A zircon grain from a granite has a measured radiogenic lead ratio (corrected for any…

PHYSICS · Multi-part · Fermi University Physics · Earth, Climate & Energy Physics · The solid Earth: structure, fields and thermal history · The solid Earth: structure, fields and thermal history

The Solid Earth, Ch Dating, heat flow and the thermal history of the Earth