"The woman is created for a man, not a man for a woman" - such a postulate ...
Lecture 2. The basic law of radioactive decay and the activity of radionuclides
The rate of decay of radionuclides is different - some disintegrate faster, others are slower. Speed \u200b\u200bindicator radioactive decay is an constant radioactive decay, λ [sec-1], which characterizes the likelihood of the decay of one atom in one second. For each radionuclide, the constant decay has its value than it is more, the faster the substance nucleus is disintegrated.
The number of decays recorded in the radioactive sample per unit of time is called activity (a. ), or sample radioactivity. The value of activity is directly proportional to the number of atoms N. Radioactive substance:
a. =λ· N. , (3.2.1)
where λ - constant radioactive decay, [s-1].
Currently, according to the current international system of UN units, the unit of measurement of radioactivity is accepted beckel [BK]. This unit received its name in honor of the French scientist Henri Becquer, who opened in 1856 the phenomenon of the natural radioactivity of uranium. One Becquer is equal to one decay per second 1 BK = 1 .
However, the incidental activity unit is often used quite often. – curie [Ki.] introduced by Curie's spouses as a measure of the decay speed of one radium gram (in which ~ 3.7 · 1010 decays per second), so
1 Ki. \u003d 3.7 · 1010 BK.
This unit is convenient for evaluating activity. large quantities radionuclides.
Reducing the concentration of radionuclide in time as a result of the decay obeys exponential dependence:
, (3.2.2)
where N. t. - the number of atoms of the radioactive element of the remaining time t. after the start of observation; N. 0 - the number of atoms at the initial moment of time ( t. =0 ); λ - Permanent radioactive decay.
The dependence described is called the main law of radioactive decay .
The time for which half of the total number of radionuclides disintegrates is called half-life, T.½ . After one period of the half-life of 100 radionuclide atoms, only 50 remain (Fig. 2.1). For the next same period of these 50 atoms, only 25 and so on.
The relationship between the half-life and the disintegration period is derived from the equation of the basic law of radioactive decay:
for t.=T.½ and
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Therefore, the law of radioactive decay can be written as follows:
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where aT. - the activity of the drug through time t. ; a.0 - The activity of the drug at the initial moment of observation.
It is often necessary to determine the activity of a given number of any radioactive substance.
Recall that the number of substance is mole. Mol is the amount of substance containing as many atoms as they are contained in 0.012 kg \u003d 12 g of carbon isotope 12c.
In one mall of any substance contains the number of Avogadro Na. Atoms:
Na. \u003d 6.02 · 1023 atoms.
For simple substances (elements), the mass of one pray is numerically corresponded to the atomic mass. BUT Element
1mol = BUT G.
For example: for magnesium: 1 mol 24mg \u003d 24 g
For 226RA: 1 mol 226RA \u003d 226 g, etc.
Taking into account what was said in m. grams of substance will be N. Atoms:
https://pandia.ru/text/80/150/images/image015_20.gif "width \u003d" 156 "height \u003d" 43 src \u003d "\u003e (3.2.6)
Example: we calculate the activity of the 1st gram of 226RA, which λ \u003d 1.38 · 10-11 s-1.
a. \u003d 1.38 · 10-11 · 1/226 · 6.02 · 1023 \u003d 3.66 · 1010 BC.
If the radioactive element is part of chemical compound, in determining the activity of the drug, it is necessary to take into account its formula. Taking into account the composition of the substance determines the mass fraction χ Radionuclide in a substance that is determined by the relation:
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An example of solving the problem
Condition:
Activity A0. radioactive element 32r per day of observation is 1000 BK. Determine the activity and number of atoms of this element in a week. Half life T.½ 32P \u003d 14.3 days.
Decision:
a) We will find the activity of phosphorus-32 after 7 days:
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Answer: After a week, the activity of the drug 32r will be 712 BK,and the number of atoms of radioactive isotope 32r - 127.14 · 106 atoms.
