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textbook:nrctextbook:chapter5 [2025-03-18 14:41]
Merja Herzig 		textbook:nrctextbook:chapter5 [2025-08-28 16:31] (current)
Merja Herzig
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 {{anchor:fission}} {{anchor:fission}}
 +{{anchor:spontaneous_fission}}
 +
 ===== 5.1.Fission ===== ===== 5.1.Fission =====
  
 ### ###
-In addition to spontaneous fission, which is one of the radioactive decay modes, induced fission is also shortly discussed here. The reason for the spontaneous fission is that the nucleus is too heavy and it is typical only for the heaviest elements (heavier than uranium). In fission, the nucleus splits into two nuclei of lighter elements, for example:+In addition to spontaneous fission, which is one of the radioactive decay modes, [[textbook:nrctextbook:chapter5#induced_fission|induced fission]] is also shortly discussed here. The reason for the spontaneous fission is that the nucleus is too heavy and it is typical only for the heaviest elements (heavier than uranium). In fission, the nucleus splits into two nuclei of lighter elements, for example:
 ### ###
  
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-{{:textbook:nrctextbook:spontaneous_fission_fig_5_1.png?400|}}+{{:textbook:nrctextbook:spontaneous_fission_of_heavy_nuclei.png?400|}} 
 + 
 +Figure V.1. Spontaneous fission of a heavy nucleus into two nuclei of lighter elements.
  
-Figure V.1. Spontaneous fission of a heavy nucleus into two nuclei of lighter elements  +{{anchor:induced_fission}}
-(http://physics.nayland.school.nz/VisualPhysics/NZP-physics%20HTML/17_NuclearEnergy/Chapter17a.html).+
  
 ### ###
-In an induced fission a nucleus is bombarded with a particle, such as a neutron, which results in fission, such as+In an induced fission a nucleus is bombarded with a particle, such as a [[textbook:nrctextbook:chapter2#neutron|neutron]], which results in fission, such as
 ### ###
  
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 (http://chemwiki.ucdavis.edu/Physical_Chemistry/Nuclear_Chemistry/Nuclear_Reactions). (http://chemwiki.ucdavis.edu/Physical_Chemistry/Nuclear_Chemistry/Nuclear_Reactions).
  
 +{{anchor:fission_products}}
 ### ###
 In addition to the lighter elements, called fission products, fission yields into emission of 2-3 neutrons and a large amount of energy, the distribution of which is shown in Table V.I. In addition to the lighter elements, called fission products, fission yields into emission of 2-3 neutrons and a large amount of energy, the distribution of which is shown in Table V.I.
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 ^Kinetic energy of neutrinos from beta decays |10 MeV| ^Kinetic energy of neutrinos from beta decays |10 MeV|
  
