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.[2]
The activity of the daughter is given by the Bateman equation:
Ad=
| A | ||||
|
x
| -λPt | |
| (e |
| -λdt | |
| -e |
) x BR+
| -λdt | |
| A | |
| d(0)e |
,
where
AP
Ad
TP
Td
λ
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:
| Ad | |
| AP |
=
| TP | |
| TP-Td |
x BR.
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:
tmax=
| 1.44 x TPTd | |
| TP-Td |
x ln
| TP | |
| Td |
,
where
TP
Td
tmax
