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--- textbook:nrctextbook:chapter6 [2025-03-25 15:59]
Merja Herzig
+++ textbook:nrctextbook:chapter6 [2025-05-07 12:01] (current)
Merja Herzig
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+{{anchor:curie_ci}}
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 Earlier //Curie// (Ci) was used as the activity unit. One Curie is  3.7×10<sup>10</sup> decays in second and thus
@@ Line 124: / Line 124: @@
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+{{anchor:dps}}
+{{anchor:dpm}}
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 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.
@@ Line 251: / Line 252: @@
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-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.
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-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.
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 {{anchor:beta_decay_chain}}
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-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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@@ Line 273: / Line 274: @@
 [VI.XV]
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+{{anchor:figure_65}}
 {{: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.
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-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.
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-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.
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 {{: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).
 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 ====
+{{anchor:long_lived_radionuclides}}
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-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.
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-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.
-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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