 +{{anchor:uranium_spontaneous_fission}}
 ### ###
 In the nature, there is only one nuclide, <sup>238</sup>U that decays spontaneously by fission. Fission is, however, not the only decay mode of <sup>238</sup>U and in fact only 0.005% of it undergoes this decay mode while the rest decays by [[textbook:nrctextbook:chapter5#alpha|alpha decay]]. Spontaneous fission of uranium has its own specific decay [[textbook:nrctextbook:chapter6#half_life|half-life]] which is 8·10<sup>15</sup> a. With transuranium and superheavy elements, spontaneous fission is more common but as with uranium, spontaneous fission is mostly a minor decay mode. For example, all plutonium [[textbook:nrctextbook:chapter2#isotope|isotopes]] with a [[textbook:nrctextbook:chapter2#mass_number|mass number]] between 235 and 244 partly decay by spontaneous fission. There are, however, some heavy radionuclides, such as <sup>256</sup>Cf and <sup>250</sup>No, which decay solely by spontaneous fission. In the nature, there is only one nuclide, <sup>238</sup>U that decays spontaneously by fission. Fission is, however, not the only decay mode of <sup>238</sup>U and in fact only 0.005% of it undergoes this decay mode while the rest decays by [[textbook:nrctextbook:chapter5#alpha|alpha decay]]. Spontaneous fission of uranium has its own specific decay [[textbook:nrctextbook:chapter6#half_life|half-life]] which is 8·10<sup>15</sup> a. With transuranium and superheavy elements, spontaneous fission is more common but as with uranium, spontaneous fission is mostly a minor decay mode. For example, all plutonium [[textbook:nrctextbook:chapter2#isotope|isotopes]] with a [[textbook:nrctextbook:chapter2#mass_number|mass number]] between 235 and 244 partly decay by spontaneous fission. There are, however, some heavy radionuclides, such as <sup>256</sup>Cf and <sup>250</sup>No, which decay solely by spontaneous fission.
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 ### ###
-Fission products, the lighter nuclides formed in fission, are radioactive. The heavy elements, such as uranium, have higher neutron to proton ratios compared to elements formed in fission. In the fission, however, only 2-3 neutrons are released and therefore the fission products have too many neutrons for stability. For example, barium isotopes formed in fission have approximately the same neutron to proton ratio as <sup>238</sup>U, 1.59. The stable barium isotopes, however, have neutron to proton  +Fission products, the lighter nuclides formed in fission, are radioactive. The heavy elements, such as uranium, have higher [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|neutron to proton ratios]] compared to elements formed in fission. In the fission, however, only 2-3 [[textbook:nrctextbook:chapter2#neutron|neutrons]] are released and therefore the fission products have too many neutrons for stability. For example, barium [[textbook:nrctextbook:chapter2#isotope|isotopes]] formed in fission have approximately the same neutron to proton ratio as <sup>238</sup>U, 1.59. The stable barium isotopes, however, have neutron to proton ratio in the range of 1.32-1.46. To obtain stability, the fission products gradually correct their neutron to proton ratio by decaying with [[textbook:nrctextbook:chapter5#beta|beta decay]] (β<sup>-</sup>)  mode, i.e. they transform excess neutrons to [[textbook:nrctextbook:chapter2#proton|protons]] until the nuclide has [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|neutron to proton ratio]] that enables stability. An example of such decay chain is shown in [[textbook:nrctextbook:chapter5#figure_53|Figure V.3]].
-ratio in the range of 1.32-1.46. To obtain stability, the fission products gradually correct their neutron to proton ratio by decaying with β<sup>-</sup> decay mode, i.e. they transform excess neutrons to protons until the nuclide has [[textbook:nrctextbook:chapter3#neutron_to_proton_ratio|neutron to proton ratio]] that enables stability. An example of such decay chain is shown in [[textbook:nrctextbook:chapter5#figure_53|Figure V.3]].+
 ### ###
 {{anchor:figure_53}} {{anchor:figure_53}}
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 ### ###
-There is a large number of fission daughter products. They are, however, not evenly formed at various [[textbook:nrctextbook:chapter2#mass_number|mass numbers]]. Instead, they are concentrated to two mass number ranges with mass numbers between 90-105 and 130-140. Graphical presentation of the fission product yields, the percentage of fissions leading to specified mass number, as a function of mass number results in the formation of a double hump curve given in [[textbook:nrctextbook:chapter5#figure_54|Figure V.4]].  The upper mass range is independent of the fissioning nuclide while the lower mass range shifts into higher mass numbers as the mass of the fissioning nuclide increases.+There is a large number of fission daughter products. They are, however, not evenly formed at various [[textbook:nrctextbook:chapter2#mass_number|mass numbers]]. Instead, they are concentrated to two mass number ranges with mass numbers between 90-105 and 130-140. Graphical presentation of the fission product yields, the percentage of fissions leading to specified mass number, as a function of mass number results in the formation of a double hump curve given in [[textbook:nrctextbook:chapter5#figure_54|Figure V.4]].  The upper mass range is independent of the fissioning [[textbook:nrctextbook:chapter2#nuclide|nuclide]] while the lower mass range shifts into higher mass numbers as the mass of the fissioning nuclide increases.
  
 ### ###
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-{{:textbook:nrctextbook:beta_decays_on_isobaric_line_fig_5_8.png?400|}}+{{:textbook:nrctextbook:beta_decay_on_isobaric_line_2.png?400|}}
  
 Figure V.8. Beta decays on isobaric line A=12. Figure V.8. Beta decays on isobaric line A=12.
  
-==== 5.3.1. Beta decay ==== 
 {{anchor:beta_decay}} {{anchor:beta_decay}}
 +==== 5.3.1. Beta decay ====
 +
  
 ### ###
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 [V.V] [V.V]
 ;;# ;;#
 +{{anchor:beta_spectrum_fig}}
 {{anchor:figure_59}} {{anchor:figure_59}}
  
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 {{anchor:pure_positron_emitters}} {{anchor:pure_positron_emitters}}
 +
 ### ###
 As in [[#5.3.1._beta_decay|beta minus decay]], also positron decay often takes place via the [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter nuclide and the excitation energy is relaxed by [[textbook:nrctextbook:chapter5#internal_transition|internal transition]]. There are, however, some radionuclides, particularly within light positron emitters, that decay solely to ground state. Examples of //pure positron emitter nuclides// are <sup>11</sup>C, <sup>13</sup>N, <sup>15</sup>O, <sup>18</sup>F. [[textbook:nrctextbook:chapter5#figure_511|Figure V.11]] shows examples of both: a pure positron emitter (<sup>18</sup>F) and a nuclide with excited states (<sup>22</sup>Na). As in [[#5.3.1._beta_decay|beta minus decay]], also positron decay often takes place via the [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter nuclide and the excitation energy is relaxed by [[textbook:nrctextbook:chapter5#internal_transition|internal transition]]. There are, however, some radionuclides, particularly within light positron emitters, that decay solely to ground state. Examples of //pure positron emitter nuclides// are <sup>11</sup>C, <sup>13</sup>N, <sup>15</sup>O, <sup>18</sup>F. [[textbook:nrctextbook:chapter5#figure_511|Figure V.11]] shows examples of both: a pure positron emitter (<sup>18</sup>F) and a nuclide with excited states (<sup>22</sup>Na).
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-{{:textbook:nrctextbook:positron_emission_and_positron_annihilation_fig_5_12.png?400|}}+{{:textbook:nrctextbook:positron_emission_and_annihilation.png?400|}}
  
