Types of nuclear transformations, alpha and beta decay

Encyclopedic YouTube

1 / 3

✪ Types of decay

✪ RADIOACTIVITY physics

✪ Alpha and Beta decays

Subtitles

Everything we've discussed so far in chemistry has been based on the stability of electrons, and where they are most likely to reside in stable shells. But if we continue to study the atom, it turns out that not only electrons are located and act in the atom. Interactions occur in the core itself; it is characterized by instability, which it seeks to weaken. This will be the topic of our video lesson. In fact, the study of these mechanisms is not included in the chemistry curriculum for freshmen, but this knowledge will definitely not be superfluous. As we study the strong nuclear force, quantum physics, and the like, we'll take a closer look at why the protons, neutrons, and quarks that make up the nuclei of atoms interact the way they do. Now let's imagine how a nucleus can decay in general... Let's start with a beam of protons. I'll draw a few. These are protons, and here there will be neutrons. I'll paint them in some suitable color. Gray color is what you need. So here they are, my neutrons. How many protons do I have? I have 1, 2, 3, 4, 5, 6, 7, 8. So there will be 1, 2, 3, 4, 5, 6, 7, 8, 9 neutrons. Let's say this is the nucleus of an atom. By the way, this is the very first video about the atomic nucleus. In general, drawing an atom is actually very difficult, because it does not have clearly defined boundaries. An electron can be anywhere at any time. But if we talk about the location of the electron 90% of the time, then it will be the radius or diameter of the atom. We have known for a long time that the nucleus is an infinitesimal part of the volume of the sphere where the electron is located 90% of the time. And from this it follows that almost everything we see around is empty space. All this is empty space. I mention this because this is an infinitesimal speck, even though it is a very small fraction of the volume of the atom, its mass is almost the entire mass of the atom - this is very important. These are not atoms, these are not electrons. We are penetrating the core. It turns out that sometimes the kernel is unstable and strives to achieve a more stable configuration. We will not go into detail about the reasons for the instability of the core. But let me just say that sometimes it emits what are called alpha particles. This phenomenon is called alpha decay. Let's write it down. Alpha decay. The nucleus emits an alpha particle, sounds fantastic. It is simply a collection of neutrons and protons. An alpha particle is two neutrons and two protons. Perhaps they feel that they don’t fit here, these ones, for example. And emission occurs. They leave the core. Let's consider what happens to an atom when something like this happens. Let's take a random element, let's call it E. It has P - protons. I'll draw the letters in the same color as the protons. So, here are the protons. Naturally, element E has an atomic mass number equal to the sum of protons and neutrons. Neutrons are gray. Alpha decay occurs, what will happen to this element? What will happen to this element? The number of protons is reduced by two. Therefore, the number of protons will be p minus 2. And the number of neutrons also decreases by two. So here we have p minus 2, plus our neutrons minus 2, so that's a total of minus 4. The mass is reduced by four, and the old element turns into a new one. Remember that elements are determined by the number of protons. In alpha decay, you lose two neutrons and two protons, but it is the protons that change that element into another. If we call this element 1, which is what I'm going to do, we now have a new element, element 2. Look closely. There is an emission of something that has two protons and two neutrons. Therefore, its mass will be equal to the mass of two protons and two neutrons. What is this? Something comes off that has a mass of four. What contains two protons and two neutrons? Right now I don't have a periodic table of elements. I forgot to cut and paste it before filming this video. But you will quickly find an element on the periodic table that has two protons, and that element is helium. Its atomic mass is actually four. Indeed, during alpha decay it is the helium nucleus that is emitted. This is a helium nucleus. Since it is a helium nucleus, it has no electrons to neutralize the charge of the protons, it is an ion. It has no electrons. It only has two protons, so it has a charge of plus 2. Let's sign the charge. An alpha particle is simply a helium ion, a helium ion with a charge of plus 2, spontaneously emitted by the nucleus to achieve a more stable state. This is one type of decay. Now others... Let's draw another core. I'll draw neutrons. I'll draw protons. Sometimes it turns out that the neutron feels uncomfortable. He looks at what the protons are doing every day and says, you know what? Somehow, when I listen to myself, I feel like I should actually be a proton. If I were a proton, the whole nucleus would be a little more stable. And what does it do to become a proton? Remember, a neutron has a neutral charge? That's what it does, it emits an electron. This seems crazy. Electrons in neutrons and all that. And I agree with you. This is madness. And one day we will study everything that is inside the nucleus. For now, let's just say that a neutron can emit an electron. Which is what he does. So here's the electron. We take its mass to be zero... In fact, this is not so, but we are now talking about units of atomic mass. If the mass of a proton is one, then the mass of an electron is 1836 times less. Therefore, we take its mass to be zero. Even though this is not true. And its charge is minus 1. So, let's return to the process. A neutron emits an electron. Of course, the neutron does not remain neutral, but turns into a proton. This is called beta decay. Let's write this down. Beta decay. And a beta particle is actually just an emitted electron. Let's return to our element. It has a certain number of protons and neutrons. Together they make up the mass number. What happens when it undergoes beta decay? Does the number of protons change? Of course, we have one more proton than we had because one neutron turned into a proton. The number of protons has increased by 1. Has the mass number changed? Let's see. The number of neutrons decreased by one, and the number of protons increased by one. Therefore, the mass number has not changed. It is still P plus N, meaning the mass remains the same, unlike the situation with alpha decay, but the element itself changes. The number of protons changes. As a result of beta decay, we