Physics
Random Nature of Radioactive Decay
The random nature of radioactive decay refers to the inherent unpredictability of when a radioactive atom will decay. This process is not influenced by external factors and occurs spontaneously. While the probability of decay can be calculated, the exact timing of decay for a single atom cannot be determined, making it a random process.
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eBook - PDFIsotopes in Nanoparticles
Fundamentals and Applications
- Jordi Llop, Vanessa Gomez-Vallejo, Jordi Llop, Vanessa Gomez-Vallejo(Authors)
- 2016(Publication Date)
- Jenny Stanford Publishing(Publisher)
In the latter state, the nucleus has an excess of internal energy and tends to move to a more stable state. The process by which the atomic nucleus moves from an unstable to a more stable state is called radioactive decay. Radioactive decay is spontaneous and is accompanied by the emission of particles and/or electromagnetic radiation. The unstable nucleus is called a radioactive atom or radionuclide. 145 During radioactive decay, the unstable atoms can become a different element via a process known as transmutation. This is the case in radioactive processes that result in the emission of alpha particles ( a , or 4 He 2+ ), electrons ( b – ), or positrons ( b + ). As an example, fluorine-18 ( 18 F) has nine protons and nine neutrons in its nucleus and is a positron emitter; on spontaneous decay a positron is emitted and, consequently, one of the protons becomes a neutron. The newly formed element, which has eight protons and ten neutrons, is oxygen-18 ( 18 O). Radioactive decay can also occur via electron capture (when a nucleus captures an orbiting electron, thereby converting a proton into a neutron with consequent transmutation), by emission of gamma ( g ) rays, by emission of a neutron, or by ejection of an orbital electron due to interaction with an excited nucleus in a process called “internal transition”. In the latter three decay modalities, the atoms before and after radioactive decay correspond to the same element because the number of protons remains unchanged and transmutation does not occur. Radioactive atoms exist in nature (and indeed are continuously produced naturally) and can be found in air, water, soil, or even living organisms. They can also be produced artificially using different technologies. Over 1500 radionuclides, both natural and artificial, have been identified. 6.2.2 Radioactive Decay Equations Radioactive decay is a stochastic process in which, according to quantum theory, it is impossible to predict when a specific atom will decay.
eBook - PDFRadiochemistry and Nuclear Chemistry
2nd Edition of Nuclear Chemistry, Theory and Applications
- Gregory Choppin, Jan-Olov Liljenzin, Jan Rydberg, JAN RYDBERG(Authors)
- 2016(Publication Date)
- Butterworth-Heinemann(Publisher)
CHAPTER 4 Unstable Nuclei and Radioactive Decay Contents 4.1. Radioactive decay 58 4.2. Conservation laws 60 4.3. Alpha decay 61 4.3.1. Detection 61 4.3.2. Decay energy 61 4.4. Beta decay 63 4.4.1. Detection 63 4.4.2. The ß-decay process 63 4.4.3. The neutrino 64 4.4.4. Double beta decay 67 4.4.5. 0--decay 67 4.4.6. Positron decay 68 4.4.7. Electron capture 68 4.4.8. Daughter recoil 69 4.5. Gamma emission and internal conversion 70 4.6. Spontaneous fission 72 4.7. Rare modes of decay 74 4.8. Decay schemes and isotope charts 74 4.9. Secondary processes in the atom 76 4.10. Closed decay energy cycles 78 4.11. Kinetics of simple radioactive decay 79 4.12. Mixed decay 82 4.13. Radioactive decay units 83 4.14. Branching decay 84 4.15. Successive radioactive decay 84 4.16. Radioisotope generators 89 4.17. Decay energy and half-life 90 4.18. The Heisenberg uncertainty principle 90 4.19. Exercises 91 4.20. Literature 93 4.1. Radioactive decay Radioactive decay is a spontaneous nuclear transformation that has been shown to be unaffected by pressure, temperature, chemical form, etc (except a few very special cases). This insensitivity to extranuclear conditions allows us to characterize radioactive nuclei by their decay period and their mode and energy of decay without regard to their physical or chemical condition. 58 Unstable Nuclei and Radioactive Decay 59 The time dependence of radioactive decay is expressed in terms of the half-life (t1/2), which is the time required for one-half of the radioactive atoms in a sample to undergo decay. In practice this is the time for the measured radioactive intensity (or simply, radioactivity of a sample) to decrease to one-half of its previous value (see Fig. 1.1). Half-lives vary from millions of years to fractions of seconds.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
______________________________ WORLD TECHNOLOGIES ______________________________ Chapter- 6 Radioactive Decay Alpha decay is one example type of radioactive decay, in which an atomic nucleus emits an alpha par-ticle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. Many other types of decays are possible. Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom (i.e., without a nuclear reaction). Usually, radioactive decay happens due to a process confined to the nucleus of the unstable atom, but, on occasion (as with the different processes of electron capture and internal conversion), an inner electron of the radioactive atom is also necessary to the process. Radioactive decay is a stochastic (i.e., random) process at the level of single atoms, in that, according to quantum theory, it is impossible to predict when a given atom will decay. However, given a large number of identical atoms (nuclides), the decay rate for the collection is predictable, via the Law of Large Numbers. The decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide , transforms to an atom with a nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide . Often the parent and daughter are different chemical elements, and in such cases the decay process results in nuclear transmutation. In an example of this, a carbon-14 atom (the parent) emits radiation (a beta particle, antineutrino, ______________________________ WORLD TECHNOLOGIES ______________________________ and a gamma ray) and transforms to a nitrogen-14 atom (the daughter).
