The basic law of radioactive decay is the half-life. Basic law of radioactive decay

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. speed indicator radioactive decay is an 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 the phenomenon in 1856 natural radioactivity uranium. 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 activity large quantities 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 in initial moment 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:

https://pandia.ru/text/80/150/images/image013_21.gif" width="89" height="39 src=">, (3.2.4)

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 the 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 a chemical compound, then when determining the activity of the drug, its formula must be taken into account. Taking into account the composition of the substance is determined mass fraction 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.

Decision:

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 activity of 90Sr a year ago, if in this moment time it is equal to 500 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 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 environment is formed mainly due to three main natural radionuclides: 40K, 238U, 232Th. share radioactive isotopes in the natural sum 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 Chernobyl disaster the formation of 241Am in the environment will be 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 Chernobyl zone alienation 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.

Necessary condition radioactive decay is that the mass of the original nucleus must exceed the sum of the masses of the decay products. Therefore, each radioactive decay occurs with the release of energy.

Radioactivity divided into natural and artificial. The first refers to radioactive nuclei that exist in natural conditions, the second - to the kernels obtained by nuclear reactions in laboratory conditions. Fundamentally, they do not differ from each other.

The main types of radioactivity include α-, β- and γ-decays. Before characterizing them in more detail, let us consider the law of the course of these processes in time common to all types of radioactivity.

Identical nuclei undergo decay at different times, which cannot be predicted in advance. Therefore, we can assume that the number of nuclei decaying in a short period of time dt, proportional to the number N available nuclei at that moment, and dt:

Integration of equation (3.4) gives:

Relation (3.5) is called the basic law of radioactive decay. As you can see, the number N of yet undecayed nuclei decreases exponentially with time.

The intensity of radioactive decay is characterized by the number of nuclei decaying per unit time. It can be seen from (3.4) that this quantity | dN / dt | = λN. It's called activity. A. Thus activity:

.

It is measured in becquerels (Bq), 1 Bq = 1 decay / s; and also in curie (Ci), 1 Ci = 3.7∙10 10 Bq.

Activity per unit mass of a radioactive preparation is called specific activity.

Let us return to formula (3.5). Along with constant λ and activity A the process of radioactive decay is characterized by two more quantities: the half-life T 1/2 and average life time τ kernels.

Half life T 1/2- the time for which the initial number of radioactive nuclei on average will decrease by two:

,

where

.

Average life time τ we define as follows. Number of cores δN(t) that experienced decay over a period of time ( t, t + dt), is determined right side expressions (3.4): δN(t) = λNdt. The lifetime of each of these nuclei is t. So the sum of the lifetimes of all N0 of the initially available nuclei is determined by integrating the expression tδN(t) in time from 0 to ∞. Dividing the sum of the lifetimes of all N0 cores per N0, we will find the average lifetime τ the kernel in question:

notice, that τ equals, as follows from (3.5), the time interval during which the initial number of nuclei decreases in e once.

Comparing (3.8) and (3.9.2), we see that the half-life T 1/2 and mean lifetime τ have the same order and are related by the relation:

.

Complex radioactive decay

Complex radioactive decay can occur in two cases:

physical meaning of these equations is that the number of nuclei 1 decreases due to their decay, and the number of nuclei 2 is replenished due to the decay of nuclei 1 and decreases due to its own decay. For example, at the initial time t= 0 available N01 cores 1 and N02 kernels 2. With such initial conditions, the solution of the system has the form:

If at the same time N02= 0, then

.

To evaluate the value N 2(t) can be used graphic method(see figure 3.2) plotting curves e−λt and (1 − e−λt). At the same time, in view of special properties functions e−λt it is very convenient to plot the ordinates of the curve for the values t corresponding T, 2T, … etc. (see table 3.1). Relationship (3.13.3) and Figure 3.2 show that the amount of radioactive daughter increases with time and t >> T2 (λ 2 t>> 1) approaches its limit value:

and is called the age-old, or secular balance. The physical meaning of the secular equation is obvious.

t	e−λt	1 − e − λt
0	1	0
1T	1/2 = 0.5	0.5
2T	(1/2) 2 = 0.25	0.75
3T	(1/2) 3 = 0.125	0.875
...	...	...
10T	(1/2) 10 ≈ 0.001	~0.999

Figure 3.3. Complex radioactive decay.