again obtain a new element. Now the situation is different. Let's say one of these protons looks at the neutrons and says, guess what? I see how they live. I love it. I think I would be more comfortable, and our group of particles inside the nucleus would be happier, if I were a neutron too. We would all be in a more stable state. And what does he do? This distressed proton has the opportunity to emit a positron rather than a proton. It emits a positron. And what is it? This is a particle that has exactly the same mass as an electron. That is, its mass is 1836 times less than the mass of a proton. But here we simply write zero, because in atomic mass units it approaches zero. But a positron has a positive charge. What's a little confusing is that it still says e. When I see the e, I think it's an electron. But no, this particle is designated e because it is the same type of particle, but instead of having a negative charge, it has a positive charge. This is a positron. Let's sign. Something unusual is starting to happen with these types of particles and matter that we are looking at. But this is a fact. And if a proton emits this particle, then its positive charge practically goes with it, and this proton turns into a neutron. This is called positron emission. Positron emission is quite easy to imagine. The name says it all. Again element E, with a certain number of protons and neutrons. What should this new element be? He loses a proton. P minus 1. It turns into a neutron. That is, the number of P decreases by one. The number N increases by one. Therefore, the mass of the whole atom does not change. It will be P plus N. But we should still have another element, right? When beta decay occurs, the number of protons increases. We've moved to the right on the periodic table, or increased, you know what I mean. When positron emission occurs, the number of protons decreases. You need to write this down in both of these reactions. So this is a positron emission, and there is one positron left. And in our beta decay one electron remains. The reactions are written exactly the same. You know it's an electron because it has a charge of minus 1. You know it's a positron because it has a charge of plus 1. There is one final type of decay that you should know about. But it does not change the number of protons or neutrons in the nucleus. It simply releases a huge amount of energy, or sometimes a high-energy proton. This phenomenon is called gamma decay. Gamma decay means that these particles change their configuration. They get a little closer. And as they come closer, they release energy in the form of electromagnetic radiation with a very short wavelength. Essentially, you can call it a gamma particle or a gamma ray. This is ultra-high energy. Gamma rays are very dangerous. They can kill you. It was all theory. Now let's solve a couple of problems and find out what type of decay we are dealing with. Here I have beryllium-7, where seven is the atomic mass. And I turn it into lithium-7. So what's going on here? The mass of the beryllium nucleus remains unchanged, but the number of protons decreases from four to three. The number of beryllium protons has decreased. The total mass has not changed. Surely this is not alpha decay. Alpha decay, as you know, is the release of helium from the nucleus. So what stands out? A positive charge, or positron, is released. This is illustrated here using the equation. This is a positron. Therefore, this type of decay of beryllium-7 to lithium-7 is positron emission. All clear. Now let's look at the following example. Uranium-238 decaying to thorium-234. And we see that the atomic mass decreases by 4, and we see that the atomic number decreases, the number of protons decreases by 2. Probably, something was released that has an atomic mass of four, and an atomic number of two, that is, helium. So this is alpha decay. Here is an alpha particle. This is an example of alpha decay. But it's not that simple. Because if out of 92 protons there are 90 protons left, there are still 92 electrons left here. Will the charge now be minus 2? And moreover, the helium that is released does not have electrons. It's just a helium nucleus. So will the charge be plus 2? If you ask this question, you will be absolutely right. But in fact, it is at the moment of decay that the thorium no longer has a reason to hold on to those two electrons, so those two electrons disappear and the thorium becomes neutral again. And helium reacts very quickly in the same way. It really needs two electrons to be stable, so it very quickly grabs two electrons and becomes stable. You can write this in any way. Let's look at another example. I have iodine here. Fine. Let's see what happens. The mass does not change. Protons must turn into neutrons or neutrons must turn into protons. We see that here I have 53 protons, and here I have 54. Apparently, one neutron turned into a proton. The neutron apparently turned into a proton. And the neutron turns into a proton, emitting an electron. And we see it during this reaction. The electron was released. So this is beta decay. This is a beta particle. Signed. The same logic applies. Wait, instead of 53 there are 54 protons. Now that I've added another proton, will I still have a positive charge? Yes, it will. But very soon - maybe not just these electrons, there are so many electrons going around - I will grab electrons from somewhere to become stable, and I will become stable again. But you will be absolutely right if you ask the question, will the particle become an ion for a small fraction of the time? Let's look at another example. Radon-222, atomic number 86, which turns into polonium -218, atomic number 84. An interesting little digression. Polonium is named after Poland because Marie Curie, who discovered it, was from there at the time, around the late 1800s - Poland did not yet exist as a separate country. Its territory was divided between Prussia, Russia and Austria. And the Poles really wanted people to know that they are one people. They made the discovery that when radon decays, this element is formed. And they named it in honor of their homeland, Poland. It is the privilege of discovering new elements. But let's get back to the task. So what happened? Atomic mass decreased by four. The atomic number has decreased by two. I repeat once again, apparently a helium particle was released. The helium nucleus has an atomic mass of four and an atomic number of two. All clear. So this is alpha decay. You can write that this is a helium nucleus. It has no electrons. We can even immediately tell that it will have a negative charge, but then it loses it. Subtitles by the Amara.org community

