Most atomic nuclei are unstable. Sooner or later they spontaneously (or, as physicists say, spontaneously) decay into smaller nuclei and elementary particles, which are commonly called decay products or child elements. Decaying particles are called starting materials or parents. All of the familiar chemicals (iron, oxygen, calcium, etc.) have at least one stable isotope. ( isotopes are called varieties of a chemical element with the same number of protons in the nucleus - this number of protons corresponds to the element's serial number - but a different number of neutrons.) The fact that these substances are well known to us indicates their stability - which means they live long enough in order to accumulate in significant quantities in natural conditions, without breaking up into components. But each of the natural elements also has unstable isotopes - their nuclei can be obtained in the process of nuclear reactions, but they do not live long, because they quickly decay.

The decay of nuclei of radioactive elements or isotopes can occur in three main ways, and the corresponding nuclear decay reactions are named by the first three letters of the Greek alphabet. At alpha decay a helium atom consisting of two protons and two neutrons is released - it is commonly called an alpha particle. Since alpha decay entails a decrease in the number of positively charged protons in an atom by two, the nucleus that emitted the alpha particle turns into the nucleus of the element two positions below it in the periodic system of Mendeleev. At beta decay the nucleus emits an electron and the element advances one position forward according to the periodic table (in this case, in essence, the neutron turns into a proton with the radiation of this very electron). Finally, gamma decay - This the decay of nuclei with the emission of high-energy photons, which are commonly called gamma rays. In this case, the nucleus loses energy, but the chemical element does not change.

However, the mere fact of instability of one or another isotope of a chemical element does not mean at all that, having brought together a certain number of nuclei of this isotope, you will get a picture of their simultaneous decay. In reality, the decay of the nucleus of a radioactive element is somewhat reminiscent of the process of frying corn in the manufacture of popcorn: grains (nucleons) fall off the "cob" (nucleus) one at a time, in a completely unpredictable order, until they all fall off. The law describing the reaction of radioactive decay, in fact, only states this fact: for a fixed period of time, a radioactive nucleus emits a number of nucleons proportional to the number of nucleons remaining in its composition. That is, the more grains-nucleons still remain in the “undercooked” cob-core, the more of them will be released during a fixed “frying” time interval. When translating this metaphor into the language of mathematical formulas, we get an equation describing radioactive decay:

d N = λN d t

where d N- the number of nucleons emitted by the nucleus with the total number of nucleons N in time d t, a λ - experimentally determined radioactivity constant the substance under study. The above empirical formula is a linear differential equation, the solution of which is the following function, which describes the number of nucleons remaining in the nucleus at the time t:

N = N 0e- λt

where N 0 is the number of nucleons in the nucleus at the initial moment of observation.

The radioactivity constant thus determines how quickly the nucleus decays. However, experimental physicists usually measure not it, but the so-called half-life nucleus (that is, the period for which the studied nucleus emits half of the nucleons contained in it). For various isotopes of various radioactive substances, the half-life varies (in full accordance with theoretical predictions) from billionths of a second to billions of years. That is, some nuclei live almost forever, and some decay literally instantly (here it is important to remember that after the half-life, half of the total mass of the original substance remains, after two half-lives - a quarter of its mass, after three half-lives - one eighth, etc. d.).

As for the occurrence of radioactive elements, they are born in different ways. In particular, the ionosphere (upper rarefied layer of the atmosphere) of the Earth is constantly bombarded by cosmic rays, consisting of particles with high energies ( cm. Elementary particles). Under their influence, long-lived atoms are split into unstable isotopes: in particular, an unstable carbon-14 isotope with 6 protons and 8 neutrons in the nucleus is constantly formed from stable nitrogen-14 in the Earth's atmosphere ( cm. radiometric dating).

But the above case is rather exotic. Much more often, radioactive elements are formed in reaction chains nuclear fission . This is the name given to a series of events during which the original (“parent”) nucleus decays into two “daughter” (also radioactive), which, in turn, into four “granddaughter” nuclei, etc. The process continues until then until stable isotopes are obtained. As an example, let's take the uranium-238 isotope (92 protons + 146 neutrons) with a half-life of about 4.5 billion years. This period, by the way, is approximately equal to the age of our planet, which means that about half of the uranium-238 from the composition of the primary matter of the formation of the Earth is still in the totality of elements of the earth's nature. Uranium-238 turns into thorium-234 (90 protons + 144 neutrons), the half-life of which is 24 days. Thorium-234 turns into palladium-234 (91 protons + 143 neutrons) with a half-life of 6 hours - and so on. After more than ten stages of decay, a stable isotope of lead-206 is finally obtained.

