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textbook:nrctextbook:chapter6 [2025-03-25 15:33]
Merja Herzig 		textbook:nrctextbook:chapter6 [2025-05-07 12:01] (current)
Merja Herzig
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 +{{anchor:curie_ci}}
 ### ###
 Earlier //Curie// (Ci) was used as the activity unit. One Curie is  3.7×10<sup>10</sup> decays in second and thus Earlier //Curie// (Ci) was used as the activity unit. One Curie is  3.7×10<sup>10</sup> decays in second and thus
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 +{{anchor:dps}} 
 +{{anchor:dpm}}
 ### ###
 Sometimes [[textbook:nrctextbook:chapter6#activity|activities]] are expressed as a dps unit, meaning disintegrations per second which are equal to activities presented as [[textbook:nrctextbook:chapter6#becquerel|Becquerels]]. In some instances, for example in [[textbook:nrctextbook:chapter12|liquid scintillation counting]], activity is also presented as //dpm// units (disintegrations per minute). One dpm is 1/60 dps or 16.7 mBq. Sometimes [[textbook:nrctextbook:chapter6#activity|activities]] are expressed as a dps unit, meaning disintegrations per second which are equal to activities presented as [[textbook:nrctextbook:chapter6#becquerel|Becquerels]]. In some instances, for example in [[textbook:nrctextbook:chapter12|liquid scintillation counting]], activity is also presented as //dpm// units (disintegrations per minute). One dpm is 1/60 dps or 16.7 mBq.
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 {{:textbook:nrctextbook:individual_and_total_activities_of_two_coexisting_radionuclides_as_a_function_of_time_fig_6_2.png |}} {{:textbook:nrctextbook:individual_and_total_activities_of_two_coexisting_radionuclides_as_a_function_of_time_fig_6_2.png |}}
  
-Figure VI.2. Individual and total activities of two coexisting radionuclides as a function of time. Top: activity in linear scale. Bottom: activity in logarithmic scale. Diamond (blue): Radionuclide with a half-life of 3 hours. Square (red): radionuclide with a half-life of 12 hours. Triangle (green): total activity.+Figure VI.2. Individual and total activities of two coexisting radionuclides as a function of time. Top: activity in linear scale. Bottom: activity in logarithmic scale. Diamond (blue): Radionuclide with a [[textbook:nrctextbook:chapter6#half_life|half-life]] of 3 hours. Square (red): radionuclide with a half-life of 12 hours. Triangle (green): total activity.
  
-  * For [[textbook:nrctextbook:chapter4#long_lived_radionuclides|long-lived radionuclides]] for which the [[textbook:nrctextbook:chapter6#activity|activity]] decreases so slowly that we cannot observe its decrease the half-life is determined by measuring both the activity and the mass of the radionuclide and calculating half-life from the equation $t_{1/2} = \frac{\ln 2 \times m \times N_A}{A \times M}$.+  * For [[textbook:nrctextbook:chapter4#long_lived_radionuclides|long-lived radionuclides]] for which the [[textbook:nrctextbook:chapter6#activity|activity]] decreases so slowly that we cannot observe its decrease the [[textbook:nrctextbook:chapter6#half_life|half-life]] is determined by measuring both the [[textbook:nrctextbook:chapter6#activity|activity]] and the mass of the radionuclide and calculating half-life from the equation $t_{1/2} = \frac{\ln 2 \times m \times N_A}{A \times M}$.
  