Theory

Alpha decay from main state is observed only in fairly heavy nuclei, for example, in radium-226 or uranium-238. Alpha radioactive nuclei in the table of nuclides appear starting with atomic number 52 (tellurium) and a mass number of about 106-110, and with an atomic number greater than 82 and a mass number greater than 200, almost all nuclides are alpha radioactive, although they may have alpha decay and a non-dominant decay mode. Among natural isotopes alpha radioactivity is observed in several nuclides of rare earth elements (neodymium-144, samarium-147, samarium-148, europium-151, gadolinium-152), as well as in several nuclides of heavy metals (hafnium-174, tungsten-180, osmium- 186, platinum-190, bismuth-209, thorium-232, uranium-235, uranium-238) and in short-lived decay products of uranium and thorium.

Alpha decay from highly excited nuclear states are also observed in a number of light nuclides, for example, lithium-7.

An alpha particle undergoes a tunnel transition through a potential barrier, caused by nuclear forces, so alpha decay is an essentially quantum process. Since the probability of the tunneling effect depends exponentially on the barrier height, the half-life of alpha-active nuclei increases exponentially with decreasing alpha particle energy (this fact constitutes the content of the Geiger-Nattall law). When the alpha particle energy is less than 2 MeV, the lifetime of alpha-active nuclei significantly exceeds the lifetime of the Universe. Therefore, although most natural isotopes heavier than cerium are in principle capable of decaying through this channel, only a few of them have actually recorded such decay. Danger to living organisms

Being quite heavy and positively charged, alpha particles from radioactive decay have a very short range in matter and, when moving through a medium, quickly lose energy at a short distance from the source. This results in all the radiation energy being released in a small volume of the substance, which increases the chances of cell damage when the radiation source enters the body. However external Radiation from radioactive sources is harmless, since alpha particles can be effectively retained by a few centimeters of air or tens of micrometers of dense matter - for example, a sheet of paper and even the stratum corneum of the epidermis, without reaching living cells. Even touching a source of pure alpha radiation is not dangerous, although it should be remembered that many sources of alpha radiation also emit much more penetrating types of radiation (beta particles, gamma rays, sometimes neutrons). However, if an alpha source enters the body, it results in significant radiation exposure. The quality factor of alpha radiation is 20 (more than all other types of ionizing radiation, with the exception of heavy nuclei and fission fragments). This means that in living tissue, an alpha particle creates an estimated 20 times more damage than a gamma ray or beta particle of equal energy.

All of the above applies to radioactive sources of alpha particles, the energies of which do not exceed 15 MeV. Alpha particles produced at an accelerator can have significantly higher energies and create a significant dose even with external irradiation of the body.

In this type of decay, a nucleus with atomic number Z and mass number A decays by emitting an alpha particle, which leads to the formation of a nucleus with atomic number Z-2 and mass number A-4:

Currently, more than 200 alpha-emitting nuclides are known, among which light and medium nuclei are almost absent. Among light nuclei, the exception is 8 Be; in addition, about 20 alpha-emitting nuclides of rare earth elements are known. The vast majority of a-emitting isotopes belong to radioactive elements, i.e. to elements with Z> 83, a significant part of which are artificial nuclides. Among natural nuclides, there are about 30 alpha-active nuclei belonging to three radioactive families (uranium, actinium, and thorium series), which are discussed above. The half-lives of known alpha radioactive nuclides range from 0.298 μs for 212 Po to >10 15 years for 144 Nd, 174 Hf. The energy of alpha particles emitted by heavy nuclei from ground states is 4-9 MeV, and by rare earth element nuclei 2-4.5 MeV.

That the probability of alpha decay increases with increasing Z, is due to the fact that this type of nuclear transformation is associated with Coulomb repulsion, which, as the size of the nuclei increases, increases proportionally Z 2, while nuclear attractive forces grow linearly with increasing mass number A.

As was shown earlier, the nucleus will be unstable with respect to a-decay if the inequality holds:

where and are the rest masses of the initial and final nuclei, respectively;

– mass of the a-particle.

Energy of α-decay of nuclei ( Eα) consists of the kinetic energy of the alpha particle emitted by the mother nucleus Tα, and the kinetic energy that the daughter nucleus acquires as a result of the emission of an alpha particle (recoil energy) T department:

Using the laws of conservation of energy and momentum, we can obtain the relation:

Where M department = – recoil core mass;

Mα is the mass of the alpha particle.

Solving equations (4.3) and (4.4) together, we obtain:

. (4.5)

And correspondingly,

. (4.6)

From equations (4.5 and 4.6) it is clear that the bulk of the alpha decay energy (about 98%) is carried away by alpha particles. The kinetic energy of the recoil nucleus is ≈100 keV (with an alpha decay energy of ≈5 MeV). It should be noted that even such seemingly small values ​​of the kinetic energy of recoil atoms are very significant and lead to the high reactivity of atoms having similar nuclei. For comparison, note that the energy of thermal motion of molecules at room temperature is approximately 0.04 eV, and the energy of chemical bonds is usually less than 2 eV. Therefore, the recoil nucleus not only breaks the chemical bond in the molecule, but also partially loses the electron shell (electrons simply cannot keep up with the recoil nucleus) with the formation of ions.

When considering different types of radioactive decay, including alpha decay, energy diagrams are used. The simplest energy diagram is shown in Fig. 4.1.

Rice. 4.1. The simplest alpha decay scheme.

The energy state of the system before and after decay is depicted by horizontal lines. An alpha particle is represented by an arrow (bold or double) going down from right to left. The arrow indicates the energy of the emitted alpha particles.

It should be borne in mind that the one shown in Fig. 4.1 diagram is the simplest case when the alpha particles emitted by the nucleus have one specific energy. Typically, the alpha spectrum has a fine structure, i.e. nuclei of the same nuclide emit alpha particles with energies that are quite close, but still differ in magnitude. It was found that if an alpha transition occurs in the excited state of the daughter nucleus, then the energy of the alpha particles will be, accordingly, less than the energy inherent in the transition between the ground states of the original and daughter nuclei of radionuclides. And if there are several such excited states, then there will be several possible alpha transitions. In this case, daughter nuclei with different energies are formed, which, upon transition to the ground or more stable state, emit gamma rays.

