1 Chapter 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 insulated 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 predict 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 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 ½ = 53.3d), the ratio of is Similarly, a fully stripped radioactive ion cannot undergo either EC or IC decay, a feature of interest in astrophysics. 2 In order to make this statement completely correct, we should say that as we double the number of nuclei present, we double the rate of particle emission. This rate is equal to the number of particles emitted per unit time, provided that the time interval is small.
2 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 radioactive 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 This relation may be expressed as follows: Note that the foregoing statement is only a proportion. By introducing the decay constant, it is possible to convert this expression into an equation, as follows: (3-1) The decay constant, λ, represents the average probability per nucleus of decay occurring per unit time. Therefore we are taking the probability of decay per nucleus, λ, and multiplying it by the number of nuclei present so as to get the rate of particle emission. The units of rate are (disintegration of nuclei/time) making the units of the decay constant (1/time), i.e., probability/time of decay. To convert the preceding word equations to mathematical statements using symbols, let N represent the number of radioactive nuclei present at time t. Then, using differential calculus, the preceding word equations may be written as
3 -3- (3-2) Note that N is constantly reducing in magnitude as a function of time. Rearrangement of Equation (3-2) to separate the variables gives (3-3) If we say that at time t = 0 we have N0 radioactive nuclei present, then integration of Equation (3-3) gives the radioactive decay law (3-4) This equation gives us the number of radioactive nuclei present at time t. However, in many experiments, we want to know the counting rate that we will get in a detector as a function of time. In other words, we want to know the activity of our samples. Still, it is easy to show that the counting rate in one s radiation detector, C, is equal to the rate of disintegration of the radioactive nuclei present in a sample, A, multiplied by a constant related to the efficiency of the radiation measuring system. Thus (3-5) where ε is the efficiency. Substituting into Equation (3-4), we get C = C 0 e λt (3-6) where C is the counting rate at some time t due to a radioactive sample that gave counting rate C0 at time t = 0. Equations (3-4) and (3-6) are the basic equations governing the number of nuclei present in a radioactive sample and the number of counts observed in one s detector as a function of time. Equation (3-6) is shown graphically as Figure 3-1. As
4 -4- seen in Figure 3-1, this exponential curve flattens out and asymptotically approaches zero. If the same plot is made on a semi logarithmic scale (Figure 3-2), the decay curve is a straight line, with a slope equal to the value of - (λ/2.303). The half- life (t½) is another representation of the decay constant. The half- life of a radionuclide is the time required for its activity to decrease by one- half. Thus after one half- life, 50% of the initial activity remains. After two half- lives, only 25% of the initial activity remains. After three half- lives, only 12.5% is yet present and so forth. Figure 3-3 shows this relation graphically. The half- life for a given nuclide can be derived from Equation (3-6) when the value of the decay constant is known. In accordance with the definition of the term half- life, when A/A0 = ½, then t = t½. Substituting these values into Equation (3-6) gives (3-7) Hence (3-8) Note that the value of the expression for t½ has the units of 1/λ or dimensions of (time). The half- lives for different nuclides range from less than 10-6 sec to yr. The half- life has been measured for all the commonly used radionuclides. When an unknown radioactive nuclide is encountered, a determination of its half- life is normally one of the first steps in its identification. This determination can be done by preparing a semi log plot of a series of activity observations made over a period of time. A short- lived nuclide may
5 -5- be observed as it decays through a complete half- life and the time interval observed directly (Figure 3-4) Example Given the data plotted below for the decay of a single radionuclide, determine the decay constant and the half- life of the nuclide. Solution The data is plotted above. The slope (- λ) is given as - λ = - (6.06-0)/(220min - 0) λ = min - 1 t1/2 = ln 2/λ = 0.693/ = 25.2 min. What nuclide might this be?