 ### ###
-For example, when the half-life is 106 years the activity decreases by 0.00007% in one year. Small differences in activity like this cannot be measured. To determine the half-life of long-lived radionuclides we need to measure the mass (m) of the radionuclide and count rate (R) obtained from the activity measurement. In addition, we also need to accurately know the counting efficiency (E) of the measurement system. If, for example, we have 1.27 mg of <sup>232</sup>Th and the count rate obtained from its measurement is 2.65 cps and counting efficiency of the measurement system +For example, when the [[textbook:nrctextbook:chapter6#half_life|half-life]] is 106 years the [[textbook:nrctextbook:chapter6#activity|activity]] decreases by 0.00007% in one year. Small differences in activity like this cannot be measured. To determine the half-life of [[textbook:nrctextbook:chapter4#long_lived_radionuclides|long-lived radionuclides]] we need to measure the mass (m) of the radionuclide and count rate (R) obtained from the activity measurement. In addition, we also need to accurately know the counting efficiency (E) of the measurement system. If, for example, we have 1.27 mg of <sup>232</sup>Th and the count rate obtained from its measurement is 2.65 cps and counting efficiency of the measurement system 
 is 51.5% (0.515) the activity of the sample is $A = \frac{R}{E} = \frac{2.65 \, \text{s}^{-1}}{0.515} = 5.15 \, \text{Bq}$. The number of thorium atoms in the sample is $1.27 \cdot 10^{-3} \, \text{g} \times \frac{6.023 \cdot 10^{23} \, \text{atoms/mole}}{232.0 \, \text{g/mole}} = 3.295 \cdot 10^{18}$. is 51.5% (0.515) the activity of the sample is $A = \frac{R}{E} = \frac{2.65 \, \text{s}^{-1}}{0.515} = 5.15 \, \text{Bq}$. The number of thorium atoms in the sample is $1.27 \cdot 10^{-3} \, \text{g} \times \frac{6.023 \cdot 10^{23} \, \text{atoms/mole}}{232.0 \, \text{g/mole}} = 3.295 \cdot 10^{18}$.
 Now the half-life can be calculated from the equation $t_{1/2} = \left( \frac{\ln 2}{A} \right) \times N = \frac{0.693 \times 3.295 \cdot 10^{18}}{5.15 \, \text{s}^{-1}} = 4.44 \cdot 10^{17} \, \text{s} = 1.41 \cdot 10^{10} \, \text{a}$. This method can also in principle be used to measure half-lives of shorter lived radionuclides but in their case the accurate measurement of the mass may either completely exclude the use of this method or at least results in inaccurate value. Now the half-life can be calculated from the equation $t_{1/2} = \left( \frac{\ln 2}{A} \right) \times N = \frac{0.693 \times 3.295 \cdot 10^{18}}{5.15 \, \text{s}^{-1}} = 4.44 \cdot 10^{17} \, \text{s} = 1.41 \cdot 10^{10} \, \text{a}$. This method can also in principle be used to measure half-lives of shorter lived radionuclides but in their case the accurate measurement of the mass may either completely exclude the use of this method or at least results in inaccurate value.
 ### ###
  
 +{{anchor:activity_equilibria}}
 ===== 6.7. Activity equilibria of consecutive decays ===== ===== 6.7. Activity equilibria of consecutive decays =====
  