Since, according to equation (3.4), λN is equal to the number of decays per unit time, then the relation λ 1 N 1 = λ 2 N 2 means that the number of decays of the daughter substance λ 2 N 2 is equal to the number of decays of the parent substance, i.e. the number of nuclei of the daughter substance formed in this case λ 1 N 1. The secular equation is widely used to determine the half-lives of long-lived radioactive substances. This equation can be used when comparing two mutually converting substances, of which the second has a much shorter half-life than the first ( T2 << T1) provided that this comparison is made at time t >> T2 (T2 << t << T1). An example of the successive decay of two radioactive substances is the transformation of radium Ra into radon Rn. It is known that 88 Ra 226, emitting with a half-life T1 >> 1600 yearsα-particles, turns into radioactive gas radon (88 Rn 222), which is itself radioactive and emits α-particles with a half-life T2 ≈ 3.8 days. In this example just T1 >> T2, so for times t << T1 the solution of equations (3.12) can be written in the form (3.13.3).

For further simplification, it is necessary that the initial number of cores Rn be equal to zero ( N02= 0 at t= 0). This is achieved by a special setting of the experiment, in which the process of transformation of Ra into Rn is studied. In this experiment, the Ra preparation is placed in a glass flask with a tube connected to a pump. During the operation of the pump, the released gaseous Rn is immediately pumped out, and its concentration in the cone is zero. If at some point while the pump is running, the cone is isolated from the pump, then from that moment, which can be taken as t= 0, the number of nuclei Rn in the cone will begin to increase according to the law (3.13.3): N Ra and N Rn- accurate weighing, and λRn- by determining the half-life Rn, which has a value of 3.8, convenient for measurements days. So the fourth value λ Ra can be calculated. This calculation gives for the half-life of radium TRa ≈ 1600 years, which coincides with the results of the determination TRa by the method of absolute counting of emitted α-particles.

The radioactivity of Ra and Rn was chosen as a reference when comparing the activities of various radioactive substances. Per unit of radioactivity - 1 Key- accepted activity of 1 g of radium or an amount of radon that is in equilibrium with it. The latter can be easily found from the following reasoning.

It is known that 1 G radium undergoes ~3.7∙10 10 per second decays. Hence.

Laws of radioactive decay of nuclei

The ability of nuclei to spontaneously decay by emitting particles is called radioactivity. Radioactive decay is a statistical process. Each radioactive nucleus can decay at any moment, and the pattern is observed only on average, in the case of the decay of a sufficiently large number of nuclei.
decay constantλ is the probability of nuclear decay per unit time.
If there are N radioactive nuclei in the sample at time t, then the number of nuclei dN that decayed during time dt is proportional to N.

dN = -λNdt. (13.1)

Integrating (1) we obtain the law of radioactive decay

N(t) \u003d N 0 e -λt. (13.2)

N 0 is the number of radioactive nuclei at time t = 0.
Average life time τ –

. (13.3)

Half life T 1/2 - the time during which the initial number of radioactive nuclei will decrease by half

T 1/2 = ln2/λ=0.693/λ = τln2. (13.4)

Activity A - the average number of nuclei decaying per unit time

A(t) = λN(t). (13.5)

Activity is measured in curies (Ci) and becquerels (Bq)

1 Ci \u003d 3.7 * 10 10 decays / s, 1 Bq \u003d 1 decay / s.

The decay of the initial nucleus 1 into the nucleus 2, with its subsequent decay into the nucleus 3, is described by a system of differential equations

(13.6)

where N 1 (t) and N 2 (t) is the number of nuclei, and λ 1 and λ 2 are the decay constants of nuclei 1 and 2, respectively. Solution of system (6) with initial conditions N 1 (0) = N 10 ; N 2 (0) = 0 will be

, (13.7a)

. (13.7b)

Figure 13. 1

The number of cores 2 reaches its maximum value at .