Knowing the energy of all alpha particles and gamma quanta, it is possible to construct an energy decay diagram.

Example. Construct a decay diagram using the following data:

· the energy of α-particles is: 4.46; 4.48; 4.61; and 4.68 MeV,

· energy of γ-quanta – 0.07; 0.13; 0.20; and 0.22 MeV.

The total decay energy is 4.68 MeV.

Solution. From the energy level of the original nucleus we draw four arrows, each of which indicates the emission of α-particles of a certain energy. By calculating the differences between the energies of individual groups of α-particles and comparing these differences with the energies of γ-quanta, we find which transitions correspond to the emission of γ-quanta of each energy

4.48 – 4.46 = 0.02 MeV there are no corresponding γ-quanta

4.61 – 4.46 = 0.15 MeV

4.61 – 4.48 = 0.13 MeV energies correspond to energies

4.68 – 4.46 = 0.22 MeV of γ quanta emitted during decay

4.68 – 4.48 = 0.20 MeV 230 Th

4.68 – 4.61 = 0.07 MeV

Rice. 4.2 – Scheme of the decay of 230 Th.

At the same time, a second case is also possible, when an alpha transition occurs from the excited state of the parent nucleus to the ground state of the daughter nucleus. These cases are usually classified as the appearance of long-range alpha particles, the emission of which arises from excited nuclei formed as a result of complex β-decay. So, as an example, Figure 4.3 shows a diagram of the emission of long-range α particles by the polonium-212 nucleus, formed as a result of the β-decay of the bismuth-212 nucleus. It can be seen that, depending on the nature of the β transition, the polonium-212 nucleus can be formed in the ground and excited states. Alpha particles emitted from excited states of the polonium-212 nucleus are long-range. However, it should be borne in mind that for alpha-active nuclei generated in this way, a transition from an excited state is more likely by emitting a γ-quantum rather than a long-range alpha particle. Therefore, long-range alpha particles are very rare.

Further, scientists have established a very important pattern: when small increasing the energy of a-particles, the half-lives change by several orders of magnitude. So for 232 Th T a = 4.08 MeV, T 1/2 = 1.41×10 10 years, and for 230 Th – T a = 4.76 MeV, T 1/2 = 1.7∙10 4 years.

Rice. 4.3. Sequential decay pattern: 212 Bi – 212 Po – 208 Pb

It can be seen that a decrease in the energy of alpha particles by approximately 0.7 MeV is accompanied by an increase in the half-life by 6 orders of magnitude. At T α < 2 МэВ период полураспада становится настолько большим, что экспериментально обнаружить альфа-активность практически невозможно. Разброс в значениях периодов полураспада, характерных для альфа-распада, весьма велик:

10 16 years ≥ T 1/2 ≥ 10 –7 sec,

and at the same time, there is a very narrow range of energies of alpha particles emitted by radioactive nuclei:

2 MeV ≤ Tα ≤ 9 MeV.

The relationship between the half-life and the energy of an alpha particle was established experimentally by Geiger and Nattall in 1911-1912. They showed that the dependence lg T 1/2 of lg Tα is well approximated by a straight line:

. (4.7)

This law holds well for even-even nuclei. Whereas for odd-odd nuclei a very significant deviation from the law is observed.

The strong dependence of the probability of alpha decay, and therefore the half-life, on energy was explained by G. Gamow and E. Condon in 1928 using the theory of a single-particle model of the nucleus. In this model, it is assumed that the alpha particle constantly exists in the nucleus, i.e. The mother nucleus consists of a daughter nucleus and an alpha particle. It is assumed that the alpha particle moves in a spherical region of radius R (R– radius of the nucleus) and is held in the nucleus by short-range Coulomb nuclear forces. At distances r greater than the radius of the daughter nucleus R, Coulomb repulsion forces act.

In Fig. Figure 4.4 shows the dependence of the potential energy between the alpha particle and the recoil nucleus on the distance between their centers.

The abscissa axis shows the distance between the daughter nucleus and the alpha particle, and the ordinate axis shows the energy of the system. Coulomb potential is cut off at a distance R, which is approximately equal to the radius of the daughter nucleus. The height of the Coulomb barrier B, which an alpha particle must overcome in order to leave the nucleus, is determined by the relation:

Where Z And z are the charges of the daughter nucleus and the alpha particle, respectively.

Rice. 4.4. Change in the potential energy of the system with the distance between the daughter nucleus and the alpha particle.

The magnitude of the potential barrier significantly exceeds the energy of alpha particles emitted by radioactive nuclei, and according to the laws of classical mechanics, an alpha particle cannot leave the nucleus. But for elementary particles whose behavior is described by the laws of quantum mechanics, it is possible for these particles to pass through a potential barrier, which is called a tunnel transition.

In accordance with the theory of alpha decay, the beginnings of which were laid by G. Gamow and E. Condon, the state of a particle is described by the wave function ψ, which, according to the normalization conditions, at any point in space is nonzero, and thus there is a finite probability of detecting an alpha particle both inside and outside the barrier. That is, the process of the so-called tunneling transition of an alpha particle through a potential barrier is possible.

Barrier permeability has been shown to be a function of atomic number, atomic mass, core radius, and potential barrier characteristics.