 ### ###
-In the following we discuss two consecutive decay processes and their activity equilibria. Equilibrium means that the activities of the parent and daughter nuclides are the same. Consecutive decays and their equilibria are especially important in natural decay chains of uranium and thorium and in beta decays chains following fissions. In these chains there are typically more than two radionuclides present at the same time. Their equilibrium calculations are rather complicated and  +In the following we discuss two consecutive decay processes and their activity equilibria. //Equilibrium means that the activities of the parent and daughter nuclides are the same//. Consecutive decays and their equilibria are especially important in [[textbook:nrctextbook:chapter4#decay_chains|natural decay chains]] of uranium and thorium and in [[textbook:nrctextbook:chapter6#beta_decay_chains|beta decay chains]] following fissions. In these chains there are typically more than two [[textbook:nrctextbook:chapter4|radionuclides]] present at the same time. Their equilibrium calculations are rather complicated and require computer programs. An example of such calculation is given in [[textbook:nrctextbook:chapter6#figure_67|Figure VI.7]] (at the end of this chapter). Here we, however, focus on equilibrium between two [[textbook:nrctextbook:chapter4|radionuclides]], the //parent nuclide////Italic Text// and the //daughter nuclide//. When considering two consecutive decays the number of the parent nuclei (N<sub>1</sub>) depends only on its characteristic decay rate, i.e. [[textbook:nrctextbook:chapter6#decay_constant|decay constant]] (λ<sub>1</sub>). The number of the daughter nuclei (N<sub>2</sub>) 
-require computer programs. An example of such calculation is given at the end of the chapter. Here we, however, focus on equilibrium between two radionuclides, the parent nuclide and the daughter nuclide. When considering two consecutive decays the number of the parent nuclei (N<sub>1</sub>) depends only on its characteristic decay rate, i.e. decay constant (λ<sub>1</sub>). The number of the daughter nuclei (N<sub>2</sub>) +
 in turn is dependent both on its own decay rate (λ<sub>2</sub>) and on the parent's decay rate (λ<sub>1</sub>). The former determines the decay (decrease) of the daughter nuclides while the latter determines the ingrowth from the parent (increase). Thus the number of daughter nuclei is in turn is dependent both on its own decay rate (λ<sub>2</sub>) and on the parent's decay rate (λ<sub>1</sub>). The former determines the decay (decrease) of the daughter nuclides while the latter determines the ingrowth from the parent (increase). Thus the number of daughter nuclei is
 ### ###
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 +{{anchor:equation_614}}
 The solution of this equation with respect to N<sub>2</sub> is   The solution of this equation with respect to N<sub>2</sub> is  
  
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 ### ###
-where //N<sub>1</sub><sup>0</sup>// and //N<sub>2</sub><sup>0</sup>// are the numbers of parent and daughter, respectively, at time point zero (t=0). The first term in the equation presents the number of daughter nuclei due to ingrowth and the decay of ingrown nuclei while the second term represents decay of those daughter nuclei that were present at time point zero. Figure VI.3 gives a graphical presentation of the Eq. VI.XIV for a case where the half-life of the daughter is clearly shorter than that of the parent nuclide, i.e. its shows the ingrowth of the daughter nuclide activity as a function of the number half-lives of the daughter nuclide. Activity is here presented as the percentage of the maximum activity obtainable.+where //N<sub>1</sub><sup>0</sup>// and //N<sub>2</sub><sup>0</sup>// are the numbers of parent and daughter, respectively, at time point zero (t=0). The first term in the equation presents the number of daughter nuclei due to ingrowth and the decay of ingrown nuclei while the second term represents decay of those daughter nuclei that were present at time point zero. [[textbook:nrctextbook:chapter6#figure_63|Figure VI.3]] gives a graphical presentation of the [[textbook:nrctextbook:chapter6#equation_614|Eq. VI.XIV]] for a case where the [[textbook:nrctextbook:chapter6#half_life|half-life]] of the daughter is clearly shorter than that of the parent nuclide, i.e. its shows the ingrowth of the daughter nuclide [[textbook:nrctextbook:chapter6#activity|activity]] as a function of the number half-lives of the daughter nuclide. Activity is here presented as the percentage of the maximum activity obtainable.
 ### ###
- + {{anchor:figure_63}}
  
  
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-   * secular equilibrium, in which the half-life of the parent nuclide is very long and the half-life of the daughter nuclide is considerably shorter than that of the parent   +   * [[textbook:nrctextbook:chapter6#secular_equilibrium|Secular equilibrium]], in which the [[textbook:nrctextbook:chapter6#half_life|half-life]] of the parent nuclide is very long and the half-life of the daughter nuclide is considerably shorter than that of the parent   
-  * transient equilibrium, in which the half-life of the parent is so short that we observe decrease in its activity in a reasonable time and the half-life of the daughter nuclide is shorter than that of the parent   +  * [[textbook:nrctextbook:chapter6#trancient_equilibrium|Trancient equilibrium]], in which the half-life of the parent is so short that we observe decrease in its activity in a reasonable time and the half-life of the daughter nuclide is shorter than that of the parent   
-  * no-equilibrium, in which the half-life of the parent nuclide is shorter than that of the daughter  +  * [[textbook:nrctextbook:chapter6#non_equilibrium|Non-equilibrium]], in which the half-life of the parent nuclide is shorter than that of the daughter 
  