If λ 2< λ 1 (), суммарная активностьN 1 (t)λ 1 + N 2 (t)λ 2 будет монотонно уменьшаться.
If λ 2 >λ 1 ()), the total activity initially grows due to the accumulation of nuclei 2.
If λ 2 >> λ 1 , with enough big times the contribution of the second exponent in (7b) becomes negligible, compared with the contribution of the first and the activities of the second A 2 = λ 2 N 2 and the first isotope A 1 = λ 1 N 1 are almost equal. In the future, the activities of both the first and second isotopes will change in time in the same way.

A 1 (t) = N 10 λ 1 = N 1 (t)λ 1 = A 2 (t) = N 2 (t)λ 2 .(13.8)

That is, the so-called secular balance, at which the number of isotope nuclei in the decay chain is related to the decay constants (half-lives) by a simple relation.

. (13.9)

Therefore, in natural state all isotopes genetically related in radioactive series are usually found in certain quantitative ratios depending on their half-lives.
AT general case, when there is a chain of decays 1→2→...n, the process is described by a system of differential equations

dN i /dt = -λ i N i +λ i-1 N i-1 .(13.10)

By solving system (10) for activities with initial conditions N 1 (0) = N 10 ; N i (0) = 0 will be

(13.12)

The prime means that in the product, which is in the denominator, the factor with i = m is omitted.

isotopes

ISOTOPS Varieties of the same chemical element that are similar in their physical chemical properties but with different atomic masses. The name "isotopes" was proposed in 1912 by the English radiochemist Frederick Soddy, who formed it from two Greek words: isos - the same and topos - place. Isotopes occupy the same place in the cell periodic system elements of Mendeleev.

An atom of any chemical element consists of a positively charged nucleus and a cloud of negatively charged electrons surrounding it ( cm.also ATOM NUCLEUS). The position of a chemical element in the periodic system of Mendeleev (its serial number) is determined by the nuclear charge of its atoms. Therefore, varieties of the same chemical element are called isotopamin, the atoms of which have the same nuclear charge (and, therefore, practically the same electron shells), but differ in the values ​​of the mass of the nucleus. According to the figurative expression of F. Soddy, the atoms of isotopes are the same "outside", but different "inside".

The neutron was discovered in 1932 – a particle that has no charge, with a mass close to the mass of the nucleus of a hydrogen atom - a proton , and created a proton-neutron model of the nucleus. As a result, science has established the final modern definition isotopes: isotopes are substances whose atomic nuclei consist of the same number protons and differ only in the number of neutrons in the nucleus . Each isotope is usually denoted by a set of symbols, where X is the symbol of a chemical element, Z is the charge of the atomic nucleus (the number of protons), A is mass number isotope (the total number of nucleons - protons and neutrons in the nucleus, A = Z + N). Since the charge of the nucleus is unambiguously associated with the symbol of the chemical element, often the notation A X is simply used for abbreviation.

Of all the isotopes known to us, only hydrogen isotopes have own names. Thus, the 2 H and 3 H isotopes are called deuterium and tritium and are designated D and T, respectively (the 1 H isotope is sometimes called protium).

They occur naturally as stable isotopes. , and unstable - radioactive, the nuclei of atoms of which are subject to spontaneous transformation into other nuclei with the emission of various particles (or the processes of the so-called radioactive decay). Now about 270 stable isotopes are known, and stable isotopes are found only in elements with atomic number Z Ј 83. The number of unstable isotopes exceeds 2000, the vast majority of them were obtained artificially as a result of various nuclear reactions. The number of radioactive isotopes in many elements is very large and can exceed two dozen. The number of stable isotopes is much less. Some chemical elements consist of only one stable isotope (beryllium, fluorine, sodium, aluminum, phosphorus, manganese, gold and a number of other elements). The largest number of stable isotopes - 10 - was found in tin, in iron, for example, there are 4 of them, and in mercury - 7.