Control questions
1) What is the activity of radionuclide?
2) Name the units of radioactivity and the relationship between them.
3) What is a constant radioactive decay?
4) Give the definition of the basic law of radioactive decay.
5) What is the half-life?
6) What is the connection between the activity and mass of the radionuclide? Write a formula.
Tasks
1. Calculate Activity 1 g. 226RA. T½ \u003d 1602 years.
2. Calculate Activity 1 g. 60Co. T½ \u003d 5.3 years.
3. One tank shell M-47 contains 4.3 kg 238U. ½ \u003d 2.5 · 109 years. Determine the activity of the projectile.
4. Calculate the activity of 137cs after 10 years, if it is 1000 in the initial moment of observation BK. T½ \u003d 30 years.
5. Calculate the 90SR a year ago, if at the moment it is equal to 500 BK. T½ \u003d 29 years.
6. What activity will create 1 kg radioisotope 131i, t½ \u003d 8.1 days?
7. Using reference data, determine activity 1 g. 238U. ½ \u003d 2.5 · 109 years.
Using reference data, determine activity 1 g. 232th, ½ \u003d 1.4 · 1010 years.
8. Calculate the activity of the compound: 239PU316O8.
9. Calculate the mass of radionuclide activity in 1 Ki.:
9.1. 131i, T1 / 2 \u003d 8.1 days;
9.2. 90SR, T1 / 2 \u003d 29 years;
9.3. 137cs, T1 / 2 \u003d 30 years;
9.4. 239PU, T1 / 2 \u003d 2.4 · 104 years.
10. Determine the mass 1 mc. Radioactive carbon isotope 14c, t 1 \u003d 5560 years.
11. It is necessary to prepare the radioactive drug of phosphorus 32p. After what period of time will remain 3% of the drug? T½ \u003d 14,29 days.
12. In the natural mixture of potassium contains 0.012% of the radioactive isotope 40K.
1) determine the mass of natural potassium, which contains 1 Ki. 40K. ½ \u003d 1.39 · 109 years \u003d 4.4 · 1018 sec.
2) Calculate the radioactivity of the soil in 40K, if it is known that the potassium content in the soil sample - 14 kg / t.
13. How many periods of the half-life are required to ensure that the initial activity of radioisotope decreased to 0.001%?
14. To determine the effect of 238U on plants, the seeds were soaked at 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. ½ \u003d 4,5 · 109 years.
15. Determine activity 1 gramma 232th, ½ \u003d 1.4 · 1010 years.
16. Determine the mass 1 Ki. 137Cs, T1 / 2 \u003d 30 years.
17. The ratio between the content of stable and radioactive isotopes of potassium in nature is a permanent value. Content 40K is 0.01%. Calculate the radioactivity of the soil in 40K, if it is known that the potassium content in the soil sample - 14 kg / t.
18. The lithogenic radioactivity of the environment is formed mainly due to the three main natural radionuclides: 40K, 238U, 232th. The share of 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 sample of soil 13600 g / t, uranium - 1 · 10-4 g / t, thorium - 6 · 10-4 g / t.
19. In the shells of bivalve mollusks discovered 23200 BK / kg 90sr. Determine the activity of the samples in 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 NPP. In bottom sediments of Oz. Azbucin in 1999 discovered 137cs with a specific activity of 1.1 · 10 BK / M2. Determine the concentration (activity) of the 137CS on M2 of bottom sediments as of 1986-1987. (12 years ago).
21. 241am (T½ \u003d 4.32 · 102 years) is formed from 241PU (T½ \u003d 14.4 years) and is an active geochemical migrant. Using reference materials, calculate up to 1% reduction in the activity of Plutonium-241 in time, in which year after Chernobyl catastrophe Education 241am B. environment It will be maximum.
22. Calculate the activity of 241am in the emissions of the Chernobyl reactor emissions as of April
2015, provided that in April 1986, the activity of 241am was 3.82 · 1012 BK,½ \u003d 4.32 · 102 years.