6 -6- It is difficult to measure the half- life of a very long- lived radionuclide. Here variation in disintegration rate may not be noticeable within a reasonable length of time. In this case, the decay constant must be calculated from the absolute decay rate according to Equation (3-2). The absolute number of atoms of the radioisotope present (N) in a given sample can be calculated according to (3-9) The total mass of the radioisotope in the given sample can be determined once the isotopic composition of the sample is ascertained by such means as mass spectrometry. When the decay constant is known, the half- life can then be readily calculated. A table for the half- lives of a number of the known nuclei can be found in the Appendices. Although the half- life of a given radionuclide is a defined value, the actual moment of disintegration for a particular atom can be anywhere from the very beginning of the nuclide s life to infinity. The average or mean life of a population of nuclei can, however, be calculated. The mean life τ is naturally related to the decay constant and is, in fact, simply the reciprocal of the decay constant: (3-10) or the mean life can be expressed in terms of the half- life: (3-11) One can understand the preceding relationship by recalling that the decay constant, λ, was defined as the average probability of decay per unit time, so the 1/λ is the average time between decays. The concept of average life allows us to calculate of the total number of
7 -7- particles emitted during a defined decay period. This number is essential in determining total radiation dose delivered by a radioisotope sample, as in medical research and therapy. During the time equal to one mean life, τ, the activity falls to 1/e of its original value. For a sample of N0 nuclei with lifetimes ti, we can write for the mean life τ (3-12) The average or mean life is also of fundamental physical significance because it is the time to be substituted in the mathematical statement of the Heisenberg uncertainty principle, i.e., In this expression relating the uncertainty in energy of a system, ΔE, to its lifetime Δt, τ Δt. The quantity ΔE is called the width, Γ. The natural unit of radioactivity is disintegrations/time, such as disintegration per second (dps) or disintegrations per minute (dpm), etc. The SI unit of radioactivity is the Becquerel (Bq) where 1 Becquerel (Bq) 1 disintegration/sec. Counting rates in a detection system are usually given in counts per second (cps), counts per minute (cpm), etc., and differ from the disintegration rates by a factor representing the detector efficiency, ε. Thus
8 -8- (dpm) ε = (cpm) An older unit of radioactivity that still finds some use is the curie (Ci). It is defined as 1 curie (Ci) = 3.7x10 10 Bq = 3.7x10 10 dis/s The curie is a huge unit of radioactivity representing a very large amount and is approximately equal to the activity of one gram of radium. The inventories of radioactivity in a nuclear reactor upon shutdown are typically 10 9 Ci while radiation sources used in tracer experiments have activities of μci and the environmental levels of radioactivity are nci or pci. Note also that because radionuclides, in general, have different half- lives, the number of nuclei per curie will differ from one species to another. For example, let us calculate how many nuclei are in 1 MBq (~27 μci) of tritium( 3 H) (t½ = yr.). We know that But Thus The same calculation carried out for 14 C(t½) = 5730 yr) would give 2.60x10 17 nuclei/mbq. It is also interesting to calculate the mass associated with 1 MBq of tritium. We have
9 -9- In other words, 1 MBq of tritium contains about 3 ng of tritium. Thus an important feature of radionuclides becomes apparent - - we routinely work with extremely small quantities of material. Pure samples of radioisotopes are called carrier- free. Unless a radionuclide is in a carrier- free state, it is mixed homogeneously with the stable nuclides of the same element. It is therefore desirable to have a simple expression to show the relative abundances of the radioisotope and the stable isotopes. This step is readily accomplished by using the concept of specific activity, which refers to the amount of radioactivity per given mass or other similar units of the total sample. The SI unit of specific activity is Bq/kg. Specific activity can also be expressed in terms of the disintegration rate (Bq or dpm), or counting rate (counts/min, cpm, or counts/sec, cps), or curies (or mci, μci) of the specific radionuclide per unit mass of the sample. 3.2 Mixture of Two Independently Decaying Radionuclides Where two or more radioisotopes with different half- lives are present in a sample and one does not or cannot distinguish the particles emitted by each isotope, a composite decay rate will be observed. The decay curve, in this situation, drawn on a semi logarithmic plot, will not be a straight line. The decay curves of each of the isotopes present usually can be resolved by graphic means if their half- lives differ sufficiently and if not more than three radioactive components are present. In the graphic example shown in Figure 3-5, line C represents the total observed activity. Only the activity of the longer- lived component A is observed after the shorter- lived component B has become exhausted through decay.
10 -10- Extrapolation of this long- time portion of the curve back to zero time gives the decay curve for component A and the activity of component A at t=0. The curve for component B is obtained by subtracting out, point by point, the activity values of component A from the total activity curve. If the half- lives of the two components in such samples are not sufficiently different to allow graphic resolution, a differential detection method may be applicable. If the radiation characteristics of the nuclides in the mixture are suitably distinct, i.e., emission of different particles or γ- rays, it may be possible to measure the activity of one component without interference from the radiation emitted by the other component. A case in point would be where one nuclide was a pure β- emitter, while the other emitted both β- and γ- rays. In the case where the half- lives of the components are known but are not sufficiently different to allow graphical resolution of the decay curve, computer techniques that utilize least squares fitting to resolve such a case are also available Example: Given the following decay data, determine the half- lives and initial activities of the radionuclides (B and C) present: t (h) A (cpm)
11 From the graph, we see: t1/2(b) = 8.0 h t1/2(c) = 0.8 h A0 (B) = 80 cpm A0(C) = 190 cpm 3.3 Radioactive Decay Equilibrium When a radionuclide decays, it does not disappear, but is transformed into a new nuclear species of lower energy and often differing Z, A, J, π, etc. The equations of radioactive decay discussed so far have focused on the decrease of the parent radionuclides but have ignored the formation (and possible decay) of daughter, granddaughter, etc., species. It is the formation and decay of these children that is the focus of this section.
