Chemistry
Spontaneous Decay
Spontaneous decay refers to the process by which an unstable atomic nucleus undergoes a transformation into a more stable configuration without external influence. This decay can result in the emission of radiation, such as alpha or beta particles, and is a fundamental concept in understanding the behavior of radioactive isotopes.
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eBook - PDFRadioisotope and Radiation Physics
An Introduction
- M Miladjenovic(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
The process by which the radioisotope is produced is called the nuclear re-action and can be written, like chemical reactions, in the form l?Co 3 2 + Ini i?Co 3 3 + y or, more briefly, as 59 Co(n, y ) 6 0 C o ; it is said to be an n-y reaction. Most radioactive isotopes used in scientific research, medicine, and technology are obtained in this way. There are a large number of other nuclear re-actions giving radioactive isotopes, some of which are (d, p ) , (d, a ) , (d, η), (ρ, ή). 3.1. Nuclear Decay as a Source of Radiation 45 As an example of their use, we mention the reactions by which the radio-active isotopes 1 4 C , 2 2 N a , 5 4 M n , and 7 4 A s are produced. They are 13 C(d, p ) 1 4 C , 24 Mg(d, a ) 2 2 N a , 5 3 Cr(
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).
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
eBook - PDFChemistry
An Atoms First Approach
- Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste, , Steven Zumdahl, Steven Zumdahl, Susan Zumdahl, Donald J. DeCoste(Authors)
- 2020(Publication Date)
- Cengage Learning EMEA(Publisher)
Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s). Editorial review has deemed that any suppressed content does not materially affect the overall learning experience. Cengage Learning reserves the right to remove additional content at any time if subsequent rights restrictions require it. ● There are also certain specific numbers of protons or neutrons that produce espe- cially stable nuclides. These magic numbers are 2, 8, 20, 28, 50, 82, and 126. This behavior parallels that for atoms in which certain numbers of electrons (2, 10, 18, 36, 54, and 86) produce special chemical stability (the noble gases). Types of Radioactive Decay Radioactive nuclei can undergo decomposition in various ways. These decay pro- cesses fall into two categories: those that involve a change in the mass number of the decaying nucleus and those that do not. We will consider the former type of process first. An alpha particle, or a particle, is a helium nucleus ( 4 2 He). Alpha-particle produc- tion is a very common mode of decay for heavy radioactive nuclides. For example, 238 92 U, the predominant (99.3%) isotope of natural uranium, decays by a-particle production: 238 92 U ¡ 4 2 He 1 234 90 Th Another a-particle producer is 230 90 Th: 230 90 Th ¡ 4 2 He 1 226 88 Ra Another decay process in which the mass number of the decaying nucleus changes is spontaneous fission, the splitting of a heavy nuclide into two lighter nuclides with similar mass numbers. Although this process occurs at an extremely slow rate for most nuclides, it is important in some cases, such as for 254 98 Cf, where spontaneous fission is the predominant mode of decay. The most common decay process in which the mass number of the decaying nu- cleus remains constant is b-particle production.
- Michael Wiescher, Khachatur Manukyan(Authors)
- 2022(Publication Date)
- Springer(Publisher)
This, we shall see later, is the general law of decay of activity in any type of active matter. (Ernest Rutherford, Radioactivity, 1904) The time dependence of all decay processes can be expressed in the general terms of simple exponential behavior, independent of the actual nature of the decay mechanism. The number of radioactive decays from a radioactive sample within a given time is expressed in terms of the activity A.t/ at time t A.t/ D NUL dN dt D SOH N.t/: (1.33) The activity is directly proportional to the number of radioactive nuclei in the sample N.t/; the constant is the decay constant and corresponds directly to the quantum mechanical probability that the nucleus changes from its initial “mother” configuration of proton and neutrons into a different “daughter” configuration. The minus sign in the equation indicates that the number of radioactive nuclei N.t/ decreases with time. This equation allows for calculating the number of radioactive nuclei in the sample at any time t after their original production .t D 0/ of the initial amount N 0 N.t/ D N.t D 0/ SOH e NUL SOHt D N 0 SOH e NUL SOHt : (1.34) This is the radioactive decay law, which expresses the exponential decay of every kind of radioac- tive nucleus with time. Similarly, the associated radioactive activity A.t/ can be expressed by the decay law in terms of the initial activity A 0 A.t/ D A 0 SOH e NUL SOHt : (1.35) 1.5. THE LAWS OF RADIOACTIVE DECAY 35 Since the decay constant defines the time scale of the decay, it has conventionally been used to define the so-called lifetime of the radioactive nucleus D 1 : (1.36) Since the decay process follows an exponential law, lifetime does not mean that after time the radioactive sample is gone but, rather, it reflects a statistical expectation value for the decay process to occur. After time, the number of radioactive nuclei is reduced to EM 66% of its original value since N.