Much can be said about radioactive decay, but a few points need to be emphasized. First, even if we take a pure sample of a single radioactive isotope as a starting material, it will decay into different components, and soon we will inevitably get a whole “bouquet” of various radioactive substances with different nuclear masses. Secondly, the natural chains of reactions of atomic decay reassure us in the sense that radioactivity is a natural phenomenon, it existed long before man, and there is no need to take a sin on the soul and blame only human civilization for having a radiation background on Earth. Uranium-238 has existed on Earth since its inception, decayed, decays - and will decay, and nuclear power plants accelerate this process, in fact, by a fraction of a percent; so that they do not have any particularly detrimental effect in addition to what is provided by nature.

Finally, the inevitability of radioactive atomic decay presents both potential challenges and opportunities for humanity. In particular, in the chain of reactions of the decay of uranium-238 nuclei, radon-222 is formed - a noble gas without color, smell and taste, which does not enter into any chemical reactions, since it is not capable of forming chemical bonds. This is inert gas, and it literally oozes from the bowels of our planet. Usually it has no effect on us - it simply dissolves in the air and remains there in a small concentration until it breaks down into even lighter elements. However, if this harmless radon stays in an unventilated room for a long time, then over time, its decay products will begin to accumulate there - and they are harmful to human health (when inhaled). This is how we get the so-called "radon problem".

On the other hand, the radioactive properties of chemical elements bring people significant benefits, if approached wisely. Radioactive phosphorus, in particular, is now injected to obtain a radiographic picture of bone fractures. The degree of its radioactivity is minimal and does not harm the health of the patient. Entering the bone tissues of the body along with ordinary phosphorus, it emits enough rays to fix them on photosensitive equipment and take pictures of a broken bone literally from the inside. Surgeons, accordingly, get the opportunity to operate on a complex fracture not blindly and at random, but having previously studied the structure of the fracture from such images. In general, the applications radiography in science, technology and medicine is innumerable. And they all work according to the same principle: the chemical properties of the atom (in fact, the properties of the outer electron shell) make it possible to attribute a substance to a specific chemical group; then, using the chemical properties of this substance, the atom is delivered “to the right place”, after which, using the property of the nuclei of this element to decay in strict accordance with the “schedule” established by the laws of physics, decay products are recorded.

The structure and properties of particles and atomic nuclei have been studied for about a hundred years in decays and reactions.
Decays are a spontaneous transformation of any object of microworld physics (nucleus or particle) into several decay products:

Both decays and reactions are subject to a series of conservation laws, among which must be mentioned, firstly, the following laws:

In what follows, other conservation laws operating in decays and reactions will be discussed. The laws listed above are the most important and, most importantly, performed in all types of interactions.(It is possible that the baryon charge conservation law is not as universal as conservation laws 1-4, but so far no violation of it has been found).
The processes of interactions of objects of the microworld, which are reflected in decays and reactions, have probabilistic characteristics.

Decays

Spontaneous decay of any object of microworld physics (nucleus or particle) is possible if the rest mass of the decay products is less than the mass of the primary particle.

Decays are characterized decay probabilities , or the reciprocal probability of average life time τ = (1/λ). The value associated with these characteristics is also often used. half-life T 1/2.
Examples of spontaneous decays

; π 0 → γ + γ; π + → μ + + ν μ ;

(2.4)

n → p + e − + e ; μ + → e + + μ + ν e ;

(2.5)

In decays (2.4) there are two particles in the final state. In decays (2.5), there are three.
We obtain the decay equation for particles (or nuclei). The decrease in the number of particles (or nuclei) over a time interval is proportional to this interval, the number of particles (nuclei) at a given time, and the decay probability:

Integration (2.6), taking into account the initial conditions, gives the relation between the number of particles at time t and the number of the same particles at the initial time t = 0:

The half-life is the time it takes for the number of particles (or nuclei) to be halved:

Spontaneous decay of any object of microworld physics (nucleus or particle) is possible if the mass of decay products is less than the mass of the primary particle. Decays into two products and into three or more are characterized by different energy spectra of the decay products. In the case of decay into two particles, the spectra of decay products are discrete. If there are more than two particles in the final state, the product spectra are continuous.

The difference between the masses of the primary particle and the decay products is distributed among the decay products in the form of their kinetic energies.
The laws of conservation of energy and momentum for decay should be written in the coordinate system associated with the decaying particle (or nucleus). To simplify the formulas, it is convenient to use the system of units = c = 1, in which energy, mass, and momentum have the same dimension (MeV). Conservation laws for this decay:

Hence we obtain for the kinetic energies of the decay products

Thus, in the case of two particles in the final state the kinetic energies of the products are determined clearly. This result does not depend on whether relativistic or nonrelativistic velocities have decay products. For the relativistic case, the formulas for the kinetic energies look somewhat more complicated than (2.10), but the solution of the equations for the energy and momentum of two particles is again the only one. It means that in the case of decay into two particles, the spectra of decay products are discrete.
If three (or more) products appear in the final state, the solution of the equations for the laws of conservation of energy and momentum does not lead to an unambiguous result. When, if there are more than two particles in the final state, the spectra of the products are continuous.(In what follows, this situation will be considered in detail using the example of -decays.)
In calculating the kinetic energies of the decay products of nuclei, it is convenient to use the fact that the number of nucleons A is conserved. (This is a manifestation baryon charge conservation law , since the baryon charges of all nucleons are equal to 1).
Let us apply the obtained formulas (2.11) to the -decay of 226 Ra (the first decay in (2.4)).

The difference between the masses of radium and its decay products
ΔM = M(226 Ra) - M(222 Rn) - M(4 He) = Δ(226 Ra) - Δ(222 Rn) - Δ(4 He) = (23.662 - 16.367 - 2.424) MeV = 4.87 MeV. (Here we used tables of excess masses of neutral atoms and the ratio M = A + for masses and so-called. excess masses Δ)
The kinetic energies of helium and radon nuclei resulting from alpha decay are equal to:

,
.

The total kinetic energy released as a result of alpha decay is less than 5 MeV and is about 0.5% of the rest mass of the nucleon. The ratio of the kinetic energy released as a result of the decay and the rest energies of particles or nuclei - criterion for the admissibility of applying the nonrelativistic approximation. In the case of alpha decays of nuclei, the smallness of the kinetic energies compared to the rest energies makes it possible to confine ourselves to the nonrelativistic approximation in formulas (2.9-2.11).

The π + meson decays into two particles: π + μ + + ν μ . The mass of the π + meson is 139.6 MeV, the mass of the muon μ is 105.7 MeV. The exact value of the muon neutrino mass ν μ is still unknown, but it has been established that it does not exceed 0.15 MeV. In an approximate calculation, it can be set equal to 0, since it is several orders of magnitude lower than the difference between the pion and muon masses. Since the difference between the masses of the π + meson and its decay products is 33.8 MeV, it is necessary to use the relativistic formulas for the relation between energy and momentum for neutrinos. In further calculations, the small neutrino mass can be neglected and the neutrino can be considered an ultrarelativistic particle. Laws of conservation of energy and momentum in the decay of π + meson:

m π = m μ + T μ + E ν
|p ν | = | p μ |

E ν = p ν

An example of a two-particle decay is also the emission of a -quantum during the transition of an excited nucleus to the lowest energy level.
In all two-particle decays analyzed above, the decay products have an "exact" energy value, i.e. discrete spectrum. However, a closer examination of this problem shows that the spectrum even of the products of two-particle decays is not a function of the energy.

.

The spectrum of decay products has a finite width Г, which is the greater, the shorter the lifetime of the decaying nucleus or particle.

(This relation is one of the formulations of the uncertainty relation for energy and time).
Examples of three-body decays are -decays.
The neutron undergoes -decay, turning into a proton and two leptons - an electron and an antineutrino: np + e - + e.
Beta decays are also experienced by leptons themselves, for example, the muon (the average muon lifetime
τ = 2.2 10 –6 sec):

.

Conservation laws for muon decay at maximum electron momentum:
For the maximum kinetic energy of the muon decay electron, we obtain the equation

The kinetic energy of an electron in this case is two orders of magnitude higher than its rest mass (0.511 MeV). The momentum of a relativistic electron practically coincides with its kinetic energy, indeed

p = (T 2 + 2mT) 1/2 = )