 Figure V.12. Positron emission and positron annihilation. Figure V.12. Positron emission and positron annihilation.
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 Figure V.13. Electron capture, formation of Auger electrons and characteristic X-rays and the ensuing X-ray spectrum. Figure V.13. Electron capture, formation of Auger electrons and characteristic X-rays and the ensuing X-ray spectrum.
 +
 {{anchor:figure_514}} {{anchor:figure_514}}
 {{:textbook:nrctextbook:decay_scheme_of_55fe_fig_5_14.png?400|}} {{:textbook:nrctextbook:decay_scheme_of_55fe_fig_5_14.png?400|}}
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 Figure V.14. Decay scheme of <sup>55</sup>Fe (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983). Figure V.14. Decay scheme of <sup>55</sup>Fe (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).
  
 +{{anchor:odd_even_problem}}
 ==== 5.3.3. Odd-even-problem ==== ==== 5.3.3. Odd-even-problem ====
  
  
 ### ###
-As mentioned in [[textbook:nrctextbook:chapter3|chapter III]] the plot of the semi empirical equation of [[textbook:nrctextbook:chapter3#nuclear_mass|nuclear mass]] for defined [[textbook:nrctextbook:chapter2#mass_number|mass number]] is parabola. The beta decaying nuclides lay on the edges of the parabola, β<sup>-</sup> nuclide on the left edge and β<sup>+</sup>/EC nuclide on the right while stable nuclide/s locate at the bottom. These parabolas are cross-sections of the energy valley presented in Figure III.3. Depending on the mass +As mentioned in [[textbook:nrctextbook:chapter3|chapter III]] the plot of the semi empirical equation of [[textbook:nrctextbook:chapter3#nuclear_mass|nuclear mass]] for defined [[textbook:nrctextbook:chapter2#mass_number|mass number]] is parabola. The beta decaying nuclides lay on the edges of the parabola, β<sup>-</sup> nuclide on the left edge and β<sup>+</sup>/EC nuclide on the right while stable nuclide/s locate at the bottom. These parabolas are cross-sections of the energy valley presented in [[textbook:nrctextbook:chapter3#figure_33|Figure III.3]]. Depending on the mass 
 number, there are either one or two parabolas: one for odd nuclides and two for even nuclides.  For odd mass numbers, there is only one stable nuclide at the bottom while for even numbers there are two or three. For even mass numbers, the nuclides on the upper parabola have both odd atomic number and odd neutron number and thus these nuclides are odd-odd nuclides. In turn the nuclides on the lower parabola the both numbers are even and these nuclides are thus even-even nuclides. number, there are either one or two parabolas: one for odd nuclides and two for even nuclides.  For odd mass numbers, there is only one stable nuclide at the bottom while for even numbers there are two or three. For even mass numbers, the nuclides on the upper parabola have both odd atomic number and odd neutron number and thus these nuclides are odd-odd nuclides. In turn the nuclides on the lower parabola the both numbers are even and these nuclides are thus even-even nuclides.
  
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 ### ###
-Figure V.15 shows an isobaric cross-section for the mass number 145. Since the mass number is odd, there is only one parabola. b- decays occur on the left edge of the parabola: <sup>145</sup><sub>58</sub>Ce decays to <sup>145</sup><sub>59</sub> Pr and this further to stable <sup>145</sup><sub>60</sub>Nd . β<sup>+</sup> and EC decays occur on the right edge: <sup>145</sup><sub>62</sub>Sm decays to <sup>145</sup><sub>61</sub>Pm and this further stable <sup>145</sup><sub>60</sub>Nd . The nuclide at the bottom of the parabola <sup>145</sup><sub>60</sub>Nd has the lowest mass, which means that it is the most stable of these nuclides. In this case, it has an even atomic number and an odd neutron number and is thus an even-odd nuclide. +[[textbook:nrctextbook:chapter5#figure_515|Figure V.15]] shows an isobaric cross-section for the mass number 145. Since the mass number is odd, there is only one parabola. [[textbook:nrctextbook:chapter5#beta_decay|β-]] decays occur on the left edge of the parabola: <sup>145</sup><sub>58</sub>Ce decays to <sup>145</sup><sub>59</sub> Pr and this further to stable <sup>145</sup><sub>60</sub>Nd. [[textbook:nrctextbook:chapter5#positron_decay|β+]] and [[textbook:nrctextbook:chapter5#electron_capture|EC]] decays occur on the right edge: <sup>145</sup><sub>62</sub>Sm decays to <sup>145</sup><sub>61</sub>Pm and this further stable <sup>145</sup><sub>60</sub>Nd . The nuclide at the bottom of the parabola <sup>145</sup><sub>60</sub>Nd has the lowest mass, which means that it is the most stable of these nuclides. In this case, it has an even [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] and an odd [[textbook:nrctextbook:chapter2#neutron_number|neutron number]] and is thus an even-odd nuclide. 
 There are 105 of this kind of isobaric cross-sections (parabolas) and the number of stable nuclides in them is obviously the same. There are 105 of this kind of isobaric cross-sections (parabolas) and the number of stable nuclides in them is obviously the same.
 ### ###
 +{{anchor:figure_515}}
  