23. In the samples of the soil discovered 390 nki / kg 137cs. Calculate the activity of the samples after 10, 30, 50, 100 years.
24. The average pollution concentration of the Lake Lis. Deep, located in Chernobyl zone Alienation is 6.3 · 104 BK 241am and 7.4 · 104 238 + 239 + 240pu per 1 m2. Calculate what year this data is obtained.
As a result of all types of radioactive transformations, the number of nuclei of this isotope gradually decreases. The number of disintegrating nuclei is occurring at the exhibitor and is written in the following form:
N \u003d N. 0 e. – t. , (10)
where N. 0 - the number of radionuclide nuclei at the time of the start of time (t \u003d 0 ); - constant decay, which for various radionuclides is different; N.- Number of radionuclide nuclei after time t.; E.- The foundation natural logarithm (E \u003d 2,713 ....). This is the main law of radioactive decay.
The output of formula (10).Natural radioactive decay of the nuclei proceeds spontaneously, without any exposure from the outside. This process is statistical, and for a separate kernel, you can only specify the likelihood of decay for a certain time. Therefore, the rate of decay can be characterized by time. Let there be a number N.radionuclide atoms. Then the number of disintegrating atoms dN.during dt.in proportion to the number of atoms N.and time interval dT:
Minus sign shows that the number N.the initial atoms decrease in time. It is experimentally shown that the properties of the nuclei do not change over time. From here it follows that the value is permanent and is called - constant decay. From (11) it follows, so that L \u003d -DN / N \u003d const, PRT \u003d 1, i.e. Permanent volatility of the breakdown of one radionuclide per unit of time.
In equation (11), we divide the right and left parts on N.and integrate:
dN / N \u003d -l.dt.(12)
(13)
ln n / n 0 \u003d - λt and n \u003d n 0 e - λt, (14)
where N. 0 There is an initial number of disintegrating atoms (N 0 etc. 0).
Formula (14) has two drawbacks. To determine the number of disintegrating nuclei, it is necessary to know N 0. The device does not exist for its definition. The second drawback is although constant decay λ it is available in tables, but direct information about the rate of decay is not caring.
To get rid of the magnitude λ the concept is introduced half-life T.(Sometimes in the literature is denoted by 1/2). The half-life is called a period of time during which the initial number of radioactive nuclei is halucing, and the number of disintegrating cores during the time T.it remains constant (λ \u003d const).
In equation (10), the right and left part divide N., and we give the mind:
N. 0 / N \u003de. t. (15)
Believing that N. 0 / N. = 2, for t. = T., receive lN.2 = T.Location:
lN.2 = 0,693 = 0,693/ T.(16)
Substitting the expression (16) in (10) we get:
N \u003d N. 0 e. -0.693T / T. (17)
On the chart (Fig. 2) shows the dependence of the number of disintegrating atoms from the time of decay. Theoretically, the exponent's curve can never merge with the abscissa axis, but in practice it can be assumed that in about 10-20 periods of the half-life, the radioactive substance falls completely.
In order to get rid of NN 0 values, use the following property of radioactivity. There are devices that register each decay. Obviously, you can determine the amount of decays for a certain period of time. This is nothing more than the rate of decay of the radionuclide, which can be called activity: the more the nuclei breaks over the same time, the greater the activity.
