The Lead Isotopic Composition of Metalliferous Deposits

The Holmes-Houtermans model makes a number of assumptions which are important to enumerate (Faure, 1986 310)  

It is important to distinguish clearly in this scenario between the general solidification of the Earth s crust, which had the effect of freezing in variations in the U/Pb and Th/Pb ratios, and the specific mineralization event which created the galena (lead sulfide, PbS) deposits, which removed the lead from the uranium and thorium, and effectively therefore froze the isotopic composition of the lead in the galena at the values representative of the time of mineralization. 

The equation for the growth of a stable daughter from a radioactive parent can be easily derived from Equation (9.6) above, which is the familiar radioactive decay curve. We can write that  

This equation expresses the growth of the daughter from the radioactive parent in terms of the amount of the parent originally present (N0). It is more useful if we use Equation (9.6) to replace N0 with N (the number of parent nuclei remaining after time t) in Equation (9.8), since N is the quantity which is actually measurable. Thus  

This is the equation for the growth of a stable radioactive daughter, assuming that no primeval D was present at time t = 0. If this was the case (and the amount is termed Da), then the equation becomes  

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