eBook - PDF- Leo J. Malone, Theodore O. Dolter(Authors)
- 2012(Publication Date)
- Wiley(Publisher)
Even if the time period doesn't work out to exactly round numbers of half-lives, the amount can be estimated. (There are also specific equations that will allow us to calculate it directly, but they are beyond our scope.) SYNTHESIS In most cases, chemical reactions occur because two individual molecules collide. In other cases, there may be just one molecule involved in the reaction but some external energy source, such as heat or light, initiates the reaction. But a nuclear decay reaction is unique in that it involves just a single type of atom, and the impetus for the reaction comes internally from the atom itself. This is why the rate at which the reaction occurs, measured by the half-life, is not dependent on concentration, temperature, pressure, or any other external factor. Half-life is an innate function of the isotope itself. E X A M P L E 1 6 - 3 Calculating the Amount of Isotope Remaining EXERCISE 16-2(a) LEVEL 1: Which isotopes decay faster: ones with long half-lives or ones with short half-lives? EXERCISE 16-2(b) LEVEL 2: What percent of an isotope has decayed after three half-lives? EXERCISE 16-2(c) LEVEL 2: After 36.0 minutes, it was found that 4.0 mg remains of a sample of a radioactive isotope that originally weighed 64 mg. What is the half- life of the isotope? EXERCISE 16-2(d) LEVEL 3: Why is it not possible to isolate a pure sample of a radioactive substance? For additional practice, work chapter problems 16-20 and 16-22. C C ASSESSING THE OBJECTIVE FOR SECTION 16-2 16-3 The Effects of Radiation LOOKING AHEAD! We tend to fear the effects of radiation. Certainly, it may cause cancer and sickness, but this same radiation can save lives when used in medical diagno- sis or cancer treatment. How radiation interacts with matter is our next subject. ■ A generation grew up with a deep fear of radiation as a result of a possible nuclear holocaust.
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)
The nonexistence in nature of elements with atomic numbers greater than 92 is explained by the fact that all the isotopes of these elements have life-times considerably shorter than the age of the earth. Radioactive decay is a random process. Among the atoms in a sample undergoing decay it is not possible to identify which specific atom will be the next to decay. We denote the decay rate by A. It is a measure of the number of disintegrations per unit time: A = —dN/dt (4.39) The decay rate is proportional to the number of radioactive atoms, N, present: A oc N. If 10 5 atoms show a decay rate of 5 atoms per second then 10 6 atoms show a decay rate of 50 atoms per second. If the number of radioactive nuclei and the number of decays per unit time are sufficiently great to permit a statistical treatment, then — dN/dt = N (4.40a) where is the proportionality constant known as the decay constant. If the time of observation At during which AN atoms decay is very small compared to t i/2 (usually < 1 %), one may simply write A = AN/At = XN (4.40b) If the number of nuclei present atsome original time t = 0 is designated as N0, (4.40a) upon integration becomes the general equation for simple radioactive decay: N = N0 e _Xl (4.41a) In Figure 4.8 the ratio of the number of nuclei at any time t to the original number at time t = 0 (i.e. N/Nq) has been plotted on both a linear (left) and logarithmic (right) scale as a function of t. The linearity of the decay curve in the semi-logarithmic graph illustrates the exponential nature of radioactive decay. Since A oc N, the equation can be rewritten as A = A q e _Xi (4.41b) Commonly, log A is plotted asa function of t since it is simpler todetermine the disintegration rate than it is to determine the number of radioactive atoms in a sample. 80 Radiochemistry and Nuclear Chemistry TIME t IN NUMBER OF HALF-LIVES FIG. 4.8. Linear and logarithm plots of simple radioactive decay.
eBook - PDFChemistry
Structure and Dynamics
- James N. Spencer, George M. Bodner, Lyman H. Rickard(Authors)
- 2011(Publication Date)
- Wiley(Publisher)
There are a number of small irregularities in the binding energy curve at the low end of the mass spectrum, as shown in Figure 15.7. The 4 He nucleus, for example, is much more stable than its nearest neighbors. The unusual stability of the 4 He nucleus explains why -particle decay is usually much faster than the spontaneous fission of a nuclide into two large fragments. 15.6 The Kinetics of Radioactive Decay Radioactive nuclei decay by first-order kinetics. The rate of radioactive decay is therefore the product of a rate constant (k) times the number of atoms of the iso- tope in the sample (N). The rate of radioactive decay doesn’t depend on the chemical state of the isotope. The rate of decay of 238 U, for example, is the same in uranium metal and ura- nium hexafluoride or any other compound of this element. The rate at which a radioactive isotope decays is called the activity of the isotope. The most common unit of activity is the curie (Ci), which was originally defined as the number of disintegrations per second in 1 gram of 226 Ra. The curie is now defined as the amount of radioactive isotope necessary to achieve an activ- ity of 3.700 10 10 disintegrations per second. rate = - d(N) dt = k(N) 235 92 U ¡ 139 56 Ba + 94 36 Kr + 2 1 0 n (fission) 700 CHAPTER 15 / NUCLEAR CHEMISTRY Fig. 15.7 The binding energy per nucleon for most stable nuclei is between 7.8 and 8.8 MeV per nucleon. There is more variability in the binding energy per nucleon for relatively light nuclei. The binding energy per nucleon for 4 He is particularly large, which explains why so many of the heavier nuclides undergo decay. 30 20 10 0 9 8 7 6 5 4 3 2 1 0 Atomic mass (amu) Binding energy per nucleon (MeV) 7 Li 4 He 9 Be 11 B 14 N 12 C 16 O 19 F 20 Ne 24 Mg 1 H 2 H 3 H 15.6 THE KINETICS OF RADIOACTIVE DECAY 701 E x e r c i s e 1 5 .