 {{:textbook:nrctextbook:beta_decay_with_mass_number_of_145_fig_5_15.png?400|}} {{:textbook:nrctextbook:beta_decay_with_mass_number_of_145_fig_5_15.png?400|}}
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 ### ###
-Isobaric cross-sections with even mass numbers have two parabolas, the upper for odd-odd nuclides and the lower for even-even nuclides. As with odd mass  +Isobaric cross-sections with even mass numbers have two parabolas, the upper for odd-odd [[textbook:nrctextbook:chapter2#nuclide|nuclides]] and the lower for even-even nuclides. As with odd mass numbers and also with even mass numbers, the beta decays occur along the edges of the parabolas, but in this case the decay takes place from one parabola to another since in each decay the nuclide changes from even-even nuclide to odd-odd nuclide or vice versa. The rarest case in this kind of beta decay processes end up to the bottom of the upper parabola where the nuclide has an odd-odd nature. There are only four such cases and all are among the lightest elements, <sup>2</sup>H, <sup>6</sup>Li, <sup>10</sup>B and <sup>14</sup>N. Heavier odd-odd nuclides are unstable due to their imparity of both [[textbook:nrctextbook:chapter2#proton|protons]] and [[textbook:nrctextbook:chapter2#neutron|neutrons]]. An example of these with the mass number 142 is presented in [[textbook:nrctextbook:chapter5#figure_516|Figure V.16]]. Here the bottom nuclide of the upper parabola is <sup>142</sup><sub>59</sub>Pr, being an odd-odd nuclide, is heavier than the adjacent nuclides on the lower parabola, <sup>142</sup><sub>58</sub>Ce and <sup>142</sup><sub>60</sub>Nd. Therefore <sup>142</sup><sub>59</sub>Pr decays to both directions, though the [[textbook:nrctextbook:chapter5#beta_decay|beta minus decay]] is clearly prevalent by 99.98%. Another example of these is <sup>64</sup>Cu ([[textbook:nrctextbook:chapter5#figure_517|Figure V.17]]) for which 61% of decays take place with β<sup>+</sup> and EC and the rest (39%) with β<sup>-</sup> decay. In the isobaric cross-section with mass number 142 ([[textbook:nrctextbook:chapter5#figure_516|Figure V.16]]) we also see that <sup>142</sup><sub>58</sub>Ce is heavier than <sup>142</sup><sub>60</sub>Nd and thus the decay to this lighter [[textbook:nrctextbook:chapter2#nuclide|nuclide]] should take place. This would, however, require that the decay process goes through a heavier <sup>142</sup><sub>59</sub>Pr nuclide, which is impossible. The only possibility is double beta decay and this kind of decay has indeed been observed. An example of this is the decay of <sup>82</sup>Se to <sup>82</sup>Kr where two [[textbook:nrctextbook:chapter5#beta_particle|beta particles]] are emitted and the [[textbook:nrctextbook:chapter2#atomic_number|atomic number]] increases by two units. The decay is, however, very slow, the [[textbook:nrctextbook:chapter6#half_life|half-life]] for it being as long as 1.7×10<sup>20</sup> years.
-numbers and also with even mass numbers, the beta decays occur along the edges of the parabolas, but in this case the decay takes place from one parabola to another since in each decay the nuclide changes from even-even nuclide to odd-odd nuclide or vice versa. The rarest case in this kind of beta decay processes end up to the bottom of the upper parabola where the nuclide has an odd-odd nature. There are only four such cases and all are among the lightest elements, <sup>2</sup>H, <sup>6</sup>Li, <sup>10</sup>B and <sup>14</sup>N. Heavier odd-odd nuclides are unstable due to their imparity of both protons and neutrons. An example of these with the mass number 142 is presented in Figure V.14. Here the bottom nuclide of the upper parabola is <sup>142</sup><sub>59</sub>Pr, being an odd-odd nuclide, is heavier than the adjacent nuclides on the lower parabola, <sup>142</sup><sub>58</sub>Ce and <sup>142</sup><sub>60</sub>Nd . Therefore <sup>142</sup><sub>59</sub>Pr decays to both directions, though the beta minus decay is clearly prevalent by 99.98%. Another example of these is <sup>64</sup>Cu (Figure V.17) for which 61% of decays take place with β<sup>+</sup> and EC and the rest (39%) with β<sup>-</sup> decay. In the isobaric cross-section with mass number 142 (Figure V.16) we also see that <sup>142</sup><sub>58</sub>Ce is heavier than <sup>142</sup><sub>60</sub>Nd and thus the decay to this lighter nuclide should take place. This would, however, require that the decay process goes through a heavier <sup>142</sup><sub>59</sub>Pr nuclide, which is impossible. The only possibility is double beta decay and this kind of decay has indeed been observed. An example of this is the decay of <sup>82</sup>Se to <sup>82</sup>Kr where two beta particles are emitted and the atomic number increases by two units. The decay is, however, very slow, the half-life for it being as long as 1.7×10<sup>20</sup> years.+
  
