The decay proceeds according to the scheme
AmZ X → AmZ − − 42 Y + 2 4He . |
IN In expression (1.13), the letter X denotes the chemical symbol of the decaying (mother) nucleus, and the letter Y denotes the chemical symbol of the resulting (daughter) nucleus. As can be seen from diagram (1.13), the atomic number of the daughter nucleus is two and the mass number is four units less than that of the original nucleus.
The alpha particle has a positive charge. Alpha particles characterize two-
by basic parameters: travel length (in air up to 9 cm, in biological tissue up to 10-3 cm) and kinetic energy in the range of 2...9 MeV.
Alpha decay is observed only in heavy nuclei with Am>200 and charge number Z>82. Inside such nuclei, the formation of isolated particles of two protons and two neutrons occurs. The separation of this group of nucleons is facilitated by the saturation of nuclear forces, so that the formed alpha particle is subject to less nuclear attractive forces than individual nucleons. At the same time, the alpha particle experiences greater Coulomb repulsion forces from the protons of the nucleus than individual protons. This explains the emission of alpha particles from the nucleus, and not individual nucleons.
IN In most cases, a radioactive substance emits several groups alpha particles of similar but different energies, i.e. groups have a spectrum of energy. This is due to the fact that a daughter nucleus can arise not only in the ground state, but also in excited states with different energy levels.
The lifetime of excited states for most nuclei lies within
affairs from 10 - 8 to 10 - 15 s. During this time, the daughter nucleus passes into the ground or lower excited state, emitting a gamma quantum of the corresponding energy equal to the difference between the energies of the previous and subsequent states. An excited nucleus can also emit any particle: a proton, neutron, electron or alpha particle. It can also transfer excess energy to one of the electrons in the inner layer surrounding the nucleus. The transfer of energy from the nucleus to the closest electron of the K-layer occurs without the emission of a gamma quantum. The electron that receives energy flies out of the atom. This process is called internal conversion. The resulting vacant position is filled with electrons from higher energy levels. Electronic transitions in the inner layers of the atom lead to the emission of X-rays having a discrete energy spectrum (characteristic X-rays). In total, about 25 natural and about 100 artificial alpha radioactive isotopes are known.
Beta decay combines three types of nuclear transformations: electronic (β−)
and positron (β+ ) decays, as well as electron capture or K-capture. The first two types of transformations consist in the fact that the nucleus emits an electron and an antineutrino (during β− decay) or a positron and neutrino (during β+ decay). Elek-
tron (positron) and antineutrino (neutrino) do not exist in atomic nuclei. These processes occur by converting one type of nucleon in the nucleus into another - a neutron into a proton or a proton into a neutron. The result of these transformations is β-decays, the schemes of which have the form:
Am Z X→ Z Am + 1 Y+ − 1 e0 + 0 ~ ν0 (β− – decay), |
|
Am Z X→ Am Z − 1 Y+ + 1 e0 + 0 ν0 (β+ – decay), |
where − 1 e0 and + 1 e0 are the designation of electron and positron,
0 ν0 and 0 ~ ν0 – designation of neutrinos and antineutrinos.
With negative beta decay, the charge number of the radionuclide increases by one, and with positive beta decay, it decreases by one.
Electronic decay (β − decay) can be experienced by both natural and artificial radionuclides. It is this type of decay that is characteristic of the overwhelming number of environmentally most dangerous radionuclides released into the environment as a result of the Chernobyl accident. Among them
134 55 Cs, 137 55 Cs, 90 38 Sr, 131 53 I, etc.
Positron decay (β + – decay) is characteristic mainly of artificial radionuclides.
Since during beta decay two particles are emitted from the nucleus, and the distribution
between them the total energy occurs statistically, then the energy spectrum of electrons (positrons) is continuous from zero to the maximum value Emax called the upper limit of the beta spectrum. For beta radioactive nuclei, the Emax value lies in the energy region from 15 keV to 15 MeV. The path length of a beta particle in air is up to 20 m, and in biological tissue up to 1.5 cm.
Beta decay is usually accompanied by the emission of gamma rays. The reason for their occurrence is the same as in the case of alpha decay: the daughter nucleus appears not only in the ground (stable) state, but also in an excited state. Then passing into a state of lower energy, the nucleus emits a gamma photon.