Discovery of isotopes, historical background. In 1808, the English naturalist John Dalton first introduced the definition of a chemical element as a substance consisting of atoms of one kind. In 1869, the chemist D.I. Mendeleev was discovered periodic law chemical elements. One of the difficulties in substantiating the concept of an element as a substance that occupies a certain place in the cell of the periodic system was the experimentally observed non-integer atomic weights of elements. In 1866 English physicist and chemist - Sir William Crookes put forward the hypothesis that each natural chemical element is a mixture of substances that are identical in their properties, but have different atomic masses, but at that time such an assumption did not yet exist. experimental confirmation and so passed little noticed.

an important step on the way to the discovery of isotopes was the discovery of the phenomenon of radioactivity and the hypothesis of radioactive decay formulated by Ernst Rutherford and Frederick Soddy: radioactivity is nothing more than the decay of an atom into a charged particle and an atom of another element, which differs in its chemical properties from the original. As a result, the concept of radioactive series or radioactive families arose. , at the beginning of which there is the first parent element, which is radioactive, and at the end - the last stable element. An analysis of the chains of transformations showed that in their course, the same radioactive elements can appear in one cell of the periodic system, differing only atomic masses. In fact, this meant the introduction of the concept of isotopes.

Independent confirmation of the existence of stable isotopes of chemical elements was then obtained in the experiments of J. J. Thomson and Aston in 1912-1920 with beams of positively charged particles (or so-called canal rays ) emerging from the discharge tube.

In 1919, Aston designed an instrument called a mass spectrograph (or mass spectrometer) . The discharge tube was still used as the ion source, but Aston found a way in which the successive deflection of the particle beam in the electrical and magnetic fields led to the focusing of particles with the same charge-to-mass ratio (regardless of their speed) at the same point on the screen. Along with Aston, a mass spectrometer of a slightly different design was created in the same years by the American Dempster. As a result of the subsequent use and improvement of mass spectrometers by the efforts of many researchers, by 1935 almost complete table isotopic compositions of all chemical elements known by that time.

Isotope separation methods. To study the properties of isotopes, and especially to use them for scientific and applied purposes, it is necessary to obtain them in more or less noticeable quantities. In conventional mass spectrometers, almost complete separation of isotopes is achieved, but their number is negligible. Therefore, the efforts of scientists and engineers were directed to the search for other possible methods of isotope separation. First of all, they mastered physical and chemical methods separations based on differences in the properties of isotopes of the same element, such as evaporation rates, equilibrium constants, rates chemical reactions etc. The most effective among them were the methods of rectification and isotope exchange, which are widely used in the industrial production of isotopes of light elements: hydrogen, lithium, boron, carbon, oxygen and nitrogen.

Another group of methods is formed by the so-called molecular-kinetic methods: gaseous diffusion, thermal diffusion, mass diffusion (diffusion in a vapor flow), and centrifugation. Gas diffusion methods based on different speed diffusion of isotopic components in highly dispersed porous media, were used during the Second World War when organizing industrial production separation of uranium isotopes in the United States in the framework of the so-called Manhattan project to create atomic bomb. To receive required quantities uranium, enriched up to 90% with the light isotope 235 U, the main "combustible" component of the atomic bomb, plants were built that occupied an area of ​​about four thousand hectares. On creation atomic center more than 2 billion dollars were allocated with plants for the production of enriched uranium. After the war, plants for the production of enriched uranium for military purposes, also based on the diffusion separation method, were developed and built in the USSR. AT last years this method has given way to a more efficient and less costly centrifugation method. In this method, the effect of separation of the isotopic mixture is achieved by various action centrifugal forces on the components of the isotopic mixture that fills the centrifuge rotor, which is a thin-walled cylinder limited from above and below, rotating at a very high speed in a vacuum chamber. Hundreds of thousands of centrifuges connected in cascades, the rotor of each of which makes more than a thousand revolutions per second, are currently used in modern separation plants both in Russia and in other developed countries of the world. Centrifuges are used not only to produce the enriched uranium needed to power the nuclear reactors of nuclear power plants, but also to produce isotopes of about thirty chemical elements in the middle part of the Periodic Table. For separation various isotopes electromagnetic separation plants with powerful ion sources are also used, in recent years laser methods separation.