 ### ###
 +{{anchor:figure_516}}
  
 {{:textbook:nrctextbook:beta_decay_at_the_isobaric_cross-section_a142_fig_5_16.png?400|}} {{:textbook:nrctextbook:beta_decay_at_the_isobaric_cross-section_a142_fig_5_16.png?400|}}
  
 Figure V.16. Beta decay at the isobaric cross-section A=142. Two stable nuclides, both even-even nuclides. Figure V.16. Beta decay at the isobaric cross-section A=142. Two stable nuclides, both even-even nuclides.
 +
 +{{anchor:figure_517}}
  
 {{:textbook:nrctextbook:decay_scheme_of_64cu_fig_5_17.png?400|}} {{:textbook:nrctextbook:decay_scheme_of_64cu_fig_5_17.png?400|}}
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 ### ###
-Below in Figure V.18 there are plots for the other cases of even mass numbers. On the left hand side there is the case with only one stable nuclide and on the right a case with three stable nuclides. The former is a typical case and there are altogether 78 of them. The latter, however, is rare and only three cases are known, for example at mass number 96 there are three stable nuclides <sup>124</sup>Xe, <sup>124</sup>Te and <sup>124</sup>Sn.+Below in [[textbook:nrctextbook:chapter5#figure_518|Figure V.18]] there are plots for the other cases of even mass numbers. On the left-hand side there is the case with only one stable [[textbook:nrctextbook:chapter2#nuclide|nuclide]] and on the right a case with three stable nuclides. The former is a typical case and there are altogether 78 of them. The latter, however, is rare and only three cases are known, for example at mass number 96 there are three stable nuclides <sup>124</sup>Xe, <sup>124</sup>Te and <sup>124</sup>Sn.
 ### ###
 +{{anchor:figure_518}}
  
 {{:textbook:nrctextbook:beta_decay_processes_at_even_mass_numbers_fig_5_18.png?400|}} {{:textbook:nrctextbook:beta_decay_processes_at_even_mass_numbers_fig_5_18.png?400|}}
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 ### ###
-The direction where neutrinos are emitted is not known, since we do observe them, but if it emits to opposite direction to beta particle the recoil energy of the daughter atom is zero. In case they both are emitted to same direction the recoil energy is its maximum (E<sub>d</sub>). Decay energy in this case is+The direction where [[textbook:nrctextbook:chapter5#neutrino|neutrinos]] are emitted is not known, since we do not observe them, but if it emits to opposite direction to [[textbook:nrctextbook:chapter5#beta_particle|beta particle]] the recoil energy of the daughter atom is zero. In case they both are emitted to same direction the recoil energy is its maximum (E<sub>d</sub>). Decay energy in this case is
 ### ###
  
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 ### ###
-where E<sub>max</sub> is the maximum energy of the beta particle. As already mentioned the recoil energies in beta decay processes are small due to the small mass of electron/positron. Thus, Q and E<sub>max</sub> are practically identical. For example, in the beta decay of <sup>14</sup>C where E<sub>max</sub> is 156 keV, E<sub>d</sub> is only 7 eV (0.004%). Compared to energies of chemical bonds, this recoil energy is, however, considerable and therefore the beta decay recoil often results in breaking chemical bonds.+where E<sub>max</sub> is the maximum energy of the [[textbook:nrctextbook:chapter5#beta_particle|beta particle]]. As already mentioned, the recoil energies in beta decay processes are small due to the small mass of [[textbook:nrctextbook:chapter5#beta_particle|electron]]/[[textbook:nrctextbook:chapter5#positron_particle|positron]]. Thus, Q and E<sub>max</sub> are practically identical. For example, in the beta decay of <sup>14</sup>C where E<sub>max</sub> is 156 keV, E<sub>d</sub> is only 7 eV (0.004%). Compared to energies of chemical bonds, this recoil energy is, however, considerable and therefore the beta decay recoil often results in breaking chemical bonds.
 ### ###
  
 +{{anchor:secondary_processes_beta_decay}}
 ==== 5.3.5. Consequences of beta decay processes ==== ==== 5.3.5. Consequences of beta decay processes ====
  
 ### ###
-Beta decay processes result in the formation of beta particles, positrons and neutrinos/antineutrinos as primary emissions. After primary processes, there are secondary processes, which lead to additional emission of radiation. These are:+Beta decay processes result in the formation of [[textbook:nrctextbook:chapter5#beta_particle|beta particles]], [[textbook:nrctextbook:chapter5#positron_particle|positrons] and [[textbook:nrctextbook:chapter5#neutrino|neutrinos]]/[[textbook:nrctextbook:chapter5#antineutrino|antineutrinos]] as primary emissions. After primary processes, there are secondary processes, which lead to additional emission of radiation. These are:
 ### ###
  
  
-  * Beta decay often occurs to the excited states of the daughter nuclide. Relaxation of the excitation occurs by internal transition (described in next section) and emission of gamma rays and conversion electrons. +  * Beta decay often occurs to the [[textbook:nrctextbook:chapter5#excited_state|excited states]] of the daughter nuclide. Relaxation of the excitation occurs by [[textbook:nrctextbook:chapter5#internal_transition|internal transition]] (described in next section) and emission of [[textbook:nrctextbook:chapter5#gamma|gamma rays]] and [[textbook:nrctextbook:chapter5#internal_transition|conversion electrons]]. 
-  * As the positrons annihilate with electrons 0.511 MeV gamma rays are formed.+  * As the positrons [[textbook:nrctextbook:chapter5#annihilation|annihilate]] with electrons 0.511 MeV gamma rays are formed.
   * {{anchor:x_rays}}In electron capture, X-rays are formed as the hole in the electron shell is filled with an electron from the upper shells. The X-rays are characteristic of the daughter atom and their energies correspond to the energy differences between the shells.   * {{anchor:x_rays}}In electron capture, X-rays are formed as the hole in the electron shell is filled with an electron from the upper shells. The X-rays are characteristic of the daughter atom and their energies correspond to the energy differences between the shells.
-  * Auger electrons are formed as a consequence of electron capture as the X-rays, formed as explained above, transfer their energy to electrons in the upper electron shells and these electrons are emitted. These Auger electrons are mono-energetic and their energies are fairly low, at most a few tens of electron volts.+  * [[textbook:nrctextbook:chapter5#auger_electrons|Auger electrons]] are formed as a consequence of [[textbook:nrctextbook:chapter5#electron_capture|electron capture]] as the X-rays, formed as explained above, transfer their energy to electrons in the upper electron shells and these electrons are emitted. These Auger electrons are mono-energetic and their energies are fairly low, at most a few tens of electron volts.
  
 {{anchor:internal_transition}} {{anchor:internal_transition}}
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 ### ###
-As mentioned, beta and alpha decays in most cases do not lead only to the ground state of the daughter but also to its excited states. These excitations are relaxed by two ways:+As mentioned, [[textbook:nrctextbook:chapter5#beta_decay|beta]] and [[textbook:nrctextbook:chapter5#alpha|alpha]] decays in most cases do not lead only to the ground state of the daughter but also to its excited states. These excitations are relaxed by two ways:
 ### ###
  
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 {{anchor:gamma}} {{anchor:gamma}}
 +{{anchor:excited_state}}
 ==== 5.4.1. Gamma decay ==== ==== 5.4.1. Gamma decay ====
  
 ### ###
-In gamma decay, the daughter nuclide releases its excitation energy by emitting electromagnetic gamma radiation (γ). When, for example, <sup>232</sup>Th decays (Figure V.19) by alpha mode to <sup>228</sup>Ra only a fraction (76.8%) of alpha particles receive the maximum energy of 4.011 MeV, the rest being decayed by emission of 3.952 MeV alpha particles (23.0%) and 3.828 MeV alpha particles (0.2%). These latter alpha energies are a cause of decay to excited states of <sup>228</sup>Ra. The energies of gamma rays emitted in the de-excitation can be calculated from the energy differences of the alpha particles, for example, 4.011 MeV - 3.952 MeV = 0.059 MeV. There are also gamma transitions from one excitation state to another, for example, 0.126 MeV gamma rays are emitted from this kind of transition in case of <sup>232</sup>Th decay.+In gamma decay, the daughter nuclide releases its excitation energy by emitting electromagnetic gamma radiation (γ). When, for example, <sup>232</sup>Th decays ([[textbook:nrctextbook:chapter5#figure_519|Figure V.19]]) by [[textbook:nrctextbook:chapter5#alpha|alpha]] mode to <sup>228</sup>Ra only a fraction (76.8%) of [[textbook:nrctextbook:chapter5#alpha_particle|alpha particles]] receive the maximum energy of 4.011 MeV, the rest being decayed by emission of 3.952 MeV alpha particles (23.0%) and 3.828 MeV alpha particles (0.2%). These latter alpha energies are a cause of decay to excited states of <sup>228</sup>Ra. The energies of gamma rays emitted in the de-excitation can be calculated from the energy differences of the alpha particles, for example, 4.011 MeV - 3.952 MeV = 0.059 MeV. There are also gamma transitions from one excitation state to another, for example, 0.126 MeV gamma rays are emitted from this kind of transition in case of <sup>232</sup>Th decay.
 ### ###
 +{{anchor:figure_519}}
  
