Transient equilibrium

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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[edit]

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_Pt}-e^{-\lambda_dt})] \times BR ) + A_d(0)e^{-\lambda_dt},

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[edit]

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[edit]

References[edit]

  1. ^ transient equilibrium[dead link]
  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.