Steady state secular equilibrium

One simple way to estimate the effect of intermediate species is as follows. After steady state (secular equilibrium) is reached, the concentrations of the intermediate species do not vary much, and the decay of would basically produce ° Pb. Hence, at the timescale longer than 2 Myr, we have... 

Secular Equilibrium A condition that occurs when a chain of radionuclides has reached a steady state condition, in which the rate of decay of daughter nuclides is balanced by their rate of formation by decay of each parent. In this condition, the radioactivity (measured in disintigrations per minute) of each radionuclide in a chain is the same. 

A steady state implies that the activity of the daughter and its precursor are equal and do not change in time. However, it is easy to see that in a finite time interval such a state of so-called secular equilibrium can only be approached and never be reached due to the fact that the primordial nucleus can never have a steady state. As a result its daughter product can never reach a steady state, etc. On the other hand, when X/A,, 1 a state of quasi equilibrium may be reached where the activity ratio of mother and daughter nuclei is given by... 

Most of the atoms of Th that are produced from decay readily attach to particles and are removed from solution. In the surface ocean there are enough particles formed to create a deficiency in Th activity from that to be expected at secular equilibrium with At steady state, the depth-integrated deficiency of the activity concentrations of Th in the euphotic zone is equal to its flux from the surface ocean on particles. If one then knows the Th C ratio in the particles, the flux of particulate carbon can be calculated. An example of Th measurements in the surface waters of the subtropical Pacific (see Fig. 6.11) indicates that difference in Th activity from that expected at secular equilibrium (equal to the activity of U) is small but readily measurable. 

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