So, activity- This is a physical quantity characterizing the number of radioactive decays per unit of time:
A \u003d.dN./ dt.(18)
Based on the definition of activity, it follows that it characterizes the speed of nuclear transitions per unit of time. On the other hand, the number of nuclear transitions depends on the constant decay l.. You can show that:
A \u003d A. 0 e. -0.693T / T. (19)
The conclusion of formula (19).The activity of the radionuclide characterizes the number of decays per unit of time (per second) and is equal to the time derivative from equation (14):
BUT = d. N /dt. = l.N. 0 e. –- t. = l.N. (20)
Accordingly, the initial activity at the time of time t \u003d 0.equal to:
BUT o. = l.N. o. (21)
Based on equation (20) and taking into account (21), we obtain:
A \u003d A. o. e. – t. or A \u003d A. 0 e. – 0,693 t. / T. (22)
The unit of activity in the SI system is accepted 1 decay / s \u003d 1 BK(Named Becquerem in honor of the French scientist (1852-1908), which opened the natural radioactivity of uranium salts in 1896). Multiple units are also used: 1 GBK \u003d 10 9 BC - Gigabekkel, 1 MBC \u003d 10 6 BK - Megabecakel, 1 CBC \u003d 10 3 BK - kilobekkel, etc.
There is a generated unit Curiewhich is removed from consumption according to GOST 8.417-81 and RD 50-454-84. However, in practice and in the literature it is used. Per 1ku.activities 1G radium adopted.
1ku \u003d 3.7 10 10 BK; 1bk \u003d 2.7 10 –11 Ki.(23)
Also use a multiple unit of megajuri 1mki \u003d 110 6 ki and dollane - milliquui, 1mki \u003d 10-3 ki; Microcures, 1MKKi \u003d 10 -6 ki.
Radioactive substances may be in different aggregate state, including aerosol, weighted state in liquid or in air. Therefore, in dosimetric practice, the amount of specific, surface or volumetric activity or the concentration of radioactive substances in the air, liquid and in the soil is often used.
Specific, volumetric and surface activity can be written accordingly in the form:
BUT m. \u003d A / m; BUT v. \u003d A / v; BUT s. \u003d A / S(24)
where: m.- mass of substance; v.- volume of substance; s.- Surface area of \u200b\u200bsubstance.
It's obvious that:
BUT m. = A./ m. = A./ s.r.h. \u003d A. s. / r.h. = A. v. / r.(25)
where: r.- the density of the soil is adopted in the Republic of Belarus equal to 1000kg / m 3; h.- the root of the soil is taken equal to 0.2 m; s.- Radioactive infection area, m 2. Then:
BUT m. = 5 10 –3 BUT s. ; BUT m. = 10 –3 A. v. (26)
BUT m. can be expressed in BC / kg or ku / kg; A. s. It can be expressed in BK / m 2, ku / m 2, ku / km 2; A. v. It 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, BK / cm 2, BK / g, etc.
In NRB-2000 radiation safety standards, several more activity units are additionally introduced, which are convenient to use when solving radiation safety tasks.
The activity is minimally significant (MZA) - Open source activity ionizing radiation In the room or in the workplace, with an exceeding the permission of the authorities of the Sanitary and Epidemiological Service of the Ministry of Health on the use of these sources, if the value is also exceeded the minimum meaning specific activity.
Activity is minimally significant specific (MEZU) - The specific activity of an open source of ionizing radiation indoors or in the workplace, with an exceeding the permission of the authorities of the sanitary and epidemiological service of the Ministry of Health to use this source, if the value is also exceeded the value of minimally significant activity.
Equivalent Equilibrium Activity (Eroa) daughters of Radon Isotopes 222 RN.and 220 RN.- Weighted amount of volumetric activity of short-lived subsidiaries of radon isotopes - 218 RO (RAA.); 214 PB. (Rab); 212 PB. (THB); 212 INi. (THC) respectively:
(Eroa) RN. \u003d 0.10 A. RAA. + 0.52 A. Rab + 0.38 A. Rac ;
(Eroa) TH. = 0,91 BUT THB + 0.09 A. THC ,
where BUT - Volumetric activity of subsidiaries of radon and thorium isotopes.
The concept of radioactivity
Law of radioactive decay
Quantitative assessment of radioactivity and its units
Ionizing radiation, their characteristics.
Sources of II
The concept of radioactivity
Radioactivity is a spontaneous process of conversion (decay) of atomic nuclei, accompanied by the emission of a special type of radiation, called radioactive.
