Thread: Calculate radiogenic isotope (3 Pb isotopes) concentrations by only the given weight%

Hi all, this is not homework, it's a part of a trial excercise for isotope geology exam,


So I'm stuck at the starting part of the question: Calculate the isotope concentrations for the different radiogenic Pb-isotopes by their weight%
206Pb = 47,2%
207Pb = 6,048%
208Pb = 0,048%


The goal is to eventually calculate lead-lead age and the initial U-isotope composition.


I know because of their radiogenic nature (concentrations depend on the decay of 238U, 235U and 232Th) you have to recalculate the 'true' atomic mass of Pb, by taking the abundance of each isotope into account, to calculate the concentrations. But the abundance isn't given, and because it are radiogenic isotopes, their isotope composition is variable, so the abundances aren't constant (in contrary to isotopes of K, O, ...) and have to be calculated too.

If the abundances were given, you could easily calculate the 'true' atomic mass by mulitplying the abundance of each isotope with the 'average' atomic mass from the periodic table, and add them all up. Then you could divide the weight% of each isotope by the 'true' atomic mass (and multiply by constant of Avogadro for number of isotopes instead mol). But like I said, no abundances are given and they're variable.
(The abundance of the 204Pb isotope can be estimated as 0, because the weight% are measured in a zircon mineral, which normally don't include initial Pb in their crystal lattice)


I have no clue how to solve this problem and urgent help is needed, the exam is on friday.


Thank you in advance!