It has been established that alpha transitions of even-even nuclei from the main level of mother nuclides to the main level of daughter nuclides are characterized by the smallest half-lives. For odd-even, even-odd and odd-odd nuclei the general trend remains, but their half-lives are 2-1000 times longer than for even-even nuclei with given Z and Tα. It is useful to remember: the energy of alpha particles emitted by radionuclides with the same mass number increases with increasing nuclear charge.

The half-lives of known α-radioactive nuclei vary widely. Thus, the tungsten isotope 182 W has a half-life T 1/2 > 8.3·10 18 years, and the protactinium isotope 219 Pa has T 1/2 = 5.3·10 -8 s.

Rice. 2.1. Dependence of the half-life of a radioactive element on the kinetic energy of an α-particle of a naturally radioactive element. The dashed line is the Geiger-Nattall law.

For even-even isotopes, the dependence of the half-life on the α-decay energy Q α described empirically Geiger-Nettall law

where Z is the charge of the final nucleus, the half-life T 1/2 is expressed in seconds, and the energy of the α-particle E α is in MeV. In Fig. Figure 2.1 shows the experimental values ​​of half-lives for α-radioactive even-even isotopes (Z varies from 74 to 106) and their description using relation (2.3).
For odd-even, even-odd and odd-odd nuclei the general tendency of the dependence
log T 1/2 of Q α is preserved, but the half-lives are 2–100 times longer than for even-even nuclei with the same Z and Q α .
In order for α decay to occur, it is necessary that the mass of the initial nucleus M(A,Z) be greater than the sum of the masses of the final nucleus M(A-4, Z-2) and the α particle M α:

where Q α = c 2 is the α-decay energy.
Since M α<< M(A-4, Z-2), the main part of the α-decay energy is carried away by α ‑ particle and only ≈ 2% - the final nucleus (A-4, Z-2).
The energy spectra of α-particles of many radioactive elements consist of several lines (fine structure of α-spectra). The reason for the appearance of the fine structure of the α spectrum is the decay of the initial nucleus (A,Z) into the excited state of the nucleus (A-4, Z-2). By measuring the spectra of alpha particles one can obtain information about the nature of excited states
cores (A-4, Z-2).
To determine the range of values ​​of A and Z nuclei for which α-decay is energetically possible, experimental data on the binding energies of nuclei are used. The dependence of the α-decay energy Q α on the mass number A is shown in Fig. 2.2.
From Fig. 2.2 it is clear that α decay becomes energetically possible starting from A ≈ 140. In the regions A = 140–150 and A ≈ 210, the value of Q α has distinct maxima, which are due to the shell structure of the nucleus. The maximum at A = 140–150 is associated with the filling of the neutron shell with the magic number N = A – Z = 82, and the maximum at A ≈ 210 is associated with the filling of the proton shell at Z = 82. It is due to the shell structure of the atomic nucleus that the first (rare earth) region of α-active nuclei begins with N = 82, and heavy α-radioactive nuclei become especially numerous starting from Z = 82.

Rice. 2.2. Dependence of α-decay energy on mass number A.

The wide range of half-lives, as well as the large values ​​of these periods for many α-radioactive nuclei, are explained by the fact that an α particle cannot “instantaneously” leave the nucleus, despite the fact that this is energetically favorable. In order to leave the nucleus, the α-particle must overcome the potential barrier - the region at the boundary of the nucleus, formed due to the potential energy of the electrostatic repulsion of the α-particle and the final nucleus and the attractive forces between nucleons. From the point of view of classical physics, an alpha particle cannot overcome a potential barrier, since it does not have the kinetic energy necessary for this. However, quantum mechanics allows for such a possibility − α ‑ the particle has a certain probability of passing through the potential barrier and leaving the nucleus. This quantum mechanical phenomenon is called the “tunnel effect” or “tunneling.” The greater the height and width of the barrier, the lower the probability of tunneling, and the half-life is correspondingly longer. Wide range of half-lives
α-emitters are explained by different combinations of kinetic energies of α-particles and heights of potential barriers. If the barrier did not exist, then the alpha particle would leave the nucleus behind the characteristic nuclear
time ≈ 10 -21 – 10 -23 s.
The simplest model of α-decay was proposed in 1928 by G. Gamow and, independently, by G. Gurney and E. Condon. In this model, it was assumed that the α particle constantly exists in the nucleus. While the alpha particle is in the nucleus, nuclear forces of attraction act on it. The radius of their action is comparable to the radius of the nucleus R. The depth of the nuclear potential is V 0. Outside the nuclear surface at r > R the potential is the Coulomb repulsive potential

V(r) = 2Ze 2 /r.

Rice. 2.3. Energies of α-particles E α depending on the number of neutrons N
in the original kernel. Lines connect isotopes of the same chemical element.

A simplified diagram of the combined action of the nuclear attractive potential and the Coulomb repulsive potential is shown in Figure 2.4. In order to leave the nucleus, an α particle with energy E α must pass through a potential barrier contained in the region from R to R c . The probability of α decay is mainly determined by the probability D of an α particle passing through a potential barrier

Within the framework of this model, it was possible to explain the strong dependence of the probability α ‑ decay from the energy of the α-particle.

Rice. 2.4. Potential energy of an α particle. Potential barrier.

