Radioactive Decay Equation. The half-life of radioactive elements - what is it and how is it determined? Half-life formula

The concept of radioactivity

Law of radioactive decay

Quantification of radioactivity and its units

Ionizing radiation, their characteristics.

Sources of AI

1. The concept of radioactivity

Radioactivity is the spontaneous process of transformation (decay) of atomic nuclei, accompanied by the emission of a special type of radiation called radioactive.

In this case, the transformation of atoms of one element into atoms of others occurs.

Radioactive transformations are characteristic only of individual substances.

A substance is considered radioactive if it contains radionuclides and the process radioactive decay.

Radionuclides (isotopes) - the nuclei of atoms capable of spontaneous decay are called radionuclides.

The symbol is used as a characteristic of the nuclide chemical element, indicate the atomic number (the number of protons) and the mass number of the nucleus (the number of nucleons, i.e. the total number of protons and neutrons).

For example, 239 94 Pu means that the nucleus of a plutonium atom contains 94 protons and 145 neutrons, for a total of 239 nucleons.

There are the following types of radioactive decay:

beta decay;

Alpha decay;

Spontaneous fission of atomic nuclei (neutron decay);

Proton radioactivity (proton fusion);

Two-proton and cluster radioactivity.

beta decay - this is the process of transformation in the nucleus of an atom of a proton into a neutron or a neutron into a proton with the release of a beta particle (positron or electron)

Alpha decay - characteristic of heavy elements, the nuclei of which, starting from the number 82 of the table of D.I. Mendeleev, are unstable, despite the excess of neutrons and spontaneously decay. The nuclei of these elements predominantly eject the nuclei of helium atoms.

Spontaneous fission of atomic nuclei (neutron decay) - this is the spontaneous fission of some nuclei of heavy elements (uranium-238, californium 240.248, 249, 250, curium 244, 248, etc.). The probability of spontaneous nuclear fission is negligible compared to alpha decay. In this case, the nucleus is divided into two fragments (nuclei) that are close in mass.

1. Law of radioactive decay

The stability of nuclei decreases as the total number of nucleons increases. It also depends on the ratio of the number of neutrons and protons.

The process of successive nuclear transformations, as a rule, ends with the formation of stable nuclei.

Radioactive transformations obey the law of radioactive decay:

N = N 0 e λ t ,

where N, N 0 is the number of atoms that have not decayed at times t and t 0 ;

λ is the radioactive decay constant.

The value λ has its own individual value for each type of radionuclide. It characterizes the decay rate, i.e. shows how many nuclei decay per unit time.

According to the equation of the law of radioactive decay, its curve is an exponential.

1. Quantification of radioactivity and its units

The time during which, due to spontaneous nuclear transformations, half of the nuclei decay, is called half-life T 1/2 . The half-life T 1/2 is associated with decay constantλ dependence:

T 1/2 \u003d ln2 / λ \u003d 0.693 / λ.

The half-life T 1/2 for different radionuclides is different and varies widely - from fractions of a second to hundreds and even thousands of years.

Half-lives of some radionuclides:

Iodine-131 - 8.04 days

Cesium-134 - 2.06 years

Strontium-90 - 29.12 years

Cesium-137 - 30 years

Plutonium-239 - 24065 years

Uranium-235 - 7.038. 10 8 years

Potassium-40 - 1.4 10 9 years.

The reciprocal of the decay constant, calledaverage lifetime of a radioactive atom t :

The decay rate is determined by the activity of substance A:

A \u003d dN / dt \u003d A 0 e λ t \u003d λ N,

where A and A 0 are the activities of the substance at times t and t 0 .

Activity is a measure of radioactivity. It is characterized by the number of decays of radioactive nuclei per unit of time.

The activity of a radionuclide is directly proportional to the total number of radioactive atomic nuclei at time t and inversely proportional to the half-life:

A \u003d 0.693 N / T 1/2.

In the SI system, the becquerel (Bq) is taken as the unit of activity. One becquerel is equal to one disintegration per second. The off-system unit of activity is the curie (Ku).

1 Ku \u003d 3.7 10 10 Bq

1Bq = 2.7 10 -11 Ku.

The unit of curie activity corresponds to the activity of 1 g of radium. In the practice of measurements, the concepts of volume A v (Bq / m 3, Ku / m 3), surface A s (Bq / m 2, Ku / m 2), specific A m (Bq / m, Ku / m) activity are also used.

1. Radioactivity. Basic law of radioactive decay. Activity.

2. The main types of radioactive decay.

3. Quantitative characteristics of interaction ionizing radiation with substance.

4. Natural and artificial radioactivity. radioactive rows.

5. Use of radionuclides in medicine.

6. Charged particle accelerators and their use in medicine.

7. Biophysical foundations of the action of ionizing radiation.

8. Basic concepts and formulas.

9. Tasks.

The interest of physicians in natural and artificial radioactivity is due to the following.

Firstly, all living things are constantly exposed to the natural radiation background, which is cosmic radiation, the radiation of radioactive elements that occur in the surface layers of the earth's crust, and the radiation of elements that enter the body of animals along with air and food.

Secondly, radioactive radiation is used in medicine itself for diagnostic and therapeutic purposes.