In this case, the conversion of atoms of some elements into the atoms of others.
Radioactive transformations are characteristic of only individual substances.
The substance is considered radioactive if it contains radionuclides, and the process of radioactive decay is underway.
Radionuclides (isotopes) - the kernels of atoms capable spontaneously disintegrate are called radionuclides.
A symbol of the chemical element is used as a characteristic of the nuclide, indicate the atomic number (proton number) and the mass number of the nucleus (the number of nucleons, i.e. total number protons and neutrons).
For example, 239 94 Pu means that the core of the plutonium atom contains 94 proton and 145 neutrons, only 239 nucleons.
There are the following types of radioactive decay:
Beta decay;
Alpha decay;
Spontaneous division of atomic nuclei (neutron decay);
Proton radioactivity (proton synthesis);
Two tube and cluster radioactivity.
Beta decay - This is the process of transformation into the nucleus of the proton atom into the neutron or neutron into the proton with the emission of beta particles (positron or electron)
Alpha decay - It is characteristic of heavy elements whose kernels, starting from the number 82 tables D.I. Imeleeev, are unstable, despite the excess neutrons and spontaneously disintegrate. The kernels of these elements advantageously discard the kernels of helium atoms.
Spontaneous division of atomic nuclei (neutron decay) - This is a spontaneous division of some chief element cores (URAN-238, California 240.248, 249, 250, Curiy 244, 248, etc.). The probability of spontaneous division of nuclei is insignificant compared to alpha decay. At the same time, the core is divided into two fragments (kernels), close by weight.
Law of radioactive decay
The stability of the nuclei is reduced 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 are subject to the law of radioactive decay:
N \u003d n 0 E λ t,
where n, n 0 is the number of atoms that have not worked at the moments of time T and T 0;
λ is a constant radioactive decay.
The value of λ has its own individual value For each type of radionuclide. It characterizes the rate of decay, i.e. Shows how many nuclei decays per unit time.
According to the equation of the law of radioactive decay, its curve is an exponent.
Quantitative assessment of radioactivity and its units
The time during which, as a result of spontaneous nuclear transformations, half nuclei decays, called half-life T. 1/2 . The half-life T 1/2 is associated with a constant decay λ dependence:
T 1/2 \u003d ln2 / λ \u003d 0.693 / λ.
The half-life of T 1/2 in different radionuclides is different and varies widely - from the fraction of a second to hundreds and even thousands of years.
Periods of a half-life of some radionuclides:
Iodine-131 - 8,04 days
Ceziy-134 - 2.06 years
Strontium-90 - 29,12 years
Cesium-137 - 30 years
Plutonium-239 - 24065 years
Uranium-235 - 7,038. 10 8 years old
Potassium-40 - 1.4 10 9 years.
The quantity, reverse constant decay, called Average life of the radioactive atom t. :
The accpair of decay is determined by the activity of the substance A:
A \u003d dn / dt \u003d a 0 e λ t \u003d λ n,
where a and a 0 is the activity of the substance at the moments of time T and T 0.
Activity - Measure of radioactivity. It is characterized by the number of decays of radioactive nuclei per unit of time.
The activity of radionuclide is directly proportional to the total number of radioactive atomic nuclei at the time T and inversely proportional to the half-life:
A \u003d 0.693 N / T 1/2.
In the system system, Becquil (BC) is adopted. One Becquer is equal to one decay per second. Introduced Activity Unit - Curie (CU).
1 ku \u003d 3.7 10 10 bk
1bk \u003d 2.7 10 -11 ku.
Curie activity unit corresponds to the activity of 1 g of radium. In the practice of measurements, the concepts of volume A V (BK / M 3, KU / M 3) are also used, surface A S (BK / M 2, KU / M 2), specific A M (BK / M, KU / M) of activity.