In order to calculate the decay constant λ, it is necessary to multiply the coefficient of passage of an α-particle through the potential barrier, firstly, by the probability w α that the α-particle was formed in the nucleus, and, secondly, by the probability that it will be at the core boundary. If an alpha particle in a nucleus of radius R has a speed v, then it will approach the boundary on average ≈ v/2R times per second. As a result, for the decay constant λ we obtain the relation

(2.6)

The speed of an α particle in the nucleus can be estimated based on its kinetic energy E α + V 0 inside the nuclear potential well, which gives v ≈ (0.1-0.2) s. It already follows from this that if there is an alpha particle in the nucleus, its probability of passing through the barrier D<10 -14 (для самых короткоживущих относительно α‑распада тяжелых ядер).
The roughness of the estimate of the pre-exponential factor is not very significant, because the decay constant depends on it incomparably less than on the exponent.
From formula (2.6) it follows that the half-life strongly depends on the radius of the nucleus R, since the radius R is included not only in the pre-exponential factor, but also in the exponent, as a limit of integration. Therefore, from α-decay data it is possible to determine the radii of atomic nuclei. The radii obtained in this way turn out to be 20–30% larger than those found in electron scattering experiments. This difference is due to the fact that in experiments with fast electrons the radius of the electric charge distribution in the nucleus is measured, and in α-decay the distance between the nucleus and the α-particle is measured, at which nuclear forces cease to act.
The presence of Planck's constant in the exponent (2.6) explains the strong dependence of the half-life on energy. Even a small change in energy leads to a significant change in the exponent and thus to a very sharp change in the half-life. Therefore, the energies of the emitted α particles are highly limited. For heavy nuclei, α-particles with energies above 9 MeV fly out almost instantly, and with energies below 4 MeV they live in the nucleus for so long that α-decay cannot even be detected. For rare earth α-radioactive nuclei, both energies are reduced by reducing the radius of the nucleus and the height of the potential barrier.
In Fig. Figure 2.5 shows the dependence of the α-decay energy of Hf isotopes (Z = 72) on the mass number A in the range of mass numbers A = 156–185. Table 2.1 shows the α-decay energies, half-lives and main decay channels of the 156–185 Hf isotopes. It can be seen how, as the mass number A increases, the α-decay energy decreases, which leads to a decrease in the probability of α-decay and an increase in the probability of β-decay (Table 2.1). The 174 Hf isotope, being a stable isotope (in the natural mixture of isotopes it is 0.16%), nevertheless decays with a half-life T 1/2 = 2·10 15 years with the emission of an α-particle.

Rice. 2.5. Dependence of the α-decay energy Q α of Hf isotopes (Z = 72)
from mass number A.

Table 2.1

Dependence of α-decay energy Q α, half-life T 1/2,
different decay modes of H f isotopes (Z = 72) depending on the mass number A

Z	N	A	Q α	T 1/2	Decay modes (%)
72	84	156	6.0350	23 ms	α(100)
72	85	157	5.8850	110 ms	α (86), e (14)
72	86	158	5.4050	2.85 s	α (44.3), e (55.7)
72	87	159	5.2250	5.6 s	α (35), e (65)
72	88	160	4.9020	13.6 s	α (0.7), e (99.3)
72	89	161	4.6980	18.2 s	α (<0.13), е (>99.87)
72	90	162	4.4160	39.4 s	α (<8·10 -3), е (99.99)
72	91	163	4.1280	40.0 s	α (<1·10 -4), е (100)
72	92	164	3.9240	111 s	e (100)
72	93	165	3.7790	76 s	e (100)
72	94	166	3.5460	6.77 min	e (100)
72	95	167	3.4090	2.05 min	e (100)
72	96	168	3.2380	25.95 min	e (100)
72	97	169	3.1450	3.24 min	e (100)
72	98	170	2.9130	16.01 h	e (100)
72	99	171	2.7390	12.1 h	e (100)
72	100	172	2.7470	1.87 h	e (100)
72	101	173	2.5350	23.4 hours	e (100)
72	102	174	2.4960	2 10 15 l	e (100)
72	103	175	2.4041	70 days	e (100)
72	104	176	2.2580	stab.
72	105	177	2.2423	stab.
72	106	178	2.0797	stab.
72	107	179	1.8040	stab.
72	108	180	1.2806	stab.
72	109	181	1.1530	42.39 days	β - (100)
72	110	182	1.2140	8.9 10 6 l	β - (100)
72	111	183	0.6850	1.07 h	β - (100)
72	112	184	0.4750	4.12 h	β - (100)
72	113	185	0.0150	3.5 min	β - (100)

Hf isotopes with A = 176–180 are stable isotopes. These isotopes also have positive α decay energy. However, the α-decay energy ~1.3–2.2 MeV is too low and the α-decay of these isotopes was not detected, despite the nonzero probability of α-decay. With a further increase in the mass number A > 180, β - decay becomes the dominant decay channel.
During radioactive decays, the final nucleus may end up not only in the ground state, but also in one of the excited states. However, the strong dependence of the probability of α-decay on the energy of the α-particle leads to the fact that decays into excited levels of the final nucleus usually occur with a very low intensity, because when the final nucleus is excited, the energy of the α-particle decreases. Therefore, only decays into rotational levels with relatively low excitation energies can be observed experimentally. Decays into excited levels of the final nucleus lead to the appearance of a fine structure in the energy spectrum of the emitted α particles.
The main factor determining the properties of α decay is the passage of α particles through a potential barrier. Other factors manifest themselves relatively weakly, but in some cases they make it possible to obtain additional information about the structure of the nucleus and the mechanism of α-decay of the nucleus. One of these factors is the emergence of a quantum mechanical centrifugal barrier. If an α particle is emitted from a nucleus (A,Z) having spin J i , and a finite nucleus is formed
(A-4, Z-2) in a state with spin J f, then the α-particle must carry away the total momentum J, determined by the relation

Since the α-particle has zero spin, its total angular momentum J coincides with the orbital angular momentum l carried away by the α-particle

As a result, a quantum mechanical centrifugal barrier appears.