 +{{anchor:secular_equilibrium}}
 ==== 6.7.1. Secular equilibrium ==== ==== 6.7.1. Secular equilibrium ====
  
 ### ###
-An example of a secular equilibrium is case where the parent nuclide is the fission product <sup>137</sup>Cs which decays by beta decay process to 137mBa which in turn decays by internal transition process to stable <sup>137</sup>Ba. The half-life of <sup>137</sup>Cs is 30 years while the half-life of <sup>137</sup>Ba is only 2.6 minutes. Figure VI.3 shows the development of activities in a case when <sup>137m</sup>Ba has been chemically separated from its parent <sup>137</sup>Cs with BaSO<sub>4</sub> precipitation and both <sup>137m</sup>Ba-bearing precipitate and remaining solution containing only <sup>137</sup>Cs are measured for their <sup>137</sup>Cs and 137mBa activities immediately after chemical separation and measurements are repeated as a function of time. <sup>137m</sup>Ba in precipitate +An example of a secular equilibrium is case where the parent nuclide is the [[textbook:nrctextbook:chapter5#fission|fission]] product <sup>137</sup>Cs which decays by [[textbook:nrctextbook:chapter5#beta_decay|beta decay]] process to <sup>137m</sup>Ba which in turn decays by [[textbook:nrctextbook:chapter5#internal_transition|internal transition]] process to stable <sup>137</sup>Ba. The [[textbook:nrctextbook:chapter6#half_life|half-life]] of <sup>137</sup>Cs is 30 years while the half-life of <sup>137</sup>Ba is only 2.6 minutes. Figure VI.3 shows the development of [[textbook:nrctextbook:chapter6#activity|activities]] in a case when <sup>137m</sup>Ba has been chemically separated from its parent <sup>137</sup>Cs with BaSO<sub>4</sub> precipitation and both <sup>137m</sup>Ba-bearing precipitate and remaining solution containing only <sup>137</sup>Cs are measured for their <sup>137</sup>Cs and <sup>137m</sup>Ba activities immediately after chemical separation and measurements are repeated as a function of time. <sup>137m</sup>Ba in precipitate 
 decays following its half-life on 2.6 minutes (red). The activity of <sup>137</sup>Cs in the solution phase (blue) remains practically constant since observation time (30 min) is extremely short compared to the half-life of <sup>137</sup>Cs (30 years). <sup>137m</sup>Ba in the solution (green) starts immediately after chemical separation to grow in and attains equilibrium with <sup>137</sup>Cs in about ten half-lives of the daughter, i.e. half an hour. Since the activities of <sup>137m</sup>Ba and <sup>137</sup>Cs are the same the total activity (curve 4) is twice the parent nuclide. decays following its half-life on 2.6 minutes (red). The activity of <sup>137</sup>Cs in the solution phase (blue) remains practically constant since observation time (30 min) is extremely short compared to the half-life of <sup>137</sup>Cs (30 years). <sup>137m</sup>Ba in the solution (green) starts immediately after chemical separation to grow in and attains equilibrium with <sup>137</sup>Cs in about ten half-lives of the daughter, i.e. half an hour. Since the activities of <sup>137m</sup>Ba and <sup>137</sup>Cs are the same the total activity (curve 4) is twice the parent nuclide.
 ### ###
      