eBook - PDF- Yuri A Berezhnoy(Author)
- 2005(Publication Date)
- WSPC(Publisher)
Chapter 4 Radioactivity of Atomic Nuclei 4.1 The Law of Radioactive Decay Human history records but a few great scientific discoveries made acciden-tally. The discovery of the radioactivity of atomic nuclei is one of them. Radioactivity is the process of spontaneous transmutation of an unstable nucleus into another one, which is accompanied by the emission of various particles and photons. Several elementary particles can undergo radioactive decay as well. In February 1896, the physics professor Becquerel was working at the Ecole Poly technique in Paris. He studied the abilities of various crystals under sunlight to emit a penetrating radiation similar to the X-rays that had been recently discovered by Roentgen. Becquerel supposed that crys-tals under the influence of light would emit rays that could register on the photographic plates covered by black paper. A screen made out of copper wires was placed between the crystal and the plate. Thus, after developing, the plate would be light-struck everywhere except the region covered by the copper wires. Among the crystals Becquerel was working with, by chance some ura-nium salts were stored, specifically uranium sodium bisulphate. Also by chance, the weather during the experiments was cloudy so that Becquerel put the plates into the box of the laboratory table together with the crystals of uranium salt. After a few days when the plates were developed, they appeared dark and demonstrated a very clear image of the screen, even though no sunlight had illuminated the uranium salt. Becquerel attributed the rays that registered on the plate to the ura-nium. Afterwards it was found that the same rays could be emitted by other elements as well. In 1898, Marie Sklodowska-Curie discovered that 89 90 The Quantum World of Nuclear Physics the same rays were emitted by thorium; she and her husband Pierre Curie subsequently discovered radium. The term radium originates from the Latin word radius, which means ray.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter 1 Radioactive Decay Alpha decay is one example type of radioactive decay, in which an atomic nucleus emits an alpha particle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. Many other types of decays are possible. Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom (i.e., without a nuclear reaction). Usually, radioactive decay happens due to a proceses confined to the nucleus of the unstable atom, but occasionally (as with the different proceses of electron capture and internal conversion) an inner electron of the radioactive atom is also necessary to the process. Radioactive decay is a stochastic (i.e. random) process on the level of single atoms, in that according to quantum theory it is impossible to predict when a given atom will decay. However, given a large number of identical atoms (nuclides) the decay rate for the collection is predictable. The decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide , transforms to an atom with a nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide . Often the parent and daughter are different chemical elements, and in such cases the decay process results in nuclear transmutation. In an example of this, a carbon-14 atom (the parent) emits radiation (a beta particle, antineutrino, and a gamma ray) and transforms to a nitrogen-14 atom (the daughter). By contrast, there exist two types of radioactive decay processes (gamma decay and internal conversion decay) that do not result in transmutation, but only
eBook - PDF- Walter D. Loveland, David J. Morrissey, Glenn T. Seaborg(Authors)
- 2017(Publication Date)
- Wiley(Publisher)
57 3 Radioactive Decay Kinetics The number of nuclei in a radioactive sample that disintegrate during a given time interval decreases exponentially with time. Because the nucleus is insu- lated by the surrounding cloud of electrons, this rate is essentially independent of pressure, temperature, the mass action law, or any other rate-limiting factors that commonly effect chemical and physical changes. 