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Radioacive decay chain: Thorium series



Unstable isotopes decay eventually reaching an uquilibrium ;low energy stable isotope. Often there are transition (ustable) isotopes  that the material transforms into on the way to transformoing into the end (stable) isotope.

The fundemental equation for the exponetial rate of decay from the parent isotope to a daughter isotope is give by:

\frac{dN}{dt} = -\lambda N

where \lambda is the decay rate.

A useful way of presenitng the decay rate is in terms of the half life theat is the amount of time taken for half the original quantity of parent isotope to decay to the daughter isotope.

t_{1/2} = \frac{\ln 2}{\lambda} = \tau \ln 2.


System Dynamics (SD) by definition handles differential equation to calculate amounts of isotope (state varible, stock, compartment) but the chin or series doeas not constitute a regular System Dynamics flow as the substance (isotope) keeps  changing. This can be modelled by having seperate compartment flow (from a cloud [source]) groups withing influences linking by the decay rates parent to daughter. Alternatively, an association submodel can be used to keep don the level of repetition as with soil layers (