12 -12- Let us begin by considering the case when a radionuclide 1 decays with decay constant λ1, forming a daughter nucleus 2 which in turn decays with decay constant λ2. Schematically we have 1 2 We can write terms for the production and depletion of 2, i.e., rate of change of 2 nuclei present at time t = rate of production of 2 - rate of decay of 2 (3-13) where N1 and N2 are the numbers of (1) and (2) present at time t. Rearranging and collecting similar terms (3-14) Remembering that (3-15) we have This is a first order linear differential equation and can be solved using the method of (3-16) integrating factors which we show below. Multiplying both sides by, we have (3-17) The left hand side is now a perfect differential (3-18) Integrating from t=0 to t=t, we have
13 -13- (3-19) λ 2 t N 2 e N 0 2 = λ 1 λ 2 λ 1 0 N 1 ( ( λ 2 λ 1)t e 1) (3-20) Multiplying by and rearranging gives (3-21) where is the number of species (2) present at t=0. The first term in Equation (3-21) represents the growth of the daughter due to the decay of the parent while the second term represents the decay of any daughter nuclei that were present initially. Remembering that A2 = λ2n2, we can write an expression for the activity of 2 as (3-22) These two equations, (3-21) and (3-22) are the general expressions for the number of daughter nuclei and the daughter activity as a function of time, respectively. The general behavior of the activity of parent and daughter species, as predicted by Equation (3-22), is shown in Figure 3-6. As one expects qualitatively for, the initial activity of the daughter is zero, rises to a maximum, and if one waits long enough, eventually decays. Thus there must be a time when the daughter activity is the maximum. We can calculate this by noting the condition for a maximum in the activity of (2) is
14 -14- (3-23) Taking the derivative of Equation (3-21) and simplifying, (3-24) Solving for t (3-25) All of this development may seem like something that would be best handled by a computer program or just represents a chance to practice one s skill with differential equations. But that is not true. It is important to understand the mathematical foundation of this development to gain insight into practical situations that such insight offers. Let us consider some cases that illustrate this point. Consider the special case where λ1 = λ2. Plugging into Equations (3-21) or (3-22), or a computer program based upon them leads to a division by zero. Does nature therefore forbid λ1 from equaling λ2 in a chain of decays? Nonsense! One simply understands that one must redo the derivation (Equations (3-13) through (3-21)) of Equations (3-21) and (3-22) for this special case (see homework). Let us now consider a number of other special cases of Equations (3-21) and (3-22) that are of practical importance. Suppose the daughter nucleus is stable (λ 2 = 0). Then we have (3-26) (3-27)
15 -15- (3-28) These relations are shown in Figure 3-7. They represent the typical decay of many radionuclides prepared by neutron capture reactions, the type of reaction that commonly occurs in a nuclear reactor. In Figure 3-8, we show the activity relationships for parent and daughter (as predicted by Equation (3-22)) for various choices of the relative values of the half- lives of the parent and daughter nuclides. In the first of these cases, we have t½ (parent) < t½ (daughter), i.e., the parent is shorter lived than the daughter. This is called the no equilibrium case because the daughter buildup (due to the decay of the parent) is faster than its loss due to decay. Essentially all of the parent nuclides are converted to daughter nuclides and the subsequent activity is due to the decay of the daughters only. Thus the name no equilibrium is used. Practical examples of this decay type are 131 Te 131 I, 210 Bi 210 Po, 92 Sr 92 Y. This situation typically occurs when one is very far from stability and the nuclei decay by β decay towards stability. A second special case of Equations (3-21) and (3-22) is called transient equilibrium (Figures 3-8b and 3-9a). In this case, the parent is significantly (~10x) longer- lived than the daughter and thus controls the decay chain. Thus λ2 > λ1 (3-29) In Equation (3-21), as t, (3-30) and we have
16 -16- (3-31) Substituting (3-32) we have (3-33) At long times, the ratio of daughter to parent activity becomes constant, and both species disappear with the effective half- life of the parent. The classic examples of this decay equilibrium are the decay of 140 Ba (t½ = 12.8 d) to 140 La (t½ = 40 hr) or the equilibrium between 222 Rn (t½ = 3.8 d) and its short- lived decay products. A third special case of Equations (3-21) and (3-22) is called secular equilibrium (Figure 3-8 (c+d), 3-9b). In this case, the parent is very much longer lived (~10 4 x) than the daughter or the parent is constantly being replenished through some other process. During the time of observation, there is no significant change in the number of parent nuclei present, although several half- lives of the daughter may occur. In the previous case of transient equilibrium, we had (3-34) Since we now also have λ1 < < < λ 2 (3-35) we can simplify even more to give (3-36)
17 -17- λ1n1 = λ2n2 (3-37) A1 = A2 In short, the activity of the parent and daughter are the same and the total activity of the sample remains effectively constant during the period of observation. The naturally occurring heavy element decay chains (see below) where 238 U 206 Pb, 235 U 207 Pb, 232 Th 208 Pb and the extinct heavy element decay series 237 Np 209 Bi are examples of secular equilibrium because of the long half- lives of the parents. Perhaps the most important cases of secular equilibrium are the production of radionuclides by a nuclear reaction in an accelerator, a reactor, a star or the upper atmosphere. In this case, we have Nuclear Reaction (2) (3-38) which produces the radionuclide 2 with rate R. If the reaction is simply the decay of a long- lived nuclide, then R=λ1N1 0 and N2 0 =0. Substitution into 3-21 gives the expression (3-39) If the reaction is slower than the decay or λ1 < < λ2 (3-40) It is most appropriate to say (since λ1 0) (3-41) or in terms of the activities (3-42)
18 -18- Equation (3-42) is known as the activation equation and is shown in Figure Initially the growth of the product radionuclide activity is nearly linear (due to the behavior of for small values of λt) but eventually the product activity becomes saturated or constant, decaying as fast as it is produced. At an irradiation time of one half- life, half the maximum activity is formed; after 2 half- lives, 3/4 of the maximum activity is formed, etc. This situation gives rise to the rough rule that irradiations that extend for periods that are greater than twice t½ of the desired radionuclide are usually not worthwhile. Equation (3-21) may be generalized to a chain of decaying nuclei of arbitrary length in using the Bateman equations (Bateman, 1910). If we assume that at t=0, none of the daughter nuclei are present,, we get (1) (2) (3),..., (n) where (3-43) These equations describe the activities produced in new fuel in a nuclear reactor. No fission or activation products are present when the fuel is loaded and they grow in as the reactions take place.