 {{:textbook:nrctextbook:decay_scheme_of_232_th_fig_5_19.png?400|}} {{:textbook:nrctextbook:decay_scheme_of_232_th_fig_5_19.png?400|}}
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 Figure V.19. Decay scheme of <sup>232</sup>Th (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983). Figure V.19. Decay scheme of <sup>232</sup>Th (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).
  
-{{anchor:excited_state}}+
 ### ###
-Typically, gamma decays take place very rapidly, in less than 10-12 seconds, i.e. practically at the same time as the alpha and beta emissions. Sometimes, the gamma decays are delayed and if their life-times are so long that they can be measured, the excited states are considered as individual nuclides, isomeric states of the daughter. These nuclides are marked with "m" with the mass number. The life-times for the isomers are expressed as half-lives since their rate of decay behaves in an identical manner with other radionuclides. For example, when <sup>137</sup>Cs decays to stable <sup>137</sup>Ba, there is in between an isomer of barium <sup>137m</sup>Ba which has a half-life of 2.6 minutes. The half-lives of isomeric radionuclides vary in a wide range and the longest half-life of 900 years is known for <sup>192m</sup>Ir.+Typically, gamma decays take place very rapidly, in less than 10<sup>-12</sup> seconds, i.e. practically at the same time as the alpha and beta emissions. Sometimes, the gamma decays are delayed and if their life-times are so long that they can be measured, the excited states are considered as individual nuclides, isomeric states of the daughter. These nuclides are marked with "m" with the mass number. The life-times for the isomers are expressed as half-lives since their rate of decay behaves in an identical manner with other radionuclides. For example, when <sup>137</sup>Cs decays to stable <sup>137</sup>Ba, there is in between an isomer of barium <sup>137m</sup>Ba which has a half-life of 2.6 minutes. The half-lives of isomeric radionuclides vary in a wide range and the longest [[textbook:nrctextbook:chapter6#half_life|half-life]] of 900 years is known for <sup>192m</sup>Ir.
 ### ###
  
  
 ### ###
-As mentioned already, the gamma decays occur from excited states to ground state or between the excited states. Since all these states have defined energy levels, the gamma rays have defined energies. Thus, also the spectrum obtained is a line spectrum. Figure V.20 shows the decay scheme and the gamma spectrum of <sup>241</sup>Am. As seen, all three gamma transitions are seen in the spectrum. The heights of the peaks depend on the intensity of each transition. Intensities are the fractions of  +As mentioned already, the gamma decays occur from excited states to ground state or between the excited states. Since all these states have defined energy levels, the gamma rays have defined energies. Thus, also the spectrum obtained is a //line spectrum//. [[textbook:nrctextbook:chapter5#figure_520|Figure V.20]] shows the decay scheme and the gamma spectrum of <sup>241</sup>Am. As seen, all three gamma transitions are seen in the spectrum. The heights of the peaks depend on the intensity of each transition. Intensities are the fractions of each transitions from total decay events. For example, the intensities of the three gamma transition in the case of <sup>198</sup>Au are 96% for γ<sub>1</sub> (412 keV), 0.8% for γ<sub>2</sub> (676 keV) and 0.2% for γ<sub>3</sub> (1088 keV). The sum of the intensities is not 100% because part of de-excitations takes place by [[textbook:nrctextbook:chapter5#internal_conversion|internal conversion]], as described later.
-each transitions from total decay events. For example, the intensities of the three gamma transition in the case of <sup>198</sup>Au are 96% for γ<sub>1</sub> (412 keV), 0.8% for γ<sub>2</sub> (676 keV) and 0.2% for γ<sub>3</sub> (1088 keV). The sum of the intensities is not 100% because part of de-excitations takes place by internal conversion, as described later.+
 ### ###
 +{{anchor:figure_520}}
  
