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In transient equilibrium, the
Bateman equation cannot be simplified by assuming the daughter's half-life is negligible compared to the parent's half-life. The ratio of daughter-to-parent activity is given by:
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In transient equilibrium, the daughter activity increases and eventually reaches a maximum value that can exceed the parent activity. The time of maximum activity is given by:
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250:{\displaystyle A_{d}=A_{P}(0){\frac {\lambda _{d}}{\lambda _{d}-\lambda _{P}}}\times (e^{-\lambda _{P}t}-e^{-\lambda _{d}t})\times BR+A_{d}(0)e^{-\lambda _{d}t},}
35:, the half-life of the daughter is not negligible compared to parent's half-life. An example of this is a molybdenum-99 generator producing technetium-99 for
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because the daughter product, in this case technetium-99, is milked at regular intervals. Transient equilibrium occurs after four half-lives, on average.
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621:{\displaystyle t_{\max }={\frac {1.44\times T_{P}T_{d}}{T_{P}-T_{d}}}\times \ln {\frac {T_{P}}{T_{d}}},}
820:(4th ed.). Philadelphia: Wolters Kluwer Health/Lippincott Williams & Wilkins. p. 1205.
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pair where the half-life of the daughter is shorter than the half-life of the parent. Contrary to
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in the above equation modulo ln(2)) of the parent and daughter, respectively, and BR is the
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487:{\displaystyle {\frac {A_{d}}{A_{P}}}={\frac {T_{P}}{T_{P}-T_{d}}}\times BR.}
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are the half-lives of the parent and daughter, respectively. In the case of
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is a situation in which equilibrium is reached by a parent-daughter
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The activity of the daughter is given by the
Bateman equation:
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Johnson, Thomas E.; Birky, Brian K.; Shleien, Bernard (2012).
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diagnostic procedures. Such a generator is sometimes called a
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are the activity of the parent and daughter, respectively.
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731:{\displaystyle {\ce {^{99\!m}Tc-^{99}Mo}}}
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849:. A Saunders Title; 3 edition.
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758:{\displaystyle t_{\max }}
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715:−
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801:Archived
769:See also
29:isotope
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631:where
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881:This
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851:ISBN
822:ISBN
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Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.