19 Example Consider the decay of a 1 µci sample of pure 222 Rn (t1/2 = 3.82 days). Use the Bateman equations to estimate the activity of its daughters ( 218 Po, 214 Pb, 214 Bi and 214 Po) after a decay time of 4 hours. The decay sequence is t1/2 3.82d 3.1m 26.8m 19.9m 164µsec activity A B C D E λ(10-4 s) x10 7 (Actually B/A = ) The reader should verify that for C, D and E, the only significant term is the term multiplying as it was for B. Thus for D/A, we have
20 -20- The reader should, as an exercise, compute the quantities of C and E present. 3.4 Branching Decay Some nuclides decay by more than one mode. Some nuclei may decay by either β + decay or electron capture; others by α- decay or spontaneous fission; still others by γ- ray emission or internal conversion, etc. In these cases, we can characterize each competing mode of decay by a separate decay constant λi for each type of decay where the total decay constant, λ, is given by the sum (3-44) Corresponding to each partial decay constant λi, there is a partial half- life where (3-45) and the total half- life, t1/2, is the sum of the reciprocals (3-46) The fraction of decays proceeding by the i th mode is given by the obvious expression (3-47) By analogy, the energy uncertainty associated with a given state, ΔE, through the Heisenberg uncertainty principle can be obtained from the lifetime contributed by each
21 -21- decay mode. If we introduce the definition ΔE Γ, the level width, then we can express Γ in terms of the partial widths for each decay mode Γi such that (3-48) where (3-49) where τi is the partial mean life associated with each decay mode. This approach is especially useful in treating the decay of states formed in nuclear reactions in which a variety of competing processes such as α emission, p emission, n emission, etc, may occur as the nucleus de- excites. In such cases, we can express the total width as Γ = Γ α + Γp + Γn (3-50) Example: Consider the nucleus 64 Cu (t1/2 = h). 64 Cu is known to decay by electron capture (61%) and β - decay (39%). What are the partial half- lives for EC and β - decay? What is the partial width for EC decay? Solution: λ = ln 2/12.700h = 5.46 x 10-2 h - 1 λ = λec + λβ = λec + (39/61)λEC λec = x 10-2 h - 1 t1/2 EC = (ln 2)/λEC = 20.8 h λβ = (39/61)λEC = x 10-2 h - 1
22 -22- t1/2 β = (ln 2)/λβ = 32.6 h τ EC = t1/2 EC /ln 2 = 30.0 h = s ΓEC = /τ EC = x MeV.s/ s = 6.1 x MeV All naturally occurring radioactive nuclei have extremely small partial widths. Did you notice that 64 Cu can decay into 64 Zn and 64 Ni? This is unusual but can occur for certain odd- odd nuclei (see Chapter 2) Natural Radioactivity There are approximately 70 naturally occurring radionuclides on earth. Most of them are heavy element radioactivities present in the natural decay chains, but there are several important light element activities, such as 3 H, 14 C, 40 K, etc. These radioactive species are ubiquitous, occurring in plants, animals, the air we breathe, the water we drink, the soil, etc. For example, in the 70 kg reference man, one finds ~ 4400 Bq of 40 K and ~ 3600 Bq of 14 C, i.e., about 8000 dis/s due to these two radionuclides alone. In a typical US diet, one ingests ~1 pci/day of 238 U, 226 Ra, and 210 Po. The air we breathe contains ~ 0.15 pci/l of 222 Rn, the water we drink contains >10 pci/l of 3 H while the earth s crust contains ~10 ppm and ~4 ppm of the radioelements Th and U. One should not forget that the interior heat budget of the planet Earth is dominated by the contributions from the radioactive decay of uranium, thorium, and potassium. The naturally occurring radionuclides can be classified as: (a) primordial - i.e., nuclides that have survived since the time the elements were formed (b) cosmogenic - i.e., shorter lived nuclides formed continuously by the interaction of cosmic rays with matter
23 -23- and (c) anthropogenic - i.e., a wide variety of nuclides introduced into the environment by the activities of man, such as nuclear weapons tests, the operation (or misoperation) of nuclear power plants, etc. The primordial radionuclides have half- lives greater than 10 9 years or are the decay products of these nuclei. This class includes 40 K (t1/2 = x 10 9 y), 87 Rb (t1/2 = 47.5 x 10 9 y), 238 U (t1/2 = x 10 9 y), 235 U (t1/2 = x 10 9 y) and 232 Th (t1/2 = x 10 9 y) as its most important members. (Additional members of this group are 115 In, 123 Te, 138 La, 144 Nd, 147 Sm, 148 Sm, 176 Lu, 174 Hf, 187 Re, and 190 Pt.) 40 K is a β - - emitting nuclide that is the predominant radioactive component of normal foods and human tissue. Due to the 1460 kev γ- ray that accompanies the β - decay, it is also an important source of background radiation detected by γ- ray spectrometers. The natural concentration in the body