Decay Equations For Common Pb-Pb Dating
There are three stable "daughter" Pb isotopes that result from the radioactive decay of uranium and thorium in nature; they are 206Pb, 207Pb, and 208Pb. 204Pb is the only non-radiogenic lead isotope, therefore is not one of the daughter isotopes. These daughter isotopes are the final decay products of U and Th radioactive decay chains beginning from 238U,235U and 232Th respectively. With the progress of time, the final decay product accumulates as the parent isotope decays at a constant rate. This shifts the ratio of radiogenic Pb versus non-radiogenic 204Pb (207Pb/204Pb or 206Pb/204Pb) in favor of radiogenic 207Pb or 206Pb. This can be expressed by the following decay equations:
where the subscripts P and I refer to present-day and initial Pb isotope ratios, λ235 and λ238 are decay constants for 235U and 238U, and t is the age.
The concept of common Pb-Pb dating (also referred to as whole rock lead isotope dating) was deduced through mathematical manipulation of the above equations. It was established by dividing the first equation above by the second, under the assumption that the U/Pb system was undisturbed. This rearranged equation formed:
where the factor of 137.88 is the present-day 238U/235U ratio. As evident by the equation, initial Pb isotope ratios, as well as the age of the system are the two factors which determine the present day Pb isotope compositions. If the sample behaved as a closed system then graphing the difference between the present and initial ratios of 207Pb/204Pb versus 206Pb/204Pb should produce a straight line. The distance the point moves along this line is dependent on the U/Pb ratio, whereas the slope of the line depends on the time since Earth’s formation. This was first established by Nier et al., 1941.
Read more about this topic: Lead-lead Dating
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