The use of isotopes. A variety of isotopes of chemical elements are widely used in scientific research, in various areas industry and agriculture, in nuclear power, modern biology and medicine, environmental studies and other fields. In scientific research (for example, in chemical analysis) usually requires small amounts of rare isotopes various elements, calculated in grams and even milligrams per year. At the same time, for a number of isotopes widely used in nuclear power engineering, medicine, and other industries, the need for their production can be many kilograms and even tons. So, in connection with the use of heavy water D 2 O in nuclear reactors its global production by the beginning of the 1990s of the last century was about 5000 tons per year. The hydrogen isotope deuterium, which is part of heavy water, the concentration of which in the natural mixture of hydrogen is only 0.015%, along with tritium, will in the future, according to scientists, become the main component of the fuel of power thermonuclear reactors operating on the basis of reactions nuclear fusion. In this case, the need for the production of hydrogen isotopes will be enormous.

In scientific research, stable and radioactive isotopes are widely used as isotope indicators (labels) in the study of the most various processes occurring in nature.

AT agriculture isotopes ("labeled" atoms) are used, for example, to study the processes of photosynthesis, the digestibility of fertilizers, and to determine the efficiency of the use of nitrogen, phosphorus, potassium, trace elements, and other substances by plants.

Isotope technologies are widely used in medicine. So in the USA, according to statistics, more than 36 thousand medical procedures are performed per day and about 100 million laboratory tests using isotopes. The most common procedures associated with computed tomography. The carbon isotope C 13 enriched up to 99% (natural content about 1%) is actively used in the so-called "diagnostic control of breathing". The essence of the test is very simple. The enriched isotope is introduced into the patient's food and, after participating in the metabolic process in various organs of the body, is excreted as exhaled by the patient. carbon dioxide CO 2 that is collected and analyzed with a spectrometer. The difference in the rates of processes associated with the release of various amounts of carbon dioxide labeled with the isotope C 13 makes it possible to judge the state of various organs of the patient. In the US, the number of patients who will undergo this test is estimated at 5 million people a year. Now, for the production of a highly enriched C 13 isotope in industrial scale laser separation methods are used.

Similar information.

The radioactive decay of atomic nuclei occurs spontaneously and leads to a continuous decrease in the number of atoms of the original radioactive isotope and the accumulation of atoms of the decay product.

The rate at which radionuclides decay is determined only by the degree of instability of their nuclei and is independent of any of the factors that normally affect the rate of physical and chemical processes(pressure, temperature, chemical form substances, etc.). The decay of each individual atom is a completely random event, probabilistic and independent of the behavior of other nuclei. However, if the system has enough a large number radioactive atoms manifest general pattern, consisting in the fact that the number of atoms of a given radioactive isotope decaying per unit time always constitutes a certain fraction characteristic of a given isotope of full number not yet decayed atoms. The number of DUU atoms that have undergone decay in a short time interval D/ is proportional to total number of undecayed radioactive atoms UU and the value of the DL interval. This law can be mathematically represented as a ratio:

-AN=X? N? D/.

The minus sign indicates that the number of radioactive atoms N decreases. Proportionality factor X is called decay constant and is a constant characteristic of a given radioactive isotope. The law of radioactive decay is usually written as differential equation:

So, radioactive decay law can be formulated as follows: per unit of time, the same part of the available nuclei of a radioactive substance always decays.

Decay constant X has the dimension of inverse time (1/s or s -1). The more x, the faster the decay of radioactive atoms, i.e. X characterizes the relative decay rate for each radioactive isotope or the probability of decay atomic nucleus in 1 s. The decay constant is the fraction of atoms decaying per unit time, an indicator of the instability of a radionuclide.

Size-- absolute speed radioactive decay -

called activity. Radionuclide activity (A) - is the number of decays of atoms that occur per unit of time. It depends on the number of radioactive atoms in this moment time (AND) and on the degree of their instability:

A=Y ( x.

The SI unit of activity is becquerel(Bq); 1 Bq is the activity at which one nuclear transformation per second occurs, regardless of the type of decay. Sometimes an off-system activity measurement unit is used - curie (Ci): 1Ci = = 3.7-10 10 Bq (the number of decays of atoms in 1 g 226 Rya per 1 s).

Since the activity depends on the number of radioactive atoms, this value serves quantitative measure content of radionuclides in the studied sample.