contributes about 17 mrem/year to the whole body dose. The specific activity of 40 K is approximately 855 pci/g potassium. Despite the high specific activity of 87 Rb of ~2400 pci/g, the low abundance of rubidium in nature makes its contribution to the overall radioactivity of the environment small. There are three naturally occurring decay series. They are the uranium (A = 4n + 2) series, in which 238 U decays through 14 intermediate nuclei to form the stable nucleus 206 Pb, the actinium or 235 U (A = 4n + 3) series in which 235 U decays through 11 intermediate nuclei to form stable 207 Pb and the thorium (A = 4n) series in which 232 Th decays through a series of 10 intermediates to stable 208 Pb (Figure 3-11). Because the half- lives of the parent nuclei are so long relative to the other members of each series, all members of each decay series are in secular equilibrium, i.e., the activities of each member of the chain are equal at equilibrium if the sample has not been chemically fractionated. Thus, the activity associated with 238 U in secular equilibrium with its
24 -24- daughters is 14x the activity of the 238 U. The notation 4n+2, 4n, 4n+3 refers to the fact that the mass number of each member of a given chain is such that it can be represented by 4n, 4n+2, 4n+3 where n is an integer. (There is an additional decay series, the 4n+1 series, that is extinct because its longest lived member, 237 Np, has a half- life of only 2.1x10 6 y, a time that is very short compared to the time of element formation.) The uranium series contains two radionuclides of special interest, 226 Ra (t1/2 = 1600 y) and its daughter, 38 d 222 Rn. 226 Ra (and its daughters) are responsible for a major fraction of the radiation dose received from internal radioactivity. Radium is present in rocks and soils, and as a consequence in water, food, and human tissue. The high specific activity and gaseous decay products of radium also make it difficult to handle in the laboratory. 226 Ra decays by α- emission to 222 Rn. This latter nuclide is the principal culprit in the radiation exposures from indoor radon. Although radon is an inert gas and is not trapped in the body, the short- lived decay products are retained in the lungs when inhaled if the 222 Rn decays while it is in the lungs. Indoor radon contributes about 2 msv/yr (200 mrem/yr) to the average radiation exposure in the U.S., i.e., about 2/3 of the dose from natural sources. Under normal circumstances, radon and its daughters attach to dust particles and are in their equilibrium amounts. These dust particles can also deposit in the lungs. It has been estimated that in the U.S., 5,000-10,000 cases of lung cancer (6-12% of all cases) are due to radon exposure. The second class of naturally occurring radionuclides is the cosmogenic nuclei, produced by the interactions of primary and secondary cosmic radiation with nuclei in the stratosphere. The most important of these nuclei are 3 H (tritium), 14 C, and 7 Be. Less
25 -25- importantly, 10 Be, 22 Na, 32 P, 33 P, 35 S and 39 Cl are also produced. These nuclei move into the troposphere through normal exchange processes and are brought by the earth s surface by rainwater. Equilibrium is established between the production rate in the primary cosmic ray interaction and the partition of the radionuclides amongst the various terrestrial compartments (atmosphere, surface waters, biosphere, etc.) leading to an approximately constant specific activity of each nuclide in a particular compartment. When an organism dies after being in equilibrium with the biosphere, the specific activity of the nuclide in that sample will decrease since it is no longer in equilibrium. This behavior allows these nuclides to act as tracers for terrestrial processes and for dating. 14 C (t1/2 = 5730 y) is formed continuously in the upper atmosphere by cosmic rays that produce neutrons giving the reaction n (slow) + 14 N 14 C + p or, in a shorthand notation, 14 N(n, p) 14 C. 14 C is a soft β - - emitter (Emax ~ 158 kev). This radiocarbon ( 14 C) reacts with oxygen and eventually exchanges with the stable carbon (mostly 12 C) in living things. If the cosmic ray flux is constant, and the terrestrial processes affecting 14 C incorporation into living things are constant, and there are no significant changes in the stable carbon content of the atmosphere, then a constant level of 14 C in all living things is found [corresponding to ~1 atom of 14 C for every atoms of 12 C or about 227 Bq/kg C]. When an organism dies, it ceases to exchange its carbon atoms with the pool of radiocarbon and its radiocarbon content decreases in accord with Equation (3-6). Measurement of the specific activity of an old object allows one to calculate the age of the object (see below).