-  
- 
 ### ###
-Secular does not mean eternal. Looking at a very long-term all secular equilibria are transient. How long-term we need to look depends on the half-life of the parent. For example, if we looked the example describe above for a hundred years period the equilibrium would appear as transient equilibrium. For <sup>230</sup>Th (t<sub>1/2</sub> = 75000 y), for example, the transient equilibrium period with <sup>226</sup>Ra would be hundreds of thousands of years.+Secular does not mean eternal. Looking at a very long-term all secular equilibria are [[textbook:nrctextbook:chapter6#transient_equilibrium|transient]]. How long-term we need to look depends on the half-life of the parent. For example, if we looked the example describe above for a hundred years period the equilibrium would appear as [[textbook:nrctextbook:chapter6#transient_equilibrium|transient equilibrium]]. For <sup>230</sup>Th (t<sub>1/2</sub> = 75000 y), for example, the transient equilibrium period with <sup>226</sup>Ra would be hundreds of thousands of years.
 ### ###
    
 {{:textbook:nrctextbook:development_of_secular_equilibrium_fig_6_4.png |}} {{:textbook:nrctextbook:development_of_secular_equilibrium_fig_6_4.png |}}
-Figure VI.4. Development of a secular radioactive equilibrium in which the half-life of the parent nuclide very long and the half-life on the daughter nuclide (<sup>137m</sup>Ba, t<sub>½</sub> = 2.6 min) is considerably shorter than that of the parent (<sup>137</sup>Cs, t<sub>½</sub> = 30 a). Left: activity on linear scale. Right: activity on logarithmic scale. Blue: <sup>137</sup>Cs. Red: <sup>137m</sup>Ba if separated from <sup>137</sup>Cs. Green: ingrowth of <sup>137m</sup>Ba with <sup>137</sup>Cs after separation of <sup>137m</sup>Ba from <sup>137</sup>Cs.   +Figure VI.4. Development of a secular radioactive equilibrium in which the half-life of the parent nuclide very long and the half-life on the daughter nuclide (<sup>137m</sup>Ba, t<sub>½</sub> = 2.6 min) is considerably shorter than that of the parent (<sup>137</sup>Cs, t<sub>½</sub> = 30 a). Left: activity on linear scale. Right: activity on logarithmic scale. Blue: <sup>137</sup>Cs. Red: <sup>137m</sup>Ba if separated from <sup>137</sup>Cs. Green: ingrowth of <sup>137m</sup>Ba with <sup>137</sup>Cs after separation of <sup>137m</sup>Ba from <sup>137</sup>Cs.  
 +  
 +{{anchor:transient_equilibrium}}
 ==== 6.7.2. Transient equilibrium ==== ==== 6.7.2. Transient equilibrium ====
 +{{anchor:beta_decay_chain}}
 ### ###
-An example of transient equilibrium is a beta decay chain where <sup>140</sup>Ba decays to <sup>140</sup>La and the latter to stable <sup>140</sup>Ce.+An example of transient equilibrium is a [[textbook:nrctextbook:chapter5#beta_decay|beta decay]] chain where <sup>140</sup>Ba decays to <sup>140</sup>La and the latter to stable <sup>140</sup>Ce.
 ### ###
    
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 [VI.XV] [VI.XV]
 ;;# ;;#
 +{{anchor:figure_65}}
 {{:textbook:nrctextbook:development_of_transient_equilibrium_fig_6_5.png |}} {{:textbook:nrctextbook:development_of_transient_equilibrium_fig_6_5.png |}}
 Figure VI.5. Development of a transient radioactive equilibrium in which the half-life of the parent (<sup>140</sup>La, t<sub>½</sub> = 40.2 d) is so short that we observe decrease in its activity in a reasonable time and the half-life on the daughter nuclide (<sup>140</sup>Ba, t<sub>½</sub> = 12.8 d) is shorter than that of the parent. Left: activity on linear scale. Right: activity on logarithmic scale. Blue: <sup>140</sup>La. Red:  <sup>140</sup>Ba.   Figure VI.5. Development of a transient radioactive equilibrium in which the half-life of the parent (<sup>140</sup>La, t<sub>½</sub> = 40.2 d) is so short that we observe decrease in its activity in a reasonable time and the half-life on the daughter nuclide (<sup>140</sup>Ba, t<sub>½</sub> = 12.8 d) is shorter than that of the parent. Left: activity on linear scale. Right: activity on logarithmic scale. Blue: <sup>140</sup>La. Red:  <sup>140</sup>Ba.  
  