33.1. Radioactivity. Basic law of radioactive decay. Activity

The phenomenon of radioactivity was discovered in 1896 by A. Becquerel, who observed the spontaneous emission of unknown radiation from uranium salts. Soon, E. Rutherford and the Curies found that during radioactive decay, He nuclei (α-particles), electrons (β-particles) and hard electromagnetic radiation (γ-rays) are emitted.

In 1934, decay with the emission of positrons (β + -decay) was discovered, and in 1940 a new type of radioactivity was discovered - spontaneous nuclear fission: a fissile nucleus breaks up into two fragments of comparable mass with the simultaneous emission of neutrons and γ -quanta. Proton radioactivity of nuclei was observed in 1982.

Radioactivity - the ability of some atomic nuclei to spontaneously (spontaneously) transform into other nuclei with the emission of particles.

Atomic nuclei are composed of protons and neutrons, which have a general name - nucleons. The number of protons in the nucleus determines Chemical properties atom and is denoted by Z (this serial number chemical element). The number of nucleons in a nucleus is called mass number and denote A. Nuclei with the same serial number and different mass numbers are called isotopes. All isotopes of one chemical element have the same Chemical properties. Physical properties isotopes can vary greatly. To designate isotopes, the symbol of a chemical element is used with two indices: A Z X. The lower index is the serial number, the upper one is the mass number. Often the subscript is omitted because the element symbol itself points to it. For example, they write 14 C instead of 14 6 C.

The ability of a nucleus to decay depends on its composition. The same element can have both stable and radioactive isotopes. For example, the 12C carbon isotope is stable, while the 14C isotope is radioactive.

Radioactive decay is a statistical phenomenon. The ability of an isotope to decay characterizes decay constantλ.

decay constant is the probability that the nucleus of a given isotope will decay per unit time.

The probability of nuclear decay in a short time dt is found by the formula

Taking into account formula (33.1), we obtain an expression that determines the number of decayed nuclei:

Formula (33.3) is called the main the law of radioactive decay.

The number of radioactive nuclei decreases with time according to an exponential law.

In practice, instead of decay constantλ often use another value called half-life.

Half life(T) - the time during which it decays half radioactive nuclei.

The law of radioactive decay using the half-life is written as follows:

Dependence graph (33.4) is shown in fig. 33.1.

The half-life can be either very long or very short (from fractions of a second to many billions of years). In table. 33.1 shows the half-lives for some elements.

Rice. 33.1. The decrease in the number of nuclei of the original substance during radioactive decay

Table 33.1. Half-lives for some elements

For rate degree of radioactivity isotopes use a special quantity called activity.

Activity - the number of nuclei of a radioactive preparation decaying per unit of time:

Unit of measure of activity in SI - becquerel(Bq), 1 Bq corresponds to one decay event per second. In practice, more

resourceful off-system unit of activity - curie(Ci) equal to the activity of 1 g of 226 Ra: 1 Ci = 3.7x10 10 Bq.

Over time, activity decreases in the same way as the number of undecayed nuclei decreases:

33.2. Main types of radioactive decay

In the process of studying the phenomenon of radioactivity, 3 types of rays emitted by radioactive nuclei were discovered, which were called α-, β- and γ-rays. Later it was found that α- and β-particles are products of two various kinds radioactive decay, and γ-rays are a by-product of these processes. In addition, γ-rays also accompany more complex nuclear transformations, which are not considered here.

Alpha decay consists in the spontaneous transformation of nuclei with emissionα -particles (helium nuclei).

The α-decay scheme is written as

where X, Y are the symbols of the parent and child nuclei, respectively. When writing α-decay, instead of "α" you can write "Not".

In this decay, the atomic number Z of the element decreases by 2, and the mass number A - by 4.

During α-decay, the daughter nucleus, as a rule, is formed in an excited state and, upon transition to the ground state, emits a γ-quantum. A common property of complex micro-objects is that they have discrete set of energy states. This also applies to cores. Therefore, the γ-radiation of excited nuclei has a discrete spectrum. Consequently, the energy spectrum of α-particles is also discrete.

The energy of emitted α-particles for almost all α-active isotopes lies within 4-9 MeV.

beta decay consists in the spontaneous transformation of nuclei with the emission of electrons (or positrons).

It has been established that β-decay is always accompanied by the emission of a neutral particle - a neutrino (or antineutrino). This particle practically does not interact with matter, and will not be considered further. The energy released during β-decay is distributed between the β-particle and the neutrino randomly. Therefore, the energy spectrum of β-radiation is continuous (Fig. 33.2).

Rice. 33.2. Energy spectrum of β-decay

There are two types of β-decay.

1. Electronicβ - -decay consists in the transformation of one nuclear neutron into a proton and an electron. In this case, another particle ν" appears - an antineutrino:

An electron and an antineutrino fly out of the nucleus. The scheme of electronic β - decay is written as

During electronic β-decay, the serial number of the Z-element increases by 1, the mass number A does not change.

The energy of β-particles lies in the range of 0.002-2.3 MeV.

2. Positronβ + -decay consists in the transformation of one nuclear proton into a neutron and a positron. In this case, another particle ν appears - a neutrino:

Electron capture itself does not generate ionizing particles, but it does accompanied by x-rays. This radiation occurs when the space vacated by the absorption of an inner electron is filled by an electron from an outer orbit.

Gamma radiation has an electromagnetic nature and is a photon with a wavelengthλ ≤ 10 -10 m.