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Basics of Nuclear Physics and Fission A basic background in nuclear physics for those who want to start at the beginning. Some of the terms used in this factsheet can be found in IEER s on-line glossary.
Atomic structure A. Introduction: In 1808, an English scientist called John Dalton proposed an atomic theory based on experimental findings. (1) Elements are made of extremely small particles called atoms.
1 Strontium-90 decays with the emission of a β-particle to form Yttrium-90. The reaction is represented by the equation 90 38 The decay constant is 0.025 year 1. 90 39 0 1 Sr Y + e + 0.55 MeV. (a) Suggest,
Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Why? Chemists are concerned with mass relationships in chemical reactions, usually run on a macroscopic scale (grams, kilograms, etc.). To deal with
Why? Nuclear Fission and Fusion Fission and fusion are two processes that alter the nucleus of an atom. Nuclear fission provides the energy in nuclear power plants and fusion is the source of the sun s
Radiological Protection For practical purposes of assessing and regulating the hazards of ionizing radiation to workers and the general population, weighting factors are used. A radiation weighting factor
Chapter 4 & 25 Notes Atomic Structure and Nuclear Chemistry Page 1 DEFINING THE ATOM Early Models of the Atom In this chapter, we will look into the tiny fundamental particles that make up matter. An atom
Nuclear Science A Guide to the Nuclear Science Wall Chart 2003 Contemporary Physics Education Project (CPEP) Chapter 15 Radiation in the Environment 1 Many forms of radiation are encountered in the natural
Potassium-Argon (K-Ar) Dating K-Ar Dating In 10,000 K atoms: 9326 39 K 673 41 K 1 40 K Potassium Decay Potassium Decay Potassium Decay Argon About 1% of atmosphere is argon Three stable isotopes of argon
The Universe Inside of You: Where do the atoms in your body come from? Matthew Mumpower University of Notre Dame Thursday June 27th 2013 Nucleosynthesis nu cle o syn the sis The formation of new atomic
.1.1 Measure the motion of objects to understand.1.1 Develop graphical, the relationships among distance, velocity and mathematical, and pictorial acceleration. Develop deeper understanding through representations
Chapter 7: Radioactivity and Nuclear Chemistry Problems: -20, 24-30, 32-46, 49-70, 74-88, 99-0 7.2 THE DISCOVERY OF RADIOACTIVITY In 896, a French physicist named Henri Becquerel discovered that uranium-containing
CHAPTER 13 NUCLEAR STRUCTURE NUCLEAR FORCE The nucleus is help firmly together by the nuclear or strong force, We can estimate the nuclear force by observing that protons residing about 1fm = 10-15m apart
The Physics of Energy sources Nuclear Fission B. Maffei Bruno.email@example.com Nuclear Fission 1 Introduction! We saw previously from the Binding energy vs A curve that heavy nuclei (above A~120)
Key Questions & Exercises Chem 115 POGIL Worksheet - Week 4 Moles & Stoichiometry Answers 1. The atomic weight of carbon is 12.0107 u, so a mole of carbon has a mass of 12.0107 g. Why doesn t a mole of
Lecture 28 High Temperature Geochemistry Formation of chemical elements Reading this week: White Ch 8.1 8.4.1(dig. 313-326) and Ch 10.1 to 10.5.3 (dig. 421-464) Today 1. Stellar processes 2. nucleosynthesis
PS-2.1 Compare the subatomic particles (protons, neutrons, electrons) of an atom with regard to mass, location, and charge, and explain how these particles affect the properties of an atom (including identity,
Section 7: In this section, we present a basic description of atomic nuclei, the stored energy contained within them, their occurrence and stability Basic Nuclear Concepts EARLY DISCOVERIES [see also Section
CLASS TEST GRADE PHYSICAL SCIENCES: CHEMISTRY Test 6: Chemical change MARKS: 45 TIME: hour INSTRUCTIONS AND INFORMATION. Answer ALL the questions. 2. You may use non-programmable calculators. 3. You may
Nuclear Reactions- chap.31 Fission vs. fusion mass defect..e=mc 2 Binding energy..e=mc 2 Alpha, beta, gamma oh my! Definitions A nucleon is a general term to denote a nuclear particle - that is, either
Instructors Guide: Atoms and Their Isotopes Standards Connections Connections to NSTA Standards for Science Teacher Preparation C.3.a.1 Fundamental structures of atoms and molecules. C.3.b.27 Applications
SACE Stage 1 Chemistry - The Essentials 1. Structure and Properties of the Atom 1.1 Atoms: A simple definition of the atom is that it is the smallest particle that contains the properties of that element.