In practice, it is more convenient to use the integral form of the law of radioactive decay, which has the following form:

where WU 0 - the number of radioactive atoms at the initial moment of time / = 0; is the number of radioactive atoms remaining by the time

time /; X- decay constant.

To characterize radioactive decay, often instead of the decay constant X use another quantity, the derivative of it - the half-life. Half-life (T]/2) is the time it takes for half of the initial quantity radioactive atoms.

Substituting into the law of radioactive decay the values ​​Г = T 1/2 and AND (= Aph/2, we get:

CU 0 /2 = # 0 e~ xt og-

1 /2 = e~ xt "/2 -, a e xt "/ 2 = 2 or XT 1/2 = 1p2.

The half-life and decay constant are related by the following relationship:

T x/2\u003d 1n2 A \u003d 0.693 /X.

Using this dependence, the law of radioactive decay can be represented in another form:

TU, = UU 0 e Apg, "t t

N = AND 0 ? e-°’ t - ( / t 02.

From this formula it follows that the longer the half-life, the slower the radioactive decay occurs. The half-lives characterize the degree of stability of the radioactive nucleus and vary widely for different isotopes - from fractions of a second to billions of years (see appendices). Depending on the half-life, radionuclides are conditionally divided into long lived and short lived.

The half-life, along with the type of decay and the energy of the radiation, is the most important characteristic any radionuclide.

On fig. 3.12 shows the decay curve of a radioactive isotope. Time is plotted along the horizontal axis (in half-lives), and vertical axis- the number of radioactive atoms (or activity, since it is proportional to the number of radioactive atoms).

Curve is exhibitor and asymptotically approaches the time axis, never crossing it. After a period of time equal to one half-life (Г 1/2), the number of radioactive atoms decreases by 2 times, after two half-lives (2Г 1/2), the number of remaining atoms again decreases by half, i.e. 4 times from their initial number, after 3 7 "1/2 - 8 times, through

4G 1/2 - 16 times, through t half-lives G]/2 - in 2 t once.

Theoretically, the set of atoms with unstable nuclei will decrease to infinity. However, from a practical point of view, a certain limit should be designated, when conditionally all radioactive nuclides have decayed. It is believed that this requires a time interval of 107^ 2 , after which less than 0.1% of radioactive atoms will remain from the initial amount. Thus, if only physical decay is taken into account, it will take 290 and 300 years, respectively, to completely cleanse the biosphere of 90 Bg (= 29 years) and |37 Cs (T|/ 2 = 30 years) of Chernobyl origin.

radioactive balance. If during the decay of a radioactive isotope (parent) a new radioactive isotope (daughter) is formed, then they are said to be genetically related to each other and form radioactive family(row).

Let us consider the case of genetically related radionuclides, of which the parent is long-lived, and the daughter is short-lived. An example is strontium 90 5g, which is converted by (3-decay ( T /2 = 64 h) and turns into a stable zirconium nuclide ^bx(See Figure 3.7). Since 90 U decays much faster than 90 5g, then after a while the moment will come when the amount of decaying 90 8g at any moment will be equal to the amount of decaying 90 U. In other words, the activity of the parent 90 8g (D,) will be equal to the activity of the child 90 U (L 2). When this happens, 90 U is considered to be in secular balance with its parent radionuclide 90 8g. In this case, the following relation holds:

A 1 \u003d L 2 or X 1? = X 2? UU 2 or: G 1/2 (1) \u003d UU 2: G 1/2 (2) .

From the above relationship it follows that the greater the probability of decay of the radionuclide (to) and, consequently, a shorter half-life (T ]/2), the less its atoms are contained in a mixture of two isotopes (AO-

To establish such an equilibrium requires a time equal to approximately 7T ]/2 daughter radionuclide. Under conditions of secular equilibrium, the total activity of the mixture of nuclides is twice the activity of the parent nuclide at a given time. For example, if at the initial moment of time the preparation contains only 90 8 g, then after 7T /2 the longest-lived member of the family (except for the ancestor of the series), secular equilibrium is established, and the decay rates of all members of the radioactive family become the same. Given that the half-lives for each member of the family are different, the relative amounts (including mass) of nuclides in equilibrium are also different. The less T )