§ 15th. Law of radioactive decay
The appearance of "manual" scintillation counters And mainly, Geiger Muller Counters, which helped automate particle counts (see § 15th), led physicists to an important conclusion. Any radioactive isotope is characterized by spontaneous weakening of radioactivity, expressing in reducing the number of disintegrating nuclei per unit of time.
Construction of graphs of activity of various radioactive isotopes led scientists to the same dependence expressed indicative function (See schedule). According to the horizontal axis, the observation time is postponed, and on the vertical - the number of unspoken nuclei. The curvature of the lines could be different, but the function itself, which was expressed by the dependence described by charts, remained the same:
This formula expresses the law of radioactive decay: The number of unprecedented nuclei is defined as the work of the initial number of nuclei by 2 to the degree equal to the ratio of the observation time by the half-life taken with a negative sign.
As it turned out in the course of the experiments, various radioactive substances can be described in various half-life - time, for which the number of unprecedented nuclei decreases twice (See Table).
Periods of half ward some isotopes of some chemical elements. The values \u200b\u200bfor both natural and artificial isotopes are given.
| Iodine-129. | 15 million years | Carbon-14. | 5.7 thousand years | |
| Iodine-131. | 8 days | Uranus-235 | 0.7 billion years | |
| Iodine-135 | 7 o'clock | Uranus-238. | 4.5 billion years old |
The half-life is a generally accepted physical value that characterizes the speed of radioactive decay. Numerous experiments show that Even with a very long observation of the radioactive substance, its half-life is constant, that is, it does not depend on the number of already broken atoms. Therefore, the law of radioactive decay found an application in the method of determining the age of archaeological and geological finds.
The method of radiocarbon analysis. Carbon - very common on earth chemical element, which includes stable carbon-12 isotopes, carbon-13 and carbon-14 radioactive isotope, whose half-life is 5.7 thousand years old (see table). Living organisms, consuming food, accumulate all three isotop in their fabrics. After the body's cessation of the body is stopped, carbon compensation stops, and over time, its content decreases naturally, due to radioactive decay. Since only carbon-14 decomposes, over the centuries and millennia, the ratio of carbon isotopes in fossil remains of living organisms changes. Measuring this "carbon proportion", one can judge the age of archaeological find.
The method of radiocarbon analysis is also applicable for geological breeds, as well as for fossil objects of human resources, but provided that the ratio of isotopes in the sample was not violated during its existence, for example, by fire or action of a strong radiation source. Injecting such reasons immediately after the opening of this method, it led to errors for several centuries and millennia. Today, "age-old calibration scales" are used for carbon isotop-14, based on its distribution in long-lived trees (for example, in the American millennial sequoy). Their age can be calculated quite accurately - on the annual rings of wood.
The limit for the application of the radio-carbon analysis method in early XXI century amounted to 60,000 years. To measure the age of more ancient samples, for example mountain breeds or meteorites, use a similar method, but instead of carbon, uranium isotopes or other elements are observed depending on the origin of the sample under study.
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\u003e\u003e The law of radioactive decay. Half life
§ 101 The law of radioactive decay. HALF LIFE
Radioactive decay is subject to statistical law. Rutherford, exploring the transformation of radioactive substances, has established an experimental way that their activity decreases over time. This was stated in the previous paragraph. So, radon's activity decreases 2 times after 1 min. The activity of such elements such as uranium, thorium and radium, also decreases with time, but much slower. For each radioactive substance there is a certain time interval, during which activity decreases by 2 times. This interval is called the half-life. The half-life T is the time during which half of the initial number of radioactive atoms decomposes.
Estimation, i.e., the number of decays per second, depending on the time for one of the radioactive drugs, is shown in Figure 13.8. The half-life of this substance is 5 days.
Now we will bring out the mathematical form of the law of radioactive decay. Let the number of radioactive atoms in the initial moment of time (T \u003d 0) equal to n 0. Then after the half-life period, this number will be equal
After another same time interval, this number will be equal to:
