An Analytical Model to Quantify Decay Chain Disequilibrium–Application to the Thorium Decay Chain

An emissivity model, generalized to disequilibrium states of radioactive decay chains, is used to study the effects of thorium decay chain disequilibrium on alpha emissivity. The results show that even if the alpha emissivity produced by the thorium decay chain is initially acceptable, it can increase significantly during the device lifetime. Three radionuclides in the thorium chain are responsible for the increase:
${}^{232}{\rm Th}$
,
${}^{228}{\rm Th}$
, and
${}^{228}{\rm Ra}$
. Their initial concentrations determine the evolution of the emissivity during the device lifetime.