 ### ###
-The transient equilibrium is otherwise identical with the secular equilibrium except that the parent nuclide decays with such a short rate that we observe decrease in activity in a reasonable time. After attaining the equilibrium in about ten half-lives of the daughter, about two weeks in case of Fig.VI.5, both parent and the daughter decay at the rate of the parent nuclide. Also, after attaining the equilibrium the total activity is twice the activity of the parent nuclide.+The transient equilibrium is otherwise identical with the [[textbook:nrctextbook:chapter6#secular_equilibrium|secular equilibrium]] except that the parent nuclide decays with such a short rate that we observe decrease in [[textbook:nrctextbook:chapter6#activity|activity]] in a reasonable time. After attaining the equilibrium in about ten half-lives of the daughter, about two weeks in case of [[textbook:nrctextbook:chapter6#figure_65|Figure VI.5]], both parent and the daughter decay at the rate of the parent nuclide. Also, after attaining the equilibrium the total activity is twice the activity of the parent nuclide.
 ### ###
  
- +{{anchor:non_equilibrium}} 
 ==== 6.7.3. No-equilibrium ==== ==== 6.7.3. No-equilibrium ====
  
 ### ###
-An example of no-equilibrium case is the alpha decay pair <sup>218</sup>Po (t<sub>½</sub> = 3 min) → <sup>214</sup>Pb (t<sub>½</sub> = 26.8 min), where the half-life of the parent is shorter than that of the daughter. No equilibrium develops since the parent decays before the daughter.+An example of no-equilibrium case is the [[textbook:nrctextbook:chapter5#alpha|alpha decay]] pair <sup>218</sup>Po (t<sub>½</sub> = 3 min) → <sup>214</sup>Pb (t<sub>½</sub> = 26.8 min), where the [[textbook:nrctextbook:chapter6#half_life|half-life]] of the parent is shorter than that of the daughter. No equilibrium develops since the parent decays before the daughter.
 ### ###
    
 {{:textbook:nrctextbook:development_of_activities_no-equilibrium_fig_6_6.png |}} {{:textbook:nrctextbook:development_of_activities_no-equilibrium_fig_6_6.png |}}
 Figure VI.6. Development of activities in case of no radioactive equilibrium, in which the half-life of the parent nuclide (<sup>218</sup>Po, t<sub>½</sub> = 3 min) is shorter than that of the daughter (<sup>214</sup>Pb, t<sub>½</sub> = 26.8 min).  Figure VI.6. Development of activities in case of no radioactive equilibrium, in which the half-life of the parent nuclide (<sup>218</sup>Po, t<sub>½</sub> = 3 min) is shorter than that of the daughter (<sup>214</sup>Pb, t<sub>½</sub> = 26.8 min). 
-Left: activity on linear scale. Right: activity on logarithmic scale. Blue: <sup>218</sup>Po . Red: <sup>214</sup>Pb.  +Left: activity on linear scale. Right: activity on logarithmic scale. Blue: <sup>218</sup>Po . Red: <sup>214</sup>Pb. 
 +  
 +{{anchor:equilibria_in_natural_decay_chains}}
 ==== 6.7.4. Equilibria in natural decay chains ==== ==== 6.7.4. Equilibria in natural decay chains ====
 +{{anchor:long_lived_radionuclides}}
 ### ###
-In natural uranium and thorium decay chains there are individual pairs in which there would not be any equilibrium if they were present separately. An example of such pairs in the 238U decay chain is <sup>234</sup>Pa parent (t<sub>½</sub> = 6.7 h) and <sup>234</sup>U daughter (t<sub>½</sub> = 245000 y). They are, however, typically in  +In natural uranium and thorium [[textbook:nrctextbook:chapter4#decay_chains|decay chains]] there are individual pairs in which there would not be any equilibrium if they were present separately. An example of such pairs in the <sup>238</sup>U decay chain is <sup>234</sup>Pa parent (t<sub>½</sub> = 6.7 h) and <sup>234</sup>U daughter (t<sub>½</sub> = 245000 y). They are, however, typically in  
-equilibrium since the grandparent of <sup>234</sup>Pa, <sup>238</sup>U (t<sub>½</sub> = 4.4 × 10<sup>9</sup> y), feeds continually new <sup>234</sup>Pa and they are in equilibrium with each other. Since <sup>238</sup>U has the longest half-life in the whole chain and therefore the activities of all subsequent radionuclides in the chain have the same activity as <sup>238</sup>U supposing that the system has been closed millions of years. In the nature there are chemical processes, such as dissolution into groundwater, that remove some component of the chains which causes disequilibria in the chains.+equilibrium since the grandparent of <sup>234</sup>Pa, <sup>238</sup>U (t<sub>½</sub> = 4.4 × 10<sup>9</sup> y), feeds continually new <sup>234</sup>Pa and they are in equilibrium with each other. Since <sup>238</sup>U has the longest [[textbook:nrctextbook:chapter6#half_life|half-life]] in the whole chain and therefore the [[textbook:nrctextbook:chapter6#activity|activities]] of all subsequent [[textbook:nrctextbook:chapter4|radionuclides]] in the chain have the same activity as <sup>238</sup>U supposing that the system has been closed millions of years. In the nature there are chemical processes, such as dissolution into groundwater, that remove some component of the chains which causes disequilibria in the chains.
 ### ###
      