eBook - PDFBasic Physics Of Radiotracers
Volume II
- Earl W. Barnes(Author)
- 2017(Publication Date)
- CRC Press(Publisher)
The half-life of a radioactive substance is defined as the length of time required for half of the original nuclei to decay. It is usually symbolized by T 1/2. Using this defini tion we can write the previous equation for the case where t = T i /2, and N (T 1/2) = N0/2. Then 40 Basic Physics of Radiotracers number Z and mass number A. This is what we have symbolized by ¿X. Nuclides with the same Z are called isotopes ; nuclides with the same A are called isobars ; nuclides with the same N are called isotones. Nuclides that have the same A and Z but are in different states of excitation are called isomers. Example — There are three stable isotopes of oxygen. The atomic number of oxygen is 8 (Z = 8); the mass numbers for the three isotopes are 16, 17, and 18. Hence the> three isotopes would be represented symbolically as: Each of the three isotopes has 8 protons in its nucleus; they have 8, 9, and 10 neutrons, respectively. Since the atomic number is redundant — inasmuch as the chemical sym bol uniquely determines it — the above isotopes might be expressed symbolically as: Let iX represent the parent nucleus. Let i* Y represent the daughter nucleus. A. Alpha Decay In terms of the above convention, alpha decay can be represented by the following: where the emitted alpha particle is shown as a helium nucleus. Since the atomic number of the daughter nucleus is different from that of the parent, the two nuclei are isotopes of different elements with different chemical properties. The above transformation also demonstrates two important conservation laws that are general for all radioactive decays: 1. Conservation of electric charge. There are Z protons before and after the decay. 2. Conservation of nucleons. There are A nucleons before and after the decay. As an example of alpha decay we will refer to the alpha decay of the most abundant isotope of uranium, 2 9 ®U: The daughter nucleus is thorium-234.
- Bo N. Nilsson(Author)
- 2015(Publication Date)
- De Gruyter Open Poland(Publisher)
© 2015 Bo Nilsson This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License. 1 Radiation Sources and Radioactive Decay . Denitions and Equations .. Radioactivity and Decay Equations Activity Activity is dened as A = d N d t = λN Unit : Bq (becquerel) = s -(1.1.1) where A is activity, d N /d t is the number of spontaneous nuclear transformations, d N , from a particular energy state in a time interval d t . λ is the decay constant (s -) and N is the number of radioactive nuclei. The specic activity is dened as the activity of a certain radionuclide per mass unit (Bq kg -). C = A m (1.1.2) Radioactive decay A radionuclide decays according to the equation N ( t ) = N e -λt = N e -t ln / T (1.1.3) where N ( t ) is the number of radioactive nuclides after a time t , N = N () is the number of radioactive nuclides at time 0 and T is the half-life ( T = ln / λ ). The equation may also be expressed as A ( t ) = A e -λt = A e -t ln / T (1.1.4) Sometimes the daughter nuclides are also radioactive and a chain of radioactive nu-clides is obtained. A general solution for the activity of a radionuclide in the chain is given by the Bateman equations. In this compilation only the rst three radionuclides in the chain will be treated. N ( t ) = N e -λ t (1.1.5) N ( t ) = N λ λ -λ ( e -λ t -e -λ t ) (1.1.6) N ( t ) = N λ λ [ e -λ t ( λ -λ )( λ -λ ) + e -λ t ( λ -λ )( λ -λ ) + e -λ t ( λ -λ )( λ -λ ) ] (1.1.7) 2 Radiation Sources and Radioactive Decay All these equations assume that N () and N () are equal to zero. If not, corrections have to be made, by adding to the equation above, the activity of the separate radionu-clides at t = corrected for the decay to the time t . E.g. N 0 ( t ) = N 0 () e -λ t (1.1.8) where N 0 () is the number of N 0 radionuclides at time, t = 0 . In some situations Eq. (1.1.6) may be simplied, as shown below.
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