1 As a result, this decay rate serves as a very useful means of identifying a given nuclide. Since radioactive decay represents the transformation of an unstable radioactive nuclide into a more stable nuclide, which may also be radioactive, it is an irreversible event for each nuclide. The unstable nuclei in a radioactive sample do not all decay simultaneously. Instead the decay of a given nucleus is an entirely random event. Consequently, studies of radioactive decay events require the use of statistical methods. With these methods, one may observe a large number of radioactive nuclei and pre- dict with fair assurance that, after a given length of time, a definite fraction of them will have disintegrated but not which ones or when. 3.1 Basic Decay Equations Radioactive decay is what chemists refer to as a first-order reaction; that is, the rate of radioactive decay is proportional to the number of each type of radioac- tive nuclei present in a given sample. So if we double the number of a given type of radioactive nuclei in a sample, we double the number of particles emitted by the sample per unit time. 2 1 In the case of electron capture and internal conversion, the chemical environment of the electrons involved may affect the decay rate. For L-electron capture in 7 Be (t 1∕2 = 53.3 days), the ratio of t BeF 2 1∕2 /t Be 1∕2 is 1.00084. Similarly, a fully stripped radioactive ion cannot undergo either EC or IC decay, a feature of interest in astrophysics.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Library Press(Publisher)
____________________ WORLD TECHNOLOGIES ____________________ Chapter- 1 Radioactive Decay Alpha decay is one example type of radioactive decay, in which an atomic nucleus emits an alpha particle, and thereby transforms (or 'decays') into an atom with a mass number 4 less and atomic number 2 less. Many other types of decays are possible. Radioactive decay is the process by which an atomic nucleus of an unstable atom loses energy by emitting ionizing particles (ionizing radiation). The emission is spontaneous, in that the atom decays without any interaction with another particle from outside the atom (i.e., without a nuclear reaction). Usually, radioactive decay happens due to a proceses confined to the nucleus of the unstable atom, but occasionally (as with the different proceses of electron capture and internal conversion) an inner electron of the radioactive atom is also necessary to the process. Radioactive decay is a stochastic (i.e. random) process on the level of single atoms, in that according to quantum theory it is impossible to predict when a given atom will decay. However, given a large number of identical atoms (nuclides) the decay rate for the collection is predictable. The decay, or loss of energy, results when an atom with one type of nucleus, called the parent radionuclide , transforms to an atom with a nucleus in a different state, or a different nucleus, either of which is named the daughter nuclide . Often the parent and daughter are different chemical elements, and in such cases the decay process results in nuclear transmutation. In an example of this, a carbon-14 atom (the parent) emits radiation (a beta particle, antineutrino, and a gamma ray) and transforms to a nitrogen-14 atom (the daughter). By contrast, there exist two types of radioactive decay processes (gamma decay and internal conversion decay) that do not result in transmutation, but only
- Maria Emilova Velinova(Author)
- 2020(Publication Date)
- Arcler Press(Publisher)
Internal Instability In spite of this simple line of reasoning, the transformation process of atoms of nuclides we called ‘radio-active’ was believed to be due to internal Radioactive Decay as A Second-Order Kinetics Transformation Process... 47 reasons, not related to interactions of these systems with something in their surroundings. This was essentially due to two reasons. The first reason was that experiments showed that, although the atoms of the radioactive nuclides are certainly non-isolated systems and therefore interacting with their surroundings, their rate of transformation did not appreciably change as the external conditions changed. Fischbach et al. (2009) correctly emphasized that few issues frame the history of natural radioactivity as fundamentally as the question of whether the decay rates of nuclides are constants of nature, unaffected by the external environment. After Henri Becquerel discovered radioactivity, in 1896, intense efforts were made to ascertain whether the decay rates of nuclides could be affected by temperature, pressure, chemical composition, electric and magnetic fields etc., and Rutherford et al. (1930) concluded that the rate of transformation of a radioactive nuclide is a constant under all conditions. The second reason was that the results of the measurements of the rate of transformation of these atomic systems can be interpreted as if the process occurred according to first-order kinetics, i.e. in terms of probability to decay (Rutherford et al., 1930). According to this interpretation, all the atoms of a radioactive nuclide have equivalent probability to decay in a certain time-span of observation.