The change in the shape of the potential barrier due to centrifugal energy is insignificant, mainly due to the fact that the centrifugal energy decreases with distance much faster than the Coulomb energy (as 1/r 2, and not as 1/r). However, since this change is divided by Planck's constant and falls into the exponent, then at large l, it leads to a change in the lifetime of the nucleus.
Table 2.2 shows the calculated permeability of the centrifugal barrier B l for α-particles emitted with orbital momentum l relative to the permeability of the centrifugal barrier B 0 for α-particles emitted with orbital momentum l = 0 for a nucleus with Z = 90, α-particle energy E α = 4.5 MeV. It can be seen that with an increase in the orbital momentum l carried away by the α particle, the permeability of the quantum mechanical centrifugal barrier drops sharply.

Table 2.2

Relative permeability of the centrifugal barrier forα -particles,
departing with orbital momentum l
(Z = 90, E α = 4.5 MeV)

A more significant factor that can dramatically redistribute the probabilities of various branches of α-decay may be the need for a significant restructuring of the internal structure of the nucleus during the emission of an α-particle. If the initial nucleus is spherical, and the ground state of the final nucleus is strongly deformed, then in order to evolve into the ground state of the final nucleus, the initial nucleus must rearrange itself in the process of emitting an alpha particle, greatly changing its shape. Such a change in the shape of the nucleus usually involves a large number of nucleons and a system with few nucleons such as α ‑ a particle leaving the nucleus may not be able to provide it. This means that the probability of the formation of the final nucleus in the ground state will be negligible. If among the excited states of the final nucleus there is a state close to spherical, then the initial nucleus can, without significant rearrangement, go into it as a result of α ‑ decay The probability of population of such a level may turn out to be large, significantly exceeding the probability of population of lower-lying states, including the ground state.
From the α-decay diagrams of the isotopes 253 Es, 225 Ac, 225 Th, 226 Ra, strong dependences of the probability of α-decay into excited states on the energy of the α-particle and on the orbital momentum l carried away by the α-particle are visible.
α decay can also occur from excited states of atomic nuclei. As an example, Tables 2.3 and 2.4 show the decay modes of the ground and isomeric states of the isotopes 151 Ho and 149 Tb.

Table 2.3

α-decays of the ground and isomeric states of 151 Ho

Table 2.4

α-decays of the ground and isomeric states of 149 Tb

In Fig. Figure 2.6 shows the energy diagrams of the decay of the ground and isomeric states of the isotopes 149 Tb and 151 Ho.

Rice. 2.6 Energy diagrams of the decay of the ground and isomeric states of the isotopes 149 Tb and 151 Ho.

α-decay from the isomeric state of the 151 Ho isotope (J P = (1/2) + , E isomer = 40 keV) is more probable (80%) than e-capture to this isomeric state. At the same time, the ground state of 151 Ho decays mainly as a result of e-capture (78%).
In the 149 Tb isotope, the decay of the isomeric state (J P = (11/2) - , E isomer = 35.8 keV) occurs in the overwhelming case as a result of e-capture. The observed features of the decay of the ground and isomeric states are explained by the magnitude of the energy of α-decay and e-capture and the orbital angular momentum carried away by the α-particle or neutrino.

The nuclei of most atoms are fairly stable formations. However, the nuclei of atoms of radioactive substances during the process of radioactive decay spontaneously transform into the nuclei of atoms of other substances. So in 1903, Rutherford discovered that radium placed in a vessel after some time turned into radon. And additional helium appeared in the vessel: (88^226)Ra→(86^222)Rn+(2^4)He. To understand the meaning of the written expression, study the topic of mass and charge number of the nucleus of an atom.

It was possible to establish that the main types of radioactive decay: alpha and beta decay occur according to the following displacement rule:

Alpha decay

During alpha decay an alpha particle (the nucleus of a helium atom) is emitted. From a substance with the number of protons Z and neutrons N in the atomic nucleus, it turns into a substance with the number of protons Z-2 and the number of neutrons N-2 and, accordingly, atomic mass A-4: (Z^A)X→(Z-2^ (A-4))Y +(2^4)He. That is, the resulting element is shifted two cells back in the periodic table.

Example of α decay:(92^238)U→(90^234)Th+(2^4)He.

Alpha decay is intranuclear process. As part of a heavy nucleus, due to a complex combination of nuclear and electrostatic forces, an independent α-particle is formed, which is pushed out by Coulomb forces much more actively than other nucleons. Under certain conditions, it can overcome the forces of nuclear interaction and fly out of the nucleus.

Beta decay

During beta decay an electron (β particle) is emitted. As a result of the decay of one neutron into a proton, electron and antineutrino, the composition of the nucleus increases by one proton, and the electron and antineutrino are emitted outward: (Z^A)X→(Z+1^A)Y+(-1^0)e+(0 ^0)v. Accordingly, the resulting element is shifted one cell forward in the periodic table.

Example of β decay:(19^40)K→(20^40)Ca+(-1^0)e+(0^0)v.

Beta decay is intranucleon process. The neutron undergoes the transformation. There is also beta plus decay or positron beta decay. In positron decay, the nucleus emits a positron and a neutrino, and the element moves back one cell on the periodic table. Positron beta decay is usually accompanied by electron capture.