During electron capture, one of the protons of the nucleus is converted into a neutron:
1 p 1+ − 1 e 0 → 0 n 1+ 0 ν 0 .
With this transformation, one of the electrons closest to the nucleus (the electron of the K-layer of the atom) disappears. A proton, turning into a neutron, “captures” an electron. This is where the term "electronic capture" comes from. Feature
This type of β-decay is the emission of one particle from the nucleus - a neutrino. The electronic capture circuit looks like
Am Z X+ − 1 e0 → Am Z − 1 Y+ 0 ν 0 . (1.16)
Electronic capture, in contrast to β± decays, is always accompanied by charac-
bacterial x-ray radiation. The latter occurs when an electron more distant from the nucleus moves to an emerging vacant place in
K-layer. The wavelength of X-rays is in the range from 10 − 7 to 10 − 11 m. Thus, during beta decay, the mass number of the nucleus is conserved, and its
the charge changes by one. Half-lives of beta radioactive nuclei
lie in a wide time range from 10 − 2 s to 2 1015 years.
To date, about 900 beta radioactive isotopes are known. Of these, only about 20 are natural, the rest are obtained artificially. The vast majority of these isotopes experience
β− -decay, i.e. with the emission of electrons.
All types of radioactive decay are accompanied by gamma radiation. Gamma rays are short-wave electromagnetic radiation, which is not an independent type of radioactivity. It has been experimentally established that gamma rays are emitted by a daughter nucleus during nuclear transitions from excited energy states to the ground or less excited state. The energy of gamma rays is equal to the difference between the energies of the initial and final energy levels of the nucleus. The wavelength of gamma rays does not exceed 0.2 nanometers.
The process of gamma radiation is not an independent type of radioactivity, since it occurs without changing the Z and Am of the nucleus.
Control questions:
1. What is meant by mass and charge numbers in the periodic table of Mendeleev?
2. The concept of “isotopes” and “isobars”. What is the difference between these terms?
3. Nuclear forces of the nucleus and their most important features.
4. Why is the mass of a nucleus less than the sum of the masses of its constituent nuclides?
5. What substances are called radioactive?
6. What characterizes and shows the radioactive decay constant?
7. Define the half-life of a substance.
8. List the units of measurement for volumetric, surface and specific activity.
9. The main types of radiation from radioactive nuclei and their parameters.
Lecture: Radioactivity. Alpha decay. Beta decay. Electronic β-decay. Positron β-decay. Gamma radiation
Radioactivity
Radioactivity was discovered completely by accident as a result of experiments carried out by A. Becquerel in 1896. The recent discovery of X-rays led scientists to want to find out whether they were produced as a result of certain elements being illuminated by sunlight. For his experiment, Becquerel chose a uranium salt.
The salt was placed on a photographic plate and wrapped in black paper to ensure the quality of the experiment. As a result of the fact that the salt lay for several hours in direct sunlight, the developed photographic plate contained a photograph that completely corresponded to the outlines of the salt crystals. This experience allowed Becquerel to speak at a conference where he spoke about new manifestations of X-rays. In a few weeks he was expected to announce new results from similar studies.
However, the weather prevented the scientist. Since it was cloudy all the time, the salt lay wrapped together with the photographic plate in black paper in the desk drawer. In desperation, the scientist developed a photographic plate, as a result of which he noticed that the salt left its mark even without sunlight.
It turned out that uranium emits some kind of rays, which are also capable of penetrating paper and leaving a mark on the plate.
This phenomenon is called radioactivity.
It later turned out that not only uranium is radioactive. The Curie family discovered similar properties in thorium, polonium, and radium.
Types of radioactive radiation
In the course of numerous experiments in which uranium was placed in a magnetic field, it was found that any radioactive element has three main types of radiation - alpha, beta and gamma.
As a result of placing a radioactive element in a lead plate exposed to a magnetic field, three spots were observed on the screen, located at some distance from each other.
1. Alpha rays (alpha particles) is a positive particle that has 4 nucleons and two positive charges. This radiation is the weakest. You can change the direction of motion of an alpha particle even with a piece of paper.
Equation and examples of such decay:
2 . Beta radiation or beta particle . This radiation occurs as a result of knocking out one negative or positive electron (positron).
3. Gamma radiation is radiation that produces an electromagnetic wave similar to x-rays.