eBook - PDFBasic Physics Of Radiotracers
Volume II
- Earl W. Barnes(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
In time it was determined that there were three types of radiations that accounted for the phenomenon that was called radioactivity. The three types of radiations were named: 1. Alpha particles (cr) 2. Beta particles ( ß) 3. Gamma rays (y) The substances that emit one or more of these radiations are called radioactive nu clides. Investigations since the early years of this century have established that the three types of radiations originate in the nucleus of certain nuclides, and that (1) alpha par ticles (a) are, in actuality, helium nuclei (2He); (2) beta particles ( ß~ and ß +) are, in actuality, negative and positive electrons (e and e+); and (3) gamma rays (y) are high energy electromagnetic radiations (photons). Radioactive disintegration is a mechanism whereby an unstable nucleus can give up energy in order to achieve a configuration of greater stability. II. THE RADIOACTIVE DECAY CURVE If N represents the number of radioactive nuclei in a certain sample at a certain time, then the rate at which the nuclei in the sample decay is given by -dN dt where the minus sign signifies that the number of nuclei in the sample decreases with time. The quantity — (dN/dt) is called the activity of the sample: -dN ACTIVITY = -------dt The activity of a radioactive substance is often measured in terms of the curie, which is defined as follows: Activity is sometimes measured in terms of the rutherford, which is defined as fol lows: disintegrations per second 39 1 rutherford (rd) = IO6 disintegrations per second (1 mrd = IO-3 rd = IO3 disintegrations per second) (1 ¡did = IO-6 rd = 1 disintegration per second) The disintegration of radioactive nuclei is a random process. However, when a large number of nuclei are considered it is found that the activity of a radioactive substance is directly proportional to the number of radioactive atoms present, i.e.: where À is a proportionality constant called the radioactive decay constant.
eBook - PDFRadioisotope and Radiation Physics
An Introduction
- M Miladjenovic(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
The above statements have been verified by every measurement of the half-life. Special evidence is provided by the composition of certain uranium ores, from which it can be concluded that their decay constants have not changed in the course of several billion years. All that we know about the decay time of a nucleus is expressed by the decay probability. There is no certitude, and it cannot be accurately pre-dicted when a particular nucleus will decay. Such a determination would require a special experiment, but even if we knew how to carry it out, after the experiment the nucleus no longer would be the same. 54 3. Radioactive Radiation The Law of Decay. The two properties of the decay constant men-tioned above are characteristic of phenomena regulated by the laws of chance. From them it follows mathematically that repeated measurements of the number of decays will display fluctuations, as shown in the above example. Furthermore, they are sufficient to mathematically formulate the law of decay exactly coresponding to the experimentally established one. If the probability that a nucleus will decay in time dt is equal to λ dt, then of Ν atoms having the same probability, dN atoms will decay in time dt; the number dN is obtained by multiplying the decay probability of the nucleus by the total number of nuclei N, that is, Since the decay constant λ is independent of t, the solution of the above equation is where N 0 is the initial number of radioactive atoms, and Ν is the number of nondisintegrated radioactive atoms at time Activity. The law of decay as defined by Eq. (3.1) involves the number of radioactive atoms N, which is not directly measured. Decays are measured experimentally. Therefore, it is convenient to introduce the activity A, which is defined as the number of decays per unit time. If the probability for an atom to decay in unit time is equal to λ, and Ν atoms are initially present, the mean number of those which will have decayed will be Νλ.
eBook - PDFPhysics of Nuclear Radiations
Concepts, Techniques and Applications
- Chary Rangacharyulu(Author)
- 2013(Publication Date)
- CRC Press(Publisher)
2 Radioactivity 2.1 Introduction Nuclear radiations are ubiquitous. They are present in the atmosphere as cosmic rays originating in outer space, sources of which are yet un-known. They are also present in vegetation as carbon contains a small but finite radioactive isotope, 1 a fact used advantageously to determine the ages of archaeological samples. Most living beings including hu-mans contain calcium, which consists of a tiny amount of long-lived ra-dioactive potassium ( 40 K isotope). The list goes on. In the 20th century, we made significant progress in harnessing energy from nuclear fis-sion, employing nuclear techniques for non-destructive testing of ma-terials, medical diagnostics and therapy. Whether we handle radioac-tive materials for applications or we are concerned about health and safety, we need to have a good grasp of some basic terminology and be able to do simple calculations to make quantitative estimates of radi-ation phenomena. When one is concerned about radiation effects, one has to consider the species and energies of the radiations emitted and the activity levels and characteristic lifetimes of the radiation emitting sources. This chapter is devoted to radioactive levels and characteristic times. 2.1.1 Exponential Decay Law It has been found that in a sample of radioactive material, the intensity of emissions (number of emissions per unit time) decreases exponen-tially with time. Exponential growths and decays are very common in physical sciences. In the case of growth, we can specify a maximum 1 See Section 2.7. 21 22 Physics of Nuclear Radiations: Concepts, Techniques and Applications limit to which a sample, left to itself, will grow after an infinite amount of time. In the case of decay, a sample will vanish only after an infinite amount of time. 2 However, as we will see below, both growth and de-cay will be quite small after some finite time.
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