Gamma decay

In addition to alpha and beta decay, there is also gamma decay. Gamma decay is the emission of gamma quanta by nuclei in an excited state, in which they have high energy compared to the unexcited state. Nuclei can come to an excited state during nuclear reactions or during radioactive decays of other nuclei. Most excited states of nuclei have a very short lifetime - less than a nanosecond.

There are also decays with the emission of a neutron, proton, cluster radioactivity and some other, very rare types of decays. But prevailing

2.3 Patternsα - Andβ -decay

ActivityAnuclidein a radioactive source, the number of decays occurring with the nuclei of a sample in 1 s is called:

Activity unit — becquerel (Bq): 1Bq - activity of a nuclide, at which one decay event occurs in 1 s.Non-system unit of activitynuclide in a radioactive source -curie (Ku): 1 Ku=3.7·1010 Bk.

Alpha decay. Alpha decay is the spontaneous transformation of an atomic nucleus with the number of protons Z and neutrons N into another (daughter) nucleus containing the number of protons Z – 2 and neutrons N – 2. In this case, an alpha particle is emitted - the nucleus of a helium atom. An example of such a process is the α-decay of radium:

Alpha particles emitted by the nuclei of radium atoms were used by Rutherford in experiments on scattering by the nuclei of heavy elements. The speed of α-particles emitted during the α-decay of radium nuclei, measured from the curvature of the trajectory in a magnetic field, is approximately equal to 1.5 107 m/s, and the corresponding kinetic energy is about 7.5 10–13 J (approximately 4.8 MeV). This value can be easily determined from the known values ​​of the masses of the mother and daughter nuclei and the helium nucleus. Although the speed of the escaping α-particle is enormous, it is still only 5% of the speed of light, so when calculating, you can use a non-relativistic expression for kinetic energy.

Research has shown that a radioactive substance can emit alpha particles with several discrete energies. This is explained by the fact that nuclei can be, like atoms, in different excited states. The daughter nucleus may end up in one of these excited states during α decay. During the subsequent transition of this nucleus to the ground state, a γ-quantum is emitted. A diagram of the α-decay of radium with the emission of α-particles with two values ​​of kinetic energies is shown in Figure 2.4.

Figure 2.4 - Energy diagram of α-decay of radium nuclei. The excited state of the radon nucleus is indicatedThe transition from the excited state of the radon nucleus to the ground state is accompanied by the emission of a γ-quantum with an energy of 0.186 MeV

Thus, α-decay of nuclei is in many cases accompanied by γ-radiation.

In the theory of α-decay, it is assumed that groups consisting of two protons and two neutrons, i.e., an α particle, can be formed inside nuclei. The mother nucleus is a potential well for α particles, which is limited by a potential barrier. The energy of the α particle in the nucleus is not sufficient to overcome this barrier (Figure 2.5). The escape of an alpha particle from the nucleus is possible only due to a quantum mechanical phenomenon called the tunneling effect. According to quantum mechanics, there is a non-zero probability of a particle passing under a potential barrier. The phenomenon of tunneling is probabilistic in nature.

Beta decay. During beta decay, an electron is ejected from the nucleus. Electrons cannot exist inside nuclei (see § 1.2); they arise during beta decay as a result of the transformation of a neutron into a proton. This process can occur not only inside the nucleus, but also with free neutrons. The average lifetime of a free neutron is about 15 minutes. When a neutron decaysturns into a protonand electron

Measurements have shown that in this process there is an apparent violation of the law of conservation of energy, since the total energy of the proton and electron resulting from the decay of a neutron is less than the energy of the neutron. In 1931, W. Pauli suggested that during the decay of a neutron, another particle with zero mass and charge is released, which takes away part of the energy. The new particle is namedneutrino(small neutron). Due to the lack of charge and mass of a neutrino, this particle interacts very weakly with the atoms of matter, so it is extremely difficult to detect in experiment. The ionizing ability of neutrinos is so small that one ionization event in the air occurs approximately 500 km of the way. This particle was discovered only in 1953. It is now known that there are several types of neutrinos. During the decay of a neutron, a particle is created, which is called an electronantineutrino. It is indicated by the symbolTherefore, the neutron decay reaction is written in the form

A similar process occurs inside nuclei during β-decay. An electron formed as a result of the decay of one of the nuclear neutrons is immediately ejected from the “parental home” (nucleus) at enormous speed, which can differ from the speed of light by only a fraction of a percent. Since the distribution of energy released during β-decay between the electron, neutrino and daughter nucleus is random, β-electrons can have different velocities over a wide range of values.

During β-decay, the charge number Z increases by one, but the mass number A remains unchanged. The daughter nucleus turns out to be the nucleus of one of the isotopes of the element, the serial number of which in the periodic table is one higher than the serial number of the original nucleus. A typical example of β-decay is the transformation of thorium isotonearising from the α-decay of uraniumto palladium

Along with electronic β decay, the so-called positron β decay was discovered+ -decay in which a positron is emitted from the nucleusand neutrinos. A positron is a particle twin of an electron, differing from it only in the sign of its charge. The existence of the positron was predicted by the outstanding physicist P. Dirac in 1928. A few years later, the positron was discovered in cosmic rays. Positrons arise as a result of the reaction of converting a proton into a neutron according to the following scheme:

Gamma decay. Unlike α- and β-radioactivity, γ-radioactivity of nuclei is not associated with a change in the internal structure of the nucleus and is not accompanied by a change in charge or mass numbers. Both during α- and β-decay, the daughter nucleus may find itself in some excited state and have an excess of energy. The transition of a nucleus from an excited state to a ground state is accompanied by the emission of one or more γ quanta, the energy of which can reach several MeV.