Gamma radiation is not an independent type of radioactive decay. Radiation of this type almost always accompanies not only α-decay and β-decay, but also more complex nuclear reactions. It is not deflected by electric and magnetic fields, has a relatively weak ionizing and very high penetrating power.

33.3. Quantitative characteristics of the interaction of ionizing radiation with matter

Impact radioactive radiation on living organisms associated with ionization, which it induces in the tissues. The ability of a particle to ionize depends both on its type and on its energy. As the particle moves deeper into the substance, it loses its energy. This process is called ionization braking.

To quantitatively characterize the interaction of a charged particle with matter, several quantities are used:

After the energy of the particle falls below the ionization energy, its ionizing effect ceases.

Average linear mileage(R) of a charged ionizing particle - the path traveled by it in a substance before losing its ionizing ability.

Consider some characteristics interactions of various types of radiation with matter.

alpha radiation

The alpha particle practically does not deviate from the initial direction of its movement, since its mass is many times greater

Rice. 33.3. Dependence of the linear ionization density on the path traveled by an α-particle in a medium

the mass of the electron with which it interacts. As it penetrates deep into the substance, the ionization density first increases, and when end of run (x = R) drops sharply to zero (Fig. 33.3). This is explained by the fact that with a decrease in the speed of movement, the time that it spends near the molecule (atom) of the medium increases. In this case, the probability of ionization increases. After the energy of the α-particle becomes comparable with the energy of molecular thermal motion, it captures two electrons in the substance and turns into a helium atom.

The electrons generated during the ionization process, as a rule, move away from the track of the α-particle and cause secondary ionization.

Characteristics of the interaction of α-particles with water and soft tissues are presented in Table. 33.2.

Table 33.2. Dependence of the characteristics of interaction with matter on the energy of α-particles

beta radiation

For movement β -particles in matter are characterized by a curvilinear unpredictable trajectory. This is due to the equality of the masses of the interacting particles.

Characteristics of interaction β -particles with water and soft tissues are presented in Table. 33.3.

Table 33.3. Dependence of the characteristics of interaction with matter on the energy of β-particles

As with α particles, the ionization power of β particles increases with decreasing energy.

Gamma radiation

Absorption γ -radiation by a substance obeys an exponential law similar to the law of absorption of x-rays:

The main processes responsible for absorption γ -radiation are the photoelectric effect and Compton scattering. This produces a relatively small amount of free electrons (primary ionization), which have a very high energy. It is they who cause the processes of secondary ionization, which is incomparably higher than the primary one.

33.4. natural and artificial

radioactivity. radioactive ranks

Terms natural and artificial radioactivity are conditional.

Natural call the radioactivity of isotopes that exist in nature, or the radioactivity of isotopes formed as a result of natural processes.

For example, the radioactivity of uranium is natural. The radioactivity of carbon 14 C, which is formed in the upper layers of the atmosphere under the influence of solar radiation, is also natural.

Artificial called the radioactivity of isotopes that arise as a result of human activities.

This is the radioactivity of all isotopes produced in particle accelerators. This also includes the radioactivity of soil, water and air, which occurs during an atomic explosion.

natural radioactivity

AT initial period the study of radioactivity, researchers could only use natural radionuclides (radioactive isotopes) contained in terrestrial rocks in sufficient in large numbers: 232 Th, 235 U, 238 U. Three radioactive series begin with these radionuclides, ending with stable Pb isotopes. Subsequently, a series starting from 237 Np was discovered, with a final stable nucleus 209 Bi. On fig. 33.4 shows a row starting with 238 U.

Rice. 33.4. Uranium-radium series

Elements of this series are the main source of internal human exposure. For example, 210 Pb and 210 Po enter the body with food - they are concentrated in fish and shellfish. Both of these isotopes accumulate in lichens and are therefore present in meat. reindeer. The most significant of all natural sources of radiation is 222 Rn - a heavy inert gas resulting from the decay of 226 Ra. It accounts for about half of the dose of natural radiation received by humans. Formed in the earth's crust, this gas seeps into the atmosphere and enters the water (it is highly soluble).

The radioactive isotope of potassium 40 K is constantly present in the earth's crust, which is part of natural potassium (0.0119%). From the soil, this element enters through the root system of plants and with plant foods (cereals, fresh vegetables and fruits, mushrooms) - into the body.

Another source of natural radiation is cosmic radiation (15%). Its intensity increases in mountainous areas due to a decrease in the protective effect of the atmosphere. Sources of natural background radiation are listed in Table. 33.4.

Table 33.4. Component of the natural radioactive background

33.5. The use of radionuclides in medicine

radionuclides called radioactive isotopes of chemical elements with a short half-life. Such isotopes do not exist in nature, so they are obtained artificially. In modern medicine, radionuclides are widely used for diagnostic and therapeutic purposes.

Diagnostic Application is based on the selective accumulation of certain chemical elements by individual organs. Iodine, for example, is concentrated in the thyroid gland, while calcium is concentrated in the bones.

The introduction of radioisotopes of these elements into the body makes it possible to detect areas of their concentration by radioactive radiation and thus obtain important diagnostic information. This diagnostic method is called by the labeled atom method.

Therapeutic use radionuclides is based on the destructive effect of ionizing radiation on tumor cells.

1. Gamma Therapy- the use of high-energy γ-radiation (source 60 Co) for the destruction of deeply located tumors. So that superficially located tissues and organs are not subjected to a destructive effect, the effect of ionizing radiation is carried out in different sessions in different directions.