1 MCQ - ENERGY and CLIMATE 1. The volume of a given mass of water at a temperature of T 1 is V 1. The volume increases to V 2 at temperature T 2. The coefficient of volume expansion of water may be calculated
Radon What is radon? Radon is a radioactive gas. It is colorless, odorless, tasteless, and chemically inert. Unless you test for it, there is no way of telling how much is present. Radon is formed by the
NUCLEAR FISSION DOE-HDBK-101/1-3 Atomic and Nuclear Physics NUCLEAR FISSION Nuclear fission is a process in which an atom splits and releases energy, fission products, and neutrons. The neutrons released
INFORMATION SHEET October 2 FINAL RADON AND HEALTH What is radon and where does it come from? Radon is a natural radioactive gas without odour, colour or taste. It cannot be detected without special equipment.
Production and Decay of Radioisotopes A resource for NSW HSC Chemistry and Physics Teachers and Students November 2011 Production and Decay of Radioisotopes This document covers a number of outcomes from
Nuclear fission -Fission: what is it? -The main steps toward nuclear energy -How does fission work? -Chain reactions What is nuclear fission? Nuclear fission is when a nucleus break into two or more nuclei.
RDCH 702: Lecture 10 Radiochemistry in reactors Readings: Radiochemistry in Light Water Reactors, Chapter 3 (on readings webpage and lecture webpage) Outline Speciation in irradiated fuel Utilization of
1 The Atom Unit 3 Atomic Structure And Nuclear Chemistry What are the basic parts of an atom? How is an atom identified? What is nuclear chemistry? How is a nuclear equation written? Atom Smallest particle
EXPERIMENT 4 The Periodic Table - Atoms and Elements INTRODUCTION Primary substances, called elements, build all the materials around you. There are more than 109 different elements known today. The elements
Conceptual Physics Fundamentals Chapter 16: THE ATOMIC NUCLEUS AND RADIOACTIVITY This lecture will help you understand: Radioactivity Alpha, Beta, and Gamma Rays The Atomic Nucleus and the Strong Force
Chapter 1: Moles and equations 1 Learning outcomes you should be able to: define and use the terms: relative atomic mass, isotopic mass and formula mass based on the 12 C scale perform calculations, including
Name CHEM 103 Spring 2006 Final Exam 5 June 2006 Multiple Choice (5 points each) Write the letter of the choice that best completes the statement or answers the question in the blank provided 1. An aqueous
ABSTRACT Comparison of Activity Determination of Radium 226 in FUSRAP Soil using Various Energy Lines - 12299 Brian Tucker*, Jough Donakowski**, David Hays*** *Shaw Environmental & Infrastructure, Stoughton,
4. The Nucleus The last several chapters have shown that an understanding of the behavior of atomic electrons can lead to an understanding of the regularities associated with chemical reactions as well
Natural and Man-Made Radiation Sources All living creatures, from the beginning of time, have been, and are still being, exposed to radiation. This chapter will discuss the sources of this radiation, which
ATOMIC THEORY The smallest component of an element that uniquely defines the identity of that element is called an atom. Individual atoms are extremely small. It would take about fifty million atoms in
Fukushima Accident: Radioactive Releases and Potential Dose Consequences Peter F. Caracappa, Ph.D., CHP Rensselaer Polytechnic Institute ANS Annual Meeting Special Session: The Accident at Fukushima Daiichi
FISSION OBJECTIVES At the conclusion of this lesson the trainee will be able to: 1. Explain where the energy released by fission comes from (mass to energy conversion). 2. Write a typical fission reaction.
CHAPTER 0 2 SECTION Nuclear Changes Nuclear Fission and Fusion KEY IDEAS As you read this section, keep these questions in mind: What holds the nucleus of an atom together? What happens when the nucleus
Tutorial 4.6 Gamma Spectrum Analysis Slide 1. Gamma Spectrum Analysis In this module, we will apply the concepts that were discussed in Tutorial 4.1, Interactions of Radiation with Matter. Slide 2. Learning
Introduction to Nuclear Physics 1. Atomic Structure and the Periodic Table According to the Bohr-Rutherford model of the atom, also called the solar system model, the atom consists of a central nucleus
9 th Grade Physical Science Springfield Local Schools Common Course Syllabi Course Description The purpose of the Physical Science course is to satisfy the Ohio Core science graduation requirement. The
1. The elements on the Periodic Table are arranged in order of increasing A) atomic mass B) atomic number C) molar mass D) oxidation number 2. Which list of elements consists of a metal, a metalloid, and
1. The atomic number of an atom is always equal to the total number of A. neutrons in the nucleus B. protons in the nucleus 2. All of the atoms of argon have the same A. mass number B. atomic number C.