 {{:textbook:nrctextbook:decay_scheme_214am_fig_5_20.png?400|}} {{:textbook:nrctextbook:decay_scheme_214am_fig_5_20.png?400|}}
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 ### ###
-Gamma-emitting radionuclides are not only constituted of the beta and alpha-decaying  +Gamma-emitting radionuclides are not only constituted of the [[textbook:nrctextbook:chapter5#beta|beta]] and [[textbook:nrctextbook:chapter5#alpha|alpha]]-decaying radionuclides with excitation states of the daughter. They can also be obtained by activation of a nuclei by electromagnetic and particles bombardments, for example with [[textbook:nrctextbook:chapter2#neutron|neutrons]]. In [[textbook:nrctextbook:chapter5#fission|fission]], gamma rays are also emitted as primary emission, i.e. instantly during the fission process.
-radionuclides with excitation states of the daughter. They can also be obtained by activation of a nuclei by electromagnetic and particles bombardments, for example with neutrons. In fission, gamma rays are also emitted as primary emission, i.e. instantly during the fission process.+
 ### ###
  
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 ### ###
-As mentioned above, a competing process to gamma decay is internal conversion (IC). In it, excitation energy is not released by gamma ray emission but transferred to a shell electron, which is then emitted. The phenomenon is analogous to formation of Auger electrons, which are emitted by the action of energy released from electron transitions from upper to lower shells. The electrons emitted in internal transitions are called conversion electrons. They are monoenergetic and their energy is the excitation energy minus the binding energy of the emitted electron. Most conversion  +As mentioned above, a competing process to gamma decay is internal conversion (IC). In it, excitation energy is not released by gamma ray emission but transferred to a shell electron, which is then emitted. The phenomenon is analogous to formation of [[textbook:nrctextbook:chapter5#auger_electrons|Auger electrons]], which are emitted by the action of energy released from electron transitions from upper to lower shells. The electrons emitted in internal transitions are called //conversion electrons//. They are monoenergetic and their energy is the excitation energy minus the binding energy of the emitted electron. Most conversion electrons come from the inner K-shell since it has a strongest interaction with the nucleus. For example, in the decay of <sup>137m</sup>Ba the conversion electrons come five times more from K shell than from the L shell. In a [[textbook:nrctextbook:chapter5#continuous_spectrum|continuous beta spectrum]], the conversion electrons are seen as peaks. An example is given in [[textbook:nrctextbook:chapter5#figure_521|Figure V.21]] where the beta spectrum of <sup>137</sup>Cs is shown. The conversion electrons, from both K and L shells, are seen as individual peaks at higher energies.
-electrons come from the inner K-shell since it has a strongest interaction with the nucleus. For example, in the decay of <sup>137m</sup>Ba the conversion electrons come five times more from K shell than from the L shell. In a continuous beta spectrum, the conversion electrons are seen as peaks. An example is given in Figure V.21 where the beta spectrum of <sup>137</sup>Cs is shown. The conversion electrons, from both K and L shells, are seen as individual peaks at higher energies.+
 ### ###
 +{{anchor:figure_521}}
  
 {{:textbook:nrctextbook:beta_and_conversion_electron_spectrum_of_137cs_fig_5_21.png?400|}} {{:textbook:nrctextbook:beta_and_conversion_electron_spectrum_of_137cs_fig_5_21.png?400|}}
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 ### ###
-Figure V.22 shows the decay scheme of <sup>137</sup>Cs. 94.6% of the beta transitions go through the 662 keV excitation state of <sup>137</sup>Ba. This excitation state relaxes by emission of 662 keV gamma rays with an intensity of 89.8% (85.1% intensity of all decay events) and the rest 10.2% (9.6%) by internal conversion. Thus the conversion coefficient is 89.8/10.2 = 0.11.+[[textbook:nrctextbook:chapter5#figure_521|Figure V.22]] shows the decay scheme of <sup>137</sup>Cs. 94.6% of the beta transitions go through the 662 keV excitation state of <sup>137</sup>Ba. This excitation state relaxes by emission of 662 keV gamma rays with an intensity of 89.8% (85.1% intensity of all decay events) and the rest 10.2% (9.6%) by internal conversion. Thus, the conversion coefficient is 89.8/10.2 = 0.11.
 ### ###
 +{{anchor:figure_522}}
  
 {{:textbook:nrctextbook:decay_scheme_of_137cs_fig_5_22.png?400|}} {{:textbook:nrctextbook:decay_scheme_of_137cs_fig_5_22.png?400|}}
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 Figure V.22. Decay scheme of <sup>137</sup>Cs (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983). Figure V.22. Decay scheme of <sup>137</sup>Cs (Radionuclide Transformations, Annals of the ICRP, ICRP Publication 38, Pergamon Press, 1983).
  
 +{{anchor:particles_and_rays_in_decay_processes}}
 ===== 5.5. Particles and rays in radioactive decay processes ===== ===== 5.5. Particles and rays in radioactive decay processes =====
  
textbook/nrctextbook/chapter5.1742305314.txt.gz · Last modified: 2025-03-18 14:41 by Merja Herzig

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