2. alpha therapy- therapeutic use of α-particles. These particles have a significant linear ionization density and are absorbed even by a small layer of air. Therefore, therapeutic

the use of alpha rays is possible with direct contact with the surface of the organ or with the introduction inside (with a needle). For superficial exposure, radon therapy (222 Rn) is used: exposure to the skin (baths), digestive organs (drinking), respiratory organs (inhalations).

In some cases, medicinal use α -particles is associated with the use of neutron flux. With this method, elements are first introduced into the tissue (tumor), the nuclei of which, under the action of neutrons, emit α -particles. After that, the diseased organ is irradiated with a neutron flux. In this manner α -particles are formed directly inside the organ, on which they should have a destructive effect.

Table 33.5 lists the characteristics of some radionuclides used in medicine.

Table 33.5. Isotope characterization

33.6. Particle accelerators and their use in medicine

Accelerator- an installation in which, under the influence of electric and magnetic fields, directed beams of charged particles with high energy (from hundreds of keV to hundreds of GeV) are obtained.

Accelerators create narrow beams of particles with a given energy and a small cross section. This allows you to provide directed impact on irradiated objects.

The use of accelerators in medicine

Electron and proton accelerators are used in medicine for radiation therapy and diagnostics. In this case, both the accelerated particles themselves and the accompanying X-ray radiation are used.

Bremsstrahlung X-ray obtained by directing a particle beam to a special target, which is the source of x-rays. This radiation differs from the X-ray tube by a much higher photon energy.

Synchrotron X-rays occurs in the process of accelerating electrons in ring accelerators - synchrotrons. Such radiation has a high degree orientation.

The direct action of fast particles is associated with their high penetrating power. Such particles pass through surface tissues without causing serious damage, and have an ionizing effect at the end of their journey. By selecting the appropriate particle energy, it is possible to achieve the destruction of tumors at a given depth.

The areas of application of accelerators in medicine are shown in Table. 33.6.

Table 33.6. Application of accelerators in therapy and diagnostics

33.7. Biophysical foundations of the action of ionizing radiation

As noted above, the impact of radioactive radiation on biological systems is associated with ionization of molecules. The process of interaction of radiation with cells can be divided into three successive stages (stages).

1. physical stage consists of energy transfer radiation to the molecules of a biological system, resulting in their ionization and excitation. The duration of this stage is 10 -16 -10 -13 s.

2. Physico-chemical the stage consists of various kinds of reactions leading to a redistribution of the excess energy of excited molecules and ions. As a result, highly active

products: radicals and new ions with a wide range chemical properties.

The duration of this stage is 10 -13 -10 -10 s.

3. Chemical stage - this is the interaction of radicals and ions with each other and with surrounding molecules. At this stage, structural damage of various types is formed, leading to a change in biological properties: the structure and functions of membranes are disrupted; lesions occur in DNA and RNA molecules.

The duration of the chemical stage is 10 -6 -10 -3 s.

4. biological stage. At this stage, damage to molecules and subcellular structures leads to a variety of functional disorders, to premature cell death as a result of the action of apoptosis mechanisms or due to necrosis. Damage received at the biological stage can be inherited.

The duration of the biological stage is from several minutes to tens of years.

We note the general patterns of the biological stage:

Large violations with low absorbed energy (a lethal dose of radiation for a person causes heating of the body by only 0.001 ° C);

Action on subsequent generations through the hereditary apparatus of the cell;

A latent, latent period is characteristic;

Different parts of cells have different sensitivity to radiation;

First of all, dividing cells are affected, which is especially dangerous for a child's body;

The destructive effect on the tissues of an adult organism, in which there is a division;

The similarity of radiation changes with the pathology of early aging.

33.8. Basic concepts and formulas

Table continuation

33.9. Tasks

1. What is the activity of the drug if 10,000 nuclei of this substance decay within 10 minutes?

4. The age of ancient wood samples can be approximately determined by the specific mass activity of the 14 6 C isotope in them. How many years ago was a tree cut down that was used to make an object if the specific mass activity of carbon in it is 75% of the specific mass activity of a growing tree? The half-life of radon is T = 5570 years.

9. After the Chernobyl accident, in some places soil contamination with radioactive caesium-137 was at the level of 45 Ci/km 2 .

After how many years the activity in these places will decrease to a relatively safe level of 5 Ci/km 2 . The half-life of cesium-137 is T = 30 years.

10. The permissible activity of iodine-131 in the human thyroid gland should be no more than 5 nCi. Some people who were in the area Chernobyl disaster, the activity of iodine-131 reached 800 nCi. After how many days did activity decrease to normal? The half-life of iodine-131 is 8 days.

11. The following method is used to determine the volume of blood in an animal. A small volume of blood is taken from the animal, the erythrocytes are separated from the plasma and placed in a solution with radioactive phosphorus, which is assimilated by the erythrocytes. Labeled erythrocytes are reintroduced into the circulatory system of the animal, and after some time the activity of the blood sample is determined.

ΔV = 1 ml of this solution was injected into the blood of some animal. The initial activity of this volume was A 0 = 7000 Bq. The activity of 1 ml of blood taken from the vein of the animal a day later was equal to 38 pulses per minute. Determine the volume of the animal's blood if the half-life of radioactive phosphorus is T = 14.3 days.