ORTEC DET-SW-UPG Latest Software Features Three Search Modes: Gamma/Neutron total count rate. SNM search mode. Sliding average "monitor" mode. (NEW) User choice of identification schemes: Classify mode
1. Which phrase describes an atom? A) a negatively charged nucleus surrounded by positively charged protons B) a negatively charged nucleus surrounded by positively charged electrons C) a positively charged
KNOWLEDGE: K1.01 [2.7/2.8] B558 Fission fragments or daughters that have a substantial neutron absorption cross section and are not fissionable are called... A. fissile materials. B. fission product poisons.
COMPENDIUM OF EPA-APPROVED ANALYTICAL METHODS FOR MEASURING RADIONUCLIDES IN DRINKING WATER June 1998 Prepared by the Office of Environmental Policy and Assistance Air, Water and Radiation Division (EH-412)
Chapter 7: The Fires of Nuclear Fission What is nuclear fission? Is using nuclear energy safe for humans and the environment? Is nuclear energy better to use than electric generated energy? What happens
Radiometric Dating why radiometric? although several different dating techniques are employed, all but radiometric dating is able to estimate ages in timescales relevant to astronomers. How it works Radiometric
Lecture 40 Chapter 34 Nuclear Fission & Fusion Nuclear Power Final Exam - Monday Dec. 20, 1045-1315 Review Lecture - Mon. Dec. 13 7-Dec-10 Short-Range Strong Nuclear Force The strong force is most effective
3/31/16 NAME: PD 3 1. Given the equation representing a nuclear reaction in which X represents a nuclide: Which nuclide is represented by X? 2. Which nuclear emission has the greatest mass and the least
Take notes while watching the following video tutorials to prepare for the Atomic Structure and Nuclear Chemistry Activity. Atomic Structure Introduction dabe page 1 Atoms & Elements Part 0: Atomic Structure
PHY 192 Half Life 1 Radioactivity III: Measurement of Half Life. Introduction This experiment will once again use the apparatus of the first experiment, this time to measure radiation intensity as a function
AP Physics 1 and 2 Lab Investigations Student Guide to Data Analysis New York, NY. College Board, Advanced Placement, Advanced Placement Program, AP, AP Central, and the acorn logo are registered trademarks
5: The Neutron Cycle B. Rouben McMaster University Course EP 4D03/6D03 Nuclear Reactor Analysis (Reactor Physics) 2015 Sept.-Dec. 2015 September 1 Reaction rates Table of Contents Reactor multiplication
Measurement of Germanium Detector Efficiency Marcus H. Wiggs 2009 Notre Dame Physics REU Advisor: Dr. Philippe Collon Mentors: Matthew Bowers, Daniel Robertson, Chris Schmitt ABSTRACT: A possible discrepancy
Atoms and Ions (adapted from Chemistry A Guided Inquiry, Moog, R. S. and Farrell, J. J.) There are 118 different elements currently on the periodic table. With the exception of technetium, all the elements
Nuclear energy - energy from the atomic nucleus. Nuclear fission (i.e. splitting of nuclei) and nuclear fusion (i.e. combining of nuclei) release enormous amounts of energy. Number of protons determines
CHAPTER 13 Page 1 Reaction Rates and Chemical Kinetics Several factors affect the rate at which a reaction occurs. Some reactions are instantaneous while others are extremely slow. Whether a commercial
Test 2 f14 Multiple Choice Identify the choice that best completes the statement or answers the question. 1. Carbon cycles through the Earth system. During photosynthesis, carbon is a. released from wood
Hf Cd Na Nb Lr Ho Bi Ce u Ac I Fl Fr Mo i Md Co P Pa Tc Uut Rh K N Dy Cl N Am b At Md H Y Bh Cm H Bi s Mo Uus Lu P F Cu Ar Ag Mg K Thomas Jefferson National Accelerator Facility - Office of cience ducation
9 Radiological aspects The objective of this chapter is to provide criteria with which to assess the safety of drinking-water with respect to its radionuclide content. The Guidelines do not differentiate
CHEM 10113, Quiz 2 September 7, 2011 Name (please print) All answers must use the correct number of significant figures, and must show units! IA Periodic Table of the Elements VIIIA (1) (18) 1 2 1 H IIA
2 ATOMIC SYSTEMATICS AND NUCLEAR STRUCTURE In this chapter the principles and systematics of atomic and nuclear physics are summarised briefly, in order to introduce the existence and characteristics of
Nuclear Reactions Fission And Fusion Describe and give an example of artificial (induced) transmutation Construct and complete nuclear reaction equations Artificial transmutation is the changing or manipulation