  
 ### ###
-In the geosphere in the natural decay chains beginning from <sup>238</sup>U, <sup>235</sup>U and <sup>232</sup>Th the activities of all members are the same in each series, identical with those of <sup>238</sup>U, <sup>235</sup>U and <sup>232</sup>Th, in systems which have been preserved without disturbances long enough. In such case the series is in equilibrium state. If some component of the series is removed, by dissolution for example, the equilibrium is disturbed and a disequilibrium state is created. If for example uranium is dissolved from a primary  +In the geosphere in the natural [[textbook:nrctextbook:chapter4#decay_chains|decay chains]] beginning from <sup>238</sup>U, <sup>235</sup>U and <sup>232</sup>Th the activities of all members are the same in each series, identical with those of <sup>238</sup>U, <sup>235</sup>U and <sup>232</sup>Th, in systems which have been preserved without disturbances long enough. In such case the series is in equilibrium state. If some component of the series is removed, by dissolution for example, the equilibrium is disturbed and a disequilibrium state is created. If for example uranium is dissolved from a primary uranium-bearing mineral by oxidation the remaining radionuclides in the series will be supported by its most [[textbook:nrctextbook:chapter4#long_lived_radionuclides|long-lived radionuclide]]  which is <sup>230</sup>Th in case of <sup>238</sup>U series. If the dissolved uranium will then be precipitated somewhere out of the system a new equilibrium will start to develop. The time required to attain the equilibrium is governed by the most long-lived daughter [[textbook:nrctextbook:chapter4|radionuclide]] in the series, <sup>230</sup>Th in case of <sup>238</sup>U series. The [[textbook:nrctextbook:chapter6#half_life|half-life]] of <sup>230</sup>Th is 75000 years and this time is required to attain 50% of the equilibrium, 150000 years for 75% equilibrium, 225000 years for 87.5% equilibrium and eight half-lives, 600000 years, for 99.6% equilibrium. The disequilibria can be utilized in dating geological events. If for example, the <sup>230</sup>Th/<sup>238</sup>U ratio is 0.5 in a uranium mineral we may calculate that this uranium mineral was precipitated 75000 years ago.  
-uranium-bearing mineral by oxidation the remaining radionuclides in the series will be supported by its most long-lived radionuclide which is <sup>230</sup>Th in case of <sup>238</sup>U series. If the dissolved uranium will then be precipitated somewhere out of the system a new equilibrium will start to develop. The time required to attain the equilibrium is governed by the most long-lived daughter radionuclide in the  +
-series, <sup>230</sup>Th in case of <sup>238</sup>U series. The half-life of <sup>230</sup>Th is 75000 years and this time is required to attain 50% of the equilibrium, 150000 years for 75% equilibrium, 225000 years for 87.5% equilibrium and eight half-lives, 600000 years, for 99.6% equilibrium. The disequilibria can be  +
-utilized in dating geological events. If for example, the <sup>230</sup>Th/<sup>238</sup>U ratio is 0.5 in a uranium mineral we may calculate that this uranium mineral was precipitated 75000 years ago.  +
  
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-To calculate activities of all members in a series manually is a cumbersome task. Computer programs for this purpose have been fortunately developed. One of them is the Decservis-2 program developed at the Laboratory of Radiochemistry, University of Helsinki, Finland. An example of such calculation carried out by Decservis-2 is shown in Figure VI.6. Here, we assume separation of <sup>226</sup>Ra (1 Bq) from the system and development of equilibrium between<sup> 226</sup>Ra and its progeny in  +To calculate [[textbook:nrctextbook:chapter6#activity|activities]] of all members in a series manually is a cumbersome task. Computer programs for this purpose have been fortunately developed. One of them is the Decservis-2 program developed at the Laboratory of Radiochemistry, University of Helsinki, Finland. An example of such calculation carried out by Decservis-2 is shown in Figure VI.6. Here, we assume separation of <sup>226</sup>Ra (1 Bq) from the system and development of equilibrium between<sup> 226</sup>Ra and its progeny in 10000 years. We have to assume that the gaseous <sup>222</sup>Rn, the daughter of <sup>226</sup>Ra, is not escaped from the system. In the first phase, up to about a month, the equilibrium is attained with <sup>222</sup>Rn, <sup>218</sup>Po, <sup>214</sup>Pb, <sup>214</sup>Bi and <sup>214</sup>Po and the time required for equilibrium is governed by the most long-lived member of these, <sup>222</sup>Rn with a half-life of 3.8 days. In the second phase, up to about 200 years, the equilibrium is attained with <sup>210</sup>Pb, <sup>210</sup>Bi and <sup>210</sup>Po and the time required for equilibrium is governed by the most long-lived member of these, <sup>210</sup>Pb with a half-life of 22 years. The half-life of<sup> 226</sup>Ra is 1600 years and decrease in its activity and correspondingly activities of its progeny can be seen after about 1000 years. 
-10000 years. We have to assume that the gaseous <sup>222</sup>Rn, the daughter of <sup>226</sup>Ra, is not escaped from the system. In the first phase, up to about a month, the equilibrium is attained with <sup>222</sup>Rn, <sup>218</sup>Po,  +
-<sup>214</sup>Pb, <sup>214</sup>Bi and <sup>214</sup>Po and the time required for equilibrium is governed by the most long-lived member of these, <sup>222</sup>Rn with a half-life of 3.8 days. In the second phase, up to about 200 years, the equilibrium is attained with <sup>210</sup>Pb, <sup>210</sup>Bi and <sup>210</sup>Po and the time required for equilibrium is governed by the most long-lived member of these, <sup>210</sup>Pb with a half-life of 22 years. The half-life of<sup> 226</sup>Ra is 1600 years and decrease in its activity and correspondingly activities of its progeny can be seen after about 1000 years. +
  
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 +{{anchor:figure_67}}
 {{:textbook:nrctextbook:attainment_of_radioactive_equilibrium_of_226ra_progeny_fig_6_7.png |}} {{:textbook:nrctextbook:attainment_of_radioactive_equilibrium_of_226ra_progeny_fig_6_7.png |}}
  
textbook/nrctextbook/chapter6.1742913215.txt.gz · Last modified: 2025-03-25 15:33 by Merja Herzig

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