MULTIMODAL DECAYS
MULTIMODAL DECAYS, BRANCHING RATIO AND DECAY CONSTANT
When an nuclide can decay by more than one pathway, it is said to exhibit multimodal decay. But the halflife of a nuclide takes account only of the rate of change of the parent nuclide, and not of the rate of decay along different pathways possible in multimodal decay. For multimodal decays, the branching ratio (or branching fraction) awards percentage probabilities to each modal pathway. The decay constant (or transition rate) takes into account the 'partial halflives' of each different route, and is related to the halflife and branching ratio by the following equation:
Decay Constant =Branching Ratio x (0.5)^{(1/Halflife)}
Decay Constant = 1 / Mean Lifetime
Mean Lifetime = Halflife / LOG_{e}(2)

In the above diagram, Rhenium186 (the central isotope) exhibits a bimodal decay; when it decays, it has a 93% probability of taking the beta decay route to become osmium186 (itself radioactive) and an 7% probability of taking the electron capture pathway to become stable tungsten186. The branching ratio is therefore 93% Beta, 7% EC. The (overall) halflife is 88.9 hours, corresponding to an overall decay constant of 0.78% per hour. The decay constant for the beta pathway is 93% of this overall value (0.73%/hour) and that for the electron capture pathway 7% of the overall value (0.05%/hour).
Overall Decay constant = Decay constant(branch 1) + Decay constant(branch 2)
A second example below shows the multimodal decay of polonium209, which decays by either alpha decay into lead205, or by inverse beta decay into bismuth209. The branching ratio for this is 99.52% alpha decay; 0.48% inverse beta decay. Therefore, after an infinite amount of time, 0.48% of the number of atoms of polonium209 end up as atoms of the stable bismuth209, whereas 99.52% ends up as atoms, not of lead205, which is itself electroncapture radioactive, but of thallium205, which is lead205's stable daughter product. Observe that the same number of alpha particles as atoms of lead205 are produced. Similarly, as many positrons are produced as are atoms of bismuth209. [Note that branching ratios do not relate to the percentage weights, but rather to the percentage atoms relative to the number of atoms of the parent isotope, polonium209 in this case].
Multimodal decay of polonium209