Transient equilibrium

From Wikipedia, the free encyclopedia

In nuclear physics, transient equilibrium is a situation in which equilibrium is reached by a parent-daughter radioactive isotope pair where the half-life of the daughter is shorter than the half-life of the parent. Contrary to secular equilibrium, 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 nuclear medicine diagnostic procedures. Such a generator is sometimes called a cow because the daughter product, in this case technetium-99, is milked at regular intervals.[1] Transient equilibrium occurs after four half-lives, on average.

Activity in transient equilibrium

The activity of the daughter is given by the Bateman equation:

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}},

where A_{P} and A_{d} are the activity of the parent and daughter, respectively. T_{P} and T_{d} are the half-lives of the parent and daughter, respectively, and BR is the branching ratio.

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:

{\frac {A_{d}}{A_{P}}}={\frac {T_{P}}{T_{P}-T_{d}}}\times BR.

Time of maximum daughter activity

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:

t_{{max}}={\frac {1.44\times T_{P}T_{d}}{T_{P}-T_{d}}}\times ln(T_{P}/T_{d}),

where T_{P} and T_{d} are the half-lives of the parent and daughter, respectively. In the case of ^{{99m}}Tc-^{{99}}Mo generator, the time of maximum activity (t_{{max}}) is approximately 24 hours which makes it convenient for medical use. [2]

See also

References

  1. ↑ transient equilibrium
  2. ↑ S.R. Cherry, J.A. Sorenson, M.E. Phelps (2003). Physics in Nuclear Medicine. A Saunders Title; 3 edition. ISBN 0-7216-8341-X. 


This article is issued from Wikipedia. The text is available under the Creative Commons Attribution/Share Alike; additional terms may apply for the media files.