Lecture 2. The basic law of radioactive decay and the activity of radionuclides

The rate of decay of radionuclides is different - some decay faster, others slower. The rate of radioactive decay is radioactive decay constant, λ [sec-1], which characterizes the probability of decay of one atom in one second. For each radionuclide, the decay constant has its own value, the larger it is, the faster the nuclei of matter decay.

The number of decays registered in a radioactive sample per unit of time is called activity (a ), or the radioactivity of the sample. The activity value is directly proportional to the number of atoms N radioactive material:

a =λ· N , (3.2.1)

where λ is the radioactive decay constant, [sec-1].

At present, according to the current international system SI units, for the unit of measurement of radioactivity is taken becquerel [Bq]. This unit got its name in honor of the French scientist Henri Becquerel, who discovered in 1856 the phenomenon of natural uranium radioactivity. One becquerel is equal to one disintegration per second 1 Bq = 1 .

However, an off-system unit of activity is still quite often used. – curie [Key], introduced by the Curies as a measure of the decay rate of one gram of radium (in which ~3.7 1010 decays per second occurs), therefore

1 Key= 3.7 1010 Bq.

This unit is convenient for assessing the activity of large quantities of radionuclides.

The decrease in the radionuclide concentration over time as a result of decay obeys an exponential dependence:

, (3.2.2)

where N t- the number of atoms of a radioactive element remaining after a while t after the start of observation; N 0 is the number of atoms at the initial moment of time ( t =0 ); λ is the radioactive decay constant.

The relationship described is called basic law of radioactive decay .

The time it takes for half of total radionuclides is called half life, T½ . After one half-life, out of 100 atoms of the radionuclide, only 50 remain (Fig. 2.1). Over the next same period, of these 50 atoms, only 25 remain, and so on.

The relationship between half-life and decay constant is derived from the equation for the basic law of radioactive decay:

at t=T½ and

we get https://pandia.ru/text/80/150/images/image006_47.gif" width="67" height="41 src="> Þ ;

https://pandia.ru/text/80/150/images/image009_37.gif" width="76" height="21">;

i.e..gif" width="81" height="41 src=">.

Therefore, the law of radioactive decay can be written as follows:

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where at - the activity of the drug over time t ; a0 – the activity of the drug at the initial moment of observation.

It is often necessary to determine the activity of a given amount of any radioactive substance.

Remember that the unit of quantity of a substance is the mole. A mole is the amount of a substance containing as many atoms as there are in 0.012 kg = 12 g of the 12C carbon isotope.

One mole of any substance contains Avogadro's number NA atoms:

NA = 6.02 1023 atoms.

For simple substances(elements) the mass of one mole numerically corresponds to atomic mass BUT element

1mol = BUT G.

For example: For magnesium: 1 mol 24Mg = 24 g.

For 226Ra: 1 mole of 226Ra = 226 g, etc.

In view of what has been said in m grams of the substance will N atoms:

https://pandia.ru/text/80/150/images/image015_20.gif" width="156" height="43 src="> (3.2.6)

Example: Let's calculate the activity of 1 gram of 226Ra, which has λ = 1.38 10-11 sec-1.

a\u003d 1.38 10-11 1 / 226 6.02 1023 \u003d 3.66 1010 Bq.

If a radioactive element is part of chemical compound, then when determining the activity of the drug, it is necessary to take into account its formula. Taking into account the composition of the substance, the mass fraction is determined χ radionuclide in a substance, which is determined by the ratio:

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Problem solution example

Condition:

Activity A0 radioactive element 32P on the day of observation is 1000 Bq. Determine the activity and number of atoms of this element in a week. Half life T½ 32P = 14.3 days.

Solution:

a) Find the activity of phosphorus-32 after 7 days:

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Answer: in a week, the activity of the 32P drug will be 712 Bq, and the number of atoms of the radioactive isotope 32P is 127.14 106 atoms.

test questions

1) What is the activity of a radionuclide?

2) Name the units of radioactivity and the relationship between them.

3) What is the radioactive decay constant?

4) Define the basic law of radioactive decay.

5) What is the half-life?

6) What is the relationship between activity and mass of a radionuclide? Write a formula.

Tasks

1. Calculate activity 1 G 226Ra. T½ = 1602 years.

2. Calculate activity 1 G 60Co. T½ = 5.3 years.

3. One M-47 tank shell contains 4.3 kg 238U. T½ = 2.5 109 years. Determine projectile activity.

4. Calculate the activity of 137Cs after 10 years, if at the initial moment of observation it is 1000 Bq. T½ = 30 years.

5. Calculate the 90Sr activity a year ago if it is 500 at the present time Bq. T½ = 29 years.

6. What activity will 1 create kg radioisotope 131I, T½ = 8.1 days?

7. Using the reference data, determine activity 1 G 238U. T½ = 2.5 109 years.

Using the reference data, determine activity 1 G 232Th, Т½ = 1.4 1010 years.

8. Calculate the activity of the compound: 239Pu316O8.

9. Calculate the mass of the radionuclide with activity in 1 Key:

9.1. 131I, T1/2=8.1 days;

9.2. 90Sr, Т1/2=29 years;

9.3. 137Cs, Т1/2=30 years;

9.4. 239Pu, Т1/2=2.4 104 years.

10. Determine the mass 1 mCi radioactive isotope of carbon 14C, T½ = 5560 years.

11. It is necessary to prepare a radioactive preparation of phosphorus 32P. How long will it take for 3% of the drug to remain? Т½ = 14.29 days.

12. The natural mixture of potassium contains 0.012% of the radioactive isotope 40K.

1) Determine the mass of natural potassium, which contains 1 Key 40K. T½ = 1.39 109 years = 4.4 1018 sec.

2) Calculate the radioactivity of the soil by 40K if it is known that the potassium content in the soil sample is 14 kg/t.

13. How many half-lives are required for the initial activity of a radioisotope to decrease to 0.001%?

14. To determine the effect of 238U on plants, the seeds were soaked in 100 ml solution UO2(NO3)2 6H2O, in which the mass of the radioactive salt was 6 G. Determine the activity and specific activity of 238U in solution. Т½ = 4.5 109 years.

15. Define Activity 1 grams 232Th, Т½ = 1.4 1010 years.

16. Determine the mass 1 Key 137Cs, Т1/2=30 years.

17. The ratio between the content of stable and radioactive isotopes of potassium in nature is a constant value. The content of 40K is 0.01%. Calculate the radioactivity of the soil by 40K if it is known that the potassium content in the soil sample is 14 kg/t.

18. Lithogenic radioactivity of the environment is formed mainly during count of three main natural radionuclides: 40K, 238U, 232Th. The share of radioactive isotopes in the natural amount of isotopes is 0.01, 99.3, ~100, respectively. Calculate radioactivity 1 t soil, if it is known that the relative content of potassium in the soil sample is 13600 g/t, uranium - 1 10-4 g/t, thorium - 6 10-4 g/t.

19. In the shells of bivalve mollusks found 23200 Bq/kg 90Sr. Determine the activity of samples after 10, 30, 50, 100 years.

20. The main pollution of the closed reservoirs of the Chernobyl zone took place in the first year after the accident at the nuclear power plant. In the bottom sediments of the lake. Azbuchin in 1999 discovered 137Cs with a specific activity of 1.1 10 Bq/m2. Determine the concentration (activity) of 137Cs deposited per m2 of bottom sediments as of 1986-1987. (12 years ago).

21. 241Am (T½ = 4.32 102 years) is formed from 241Pu (T½ = 14.4 years) and is an active geochemical migrant. Taking advantage reference materials, calculate with an accuracy of 1% the decrease in the activity of plutonium-241 in time, in which year after the Chernobyl disaster, the formation of 241Am in environment will be the maximum.

22. Calculate the activity of 241Am in the products of emissions from the Chernobyl reactor as of April
2015, provided that in April 1986 the activity of 241Am was 3.82 1012 Bq,Т½ = 4.32 102 years.

23. 390 found in soil samples nCi/kg 137Cs. Calculate the activity of samples after 10, 30, 50, 100 years.

24. The average concentration of pollution in the bed of the lake. Deep, located in the Chernobyl exclusion zone, is 6.3 104 Bq 241Am and 7.4 104 238+239+240Pu per 1 m2. Calculate the year in which these data were obtained.

LAB #19

STUDYING THE LAW OF RADIOACTIVE DECAY

AND WAYS OF PROTECTION AGAINST RADIOACTIVE RADIATION

Objective : 1) study of the law of radioactive decay; 2) study of the law of absorption of g- and b-rays by matter.

Work tasks : 1) determination of linear absorption coefficients of radioactive radiation various materials; 2) determination of the thickness of the half attenuation layer of these materials; 3) determination of the half-life and decay constant of a chemical element.

Supporting funds : Windows computer.

THEORETICAL PART

Introduction

The composition of the atomic nucleus

The nucleus of any atom consists of particles of two types - protons and neutrons. The proton is the nucleus of the simplest atom - hydrogen. He has positive charge, equal in magnitude to the electron charge, and a mass of 1.67 × 10-27 kg. The neutron, whose existence was established only in 1932 by the Englishman James Chadwick, is electrically neutral, and the mass is almost the same as that of the proton. Neutrons and protons, which are two constituent elements of the atomic nucleus, are united by the common name of nucleons. The number of protons in a nucleus (or in a nuclide) is called the atomic number and is denoted by the letter Z. The total number of nucleons, i.e. neutrons and protons, denoted by the letter A and is called the mass number. Usually, chemical elements are usually denoted by the symbol or, where X is the symbol of the chemical element.

Radioactivity

The phenomenon of radioactivity consists in the spontaneous (spontaneous) transformation of the nuclei of some chemical elements into the nuclei of other elements with the emission of radioactive radiation..

Nuclei subject to such decay are called radioactive. Nuclei that do not undergo radioactive decay are called stable. In the process of decay, the nucleus can change both the atomic number Z and the mass number A.

Radioactive transformations proceed spontaneously. The speed of their flow is not affected by changes in temperature and pressure, the presence of electric and magnetic fields, the type of chemical compound of a given radioactive element and its state of aggregation.

Radioactive decay is characterized by the time of its occurrence, the type and energies of the emitted particles, and when several particles are emitted from the nucleus, also by the relative angles between the directions of particle emission. Historically, radioactivity is the first nuclear process discovered by man (A. Becquerel, 1896).

Distinguish between natural and artificial radioactivity.

Natural radioactivity occurs in unstable nuclei that exist in natural conditions. Artificial is called the radioactivity of nuclei formed as a result of various nuclear reactions. There is no fundamental difference between artificial and natural radioactivity. They have common patterns.

Four main types of radioactivity are possible and actually observed in atomic nuclei: a-decay, b-decay, g-decay, and spontaneous fission.

The phenomenon of a-decay is that heavy nuclei spontaneously emit a-particles (helium nuclei 2 H 4). In this case, the mass number of the nucleus decreases by four units, and the atomic number - by two:

Z X A ® Z -2 Y A-4 + 2 H 4.

a-particle consists of four nucleons: two neutrons and two protons.

In the process of radioactive decay, the nucleus can emit not only the particles that make up its composition, but also new particles that are born in the process of decay. Processes of this kind are b- and g-decays.

The concept of b-decay combines three types of nuclear transformations: electronic (b -) decay, positron (b +) decay and electron capture.

The phenomenon of b - decay consists in the fact that the nucleus spontaneously emits an electron e - and the lightest electrically neutral particle antineutrino, while passing into a nucleus with the same mass number A, but with an atomic number Z, but one greater:

Z X A ® Z +1 Y A + e - + .

It must be emphasized that the electron emitted during b - decay has nothing to do with orbital electrons. It is born inside the nucleus itself: one of the neutrons turns into a proton and at the same time emits an electron.

Another type of b-decay is a process in which the nucleus emits a positron e + and another lightest electrically neutral particle - a neutrino n. In this case, one of the protons turns into a neutron:

Z X A ® Z -1 Y A + e + + n.

This decay is called positron or b + decay.

The range of b-decay phenomena also includes electron capture (often also called K-capture), in which the nucleus absorbs one of the electrons of the atomic shell (usually from the K-shell), emitting neutrinos. In this case, as in positron decay, one of the protons turns into a neutron:

e - + Z X A ® Z -1 Y A + n.

To g-radiation include electromagnetic waves, whose length is much less than the interatomic distances:

where d - has the order of 10 -8 cm. In the corpuscular picture, this radiation is a stream of particles called g-quanta. The lower limit of the energy of g-quanta

E= 2p s/l

is on the order of tens of keV. There is no natural upper limit. Modern accelerators produce quanta with energies up to 20 GeV.

The decay of the nucleus with the emission of g - radiation in many respects resembles the emission of photons by excited atoms. Like an atom, a nucleus can be in an excited state. Upon transition to a lower energy state, or ground state, the nucleus emits a photon. Since g-radiation does not carry a charge, during g-decay there is no transformation of one chemical element into another.

Basic law of radioactive decay

radioactive decay is a statistical phenomenon: it is impossible to predict when a given unstable nucleus will decay, one can only make some probabilistic judgments about this event. For a large set of radioactive nuclei, one can obtain a statistical law expressing the dependence of undecayed nuclei on time.

Let the nuclei decay in a sufficiently small time interval. This number is proportional to the time interval, and also total number radioactive nuclei:

, (1)

where is the decay constant proportional to the decay probability of a radioactive nucleus and different for different radioactive substances. The "-" sign is placed because< 0, так как число не распавшихся радиоактивных ядер убывает со временем.

Separate the variables and integrate (1) taking into account that the lower limits of integration correspond to the initial conditions (at , where is the initial number of radioactive nuclei), and the upper limits correspond to the current values ​​and :

Potentiating expression (3), we have

That's what it is basic law of radioactive decay: the number of undecayed radioactive nuclei decreases with time according to an exponential law.

Figure 1 shows decay curves 1 and 2, corresponding to substances with different decay constants (λ 1 > λ 2), but with the same initial number of radioactive nuclei. Line 1 corresponds to the more active element.

In practice, instead of the decay constant, another characteristic of a radioactive isotope is often used - half life . This is the time it takes for half of the radioactive nuclei to decay. Naturally, this definition is valid for a sufficiently large number of nuclei. Figure 1 shows how curves 1 and 2 can be used to find the half-lives of nuclei: a straight line is drawn parallel to the abscissa axis through a point with ordinate , until it intersects with the curves. The abscissas of the points of intersection of the straight line and lines 1 and 2 give the half-lives T 1 and T 2.

As a result of all types of radioactive transformations, the number of nuclei of a given isotope gradually decreases. The decrease in the number of decaying nuclei occurs exponentially and is written in the following form:

N=N 0 e –  t , (10)

where N 0 - the number of radionuclide nuclei at the time of the beginning of the time reference (t=0 );  - decay constant, which is different for different radionuclides; N is the number of radionuclide nuclei after time t; e- the base of the natural logarithm (e = 2.713 ....). This is the basic law of radioactive decay.

Derivation of formula (10). The natural radioactive decay of nuclei proceeds spontaneously, without any external influence. This process is statistical, and for a single nucleus, one can only indicate the probability of decay in a certain time. Therefore, the decay rate can be characterized by time t. Let there be a number N atoms of the radionuclide. Then, the number of decaying atoms dN during dt proportional to the number of atoms N and time interval dt:

The minus sign indicates that the number N initial atoms decreases with time. It has been experimentally shown that the properties of nuclei do not change with time. It follows from this that l is a constant value and is called the decay constant. From (11) it follows that l= –dN/N=const, at dt= 1, i.e. the constant l is equal to the probability of decay of one radionuclide per unit time.

In equation (11), we divide the right and left parts by N and integrate:

dN/N = –ldt(12)

(13)

ln N/N 0 = – λt and N = N 0 e – λt , (14)

where N 0 is the initial number of decaying atoms (N 0 at t=0).

Formula (14) has two drawbacks. To determine the number of decaying nuclei, it is necessary to know N 0 . There is no device to determine it. The second disadvantage is that although the decay constant λ is available in the tables, but it does not carry direct information about the decay rate.

To get rid of the value λ the concept half-life T(sometimes referred to in the literature as T 1/2). The half-life is the period of time during which the initial number of radioactive nuclei is halved, and the number of decaying nuclei during the time T remains constant (λ=const).

In equation (10), we divide the right and left parts by N, and bring to mind:

N 0 /N=e  t (15)

Assuming that N 0 / N = 2, at t = T, we get ln2 =  T, where:

ln2 = 0,693  = 0,693/ T(16)

Substituting expression (16) into (10) we get:

N = N 0 e –0.693t/T (17)

The graph (Fig. 2.) shows the dependence of the number of decaying atoms on the decay time. Theoretically, the exponential curve can never merge with the x-axis, but in practice it can be considered that after about 10–20 half-lives, the radioactive substance decays completely.

In order to get rid of the values ​​of N and N 0, the following property of the phenomenon of radioactivity is used. There are devices that register every decay. Obviously, it is possible to determine the number of decays in a certain period of time. This is nothing but the decay rate of a radionuclide, which can be called activity: the more nuclei decay in the same time, the greater the activity.

So, activity is a physical quantity that characterizes the number of radioactive decays per unit time:

A =dN/ dt(18)

Based on the definition of activity, it follows that it characterizes the rate of nuclear transitions per unit time. On the other hand, the number of nuclear transitions depends on the decay constant l. It can be shown that:

A=A 0 e -0.693t/T (19)

Derivation of formula (19). The radionuclide activity characterizes the number of decays per unit time (per second) and is equal to the time derivative of equation (14):

BUT = d N/dt = lN 0 e –-  t = lN (20)

Accordingly, the initial activity at the time t = 0 is equal to:

BUT o = lN o (21)

Based on equation (20) and taking into account (21), we obtain:

A = A o e –  t or A = A 0 e – 0,693 t / T (22)

The unit of activity in the SI system is accepted 1 decay/s=1 Bq(named by Becquerel in honor of the French scientist (1852–1908), who discovered the natural radioactivity of uranium salts in 1896). Multiple units are also used: 1 GBq=10 9 Bq - gigabecquerel, 1 MBq=10 6 Bq - megabecquerel, 1 kBq=10 3 Bq - kilobecquerel, etc.

There is also an off-system unit curie, which is withdrawn from use in accordance with GOST 8.417-81 and RD 50-454-84. However, it is used in practice and in the literature. Per 1Ku the activity of 1 g of radium is accepted.

1Ku = 3.7 10 10 Bq; 1Bq = 2.7 10 –11 Key(23)

A multiple unit of megacurie is also used 1Mcu=110 6 Ci and submultiple - millicurie, 1mCi=10 -3 Ci; microcurie, 1 μCi=10 –6 Ci.

Radioactive substances can be in various states of aggregation, including aerosol, suspended state in a liquid or in air. Therefore, in dosimetric practice, the value of specific, surface or volumetric activity or the concentration of radioactive substances in air, liquid and soil is often used.

Specific, volumetric and surface activity can be written respectively as:

BUT m = A/m; BUT v = A/v; BUT s = A/s(24)

where: m is the mass of the substance; v is the volume of the substance; s is the surface area of ​​the substance.

It's obvious that:

BUT m = A/ m = A/ srh= A s / rh = A v / r(25)

where: r- soil density, taken in the Republic of Belarus equal to 1000 kg / m 3; h- root-inhabited soil layer, taken equal to 0.2 m; s is the area of ​​radioactive contamination, m 2 . Then:

BUT m = 5  10 –3 BUT s ; BUT m = 10 –3 A v (26)

BUT m may be expressed in Bq/kg or Ku/kg; A s can be expressed in Bq / m 2, Ku / m 2, Ku / km 2; A v can be expressed in Bq/m 3 or Ku/m 3 .

In practice, both enlarged and fractional units of measurement can be used. For example: Ku / km 2, Bq / cm 2, Bq / g, etc.

The NRB-2000 radiation safety standards additionally introduce several more activity units, which are convenient to use when solving radiation safety problems.

Minimum significant activity (MSA) - activity of an open source of ionizing radiation in a room or at a workplace, above which permission is required from the sanitary and epidemiological service of the Ministry of Health to use these sources, if the value of the minimum significant specific activity is also exceeded.

Minimum significant specific activity (MSUA) - specific activity of an open source of ionizing radiation in a room or at a workplace, above which permission is required from the sanitary and epidemiological service of the Ministry of Health to use this source, if the value of the minimum significant activity is also exceeded.

Equivalent equilibrium activity (EROA) progeny of radon isotopes 222 Rn and 220 Rn is the weighted sum of the volumetric activities of the short-lived daughter products of radon isotopes, 218 Ro (RaA); 214 Pb (RaB); 212 Pb (ThB); 212 ATi (ThC) respectively:

(EROA) Rn = 0.10 A RaA + 0.52 A RaB + 0.38 A RaC ;

(EROA) Th = 0,91 BUT ThB + 0.09 A ThC ,

where BUT are the volumetric activities of the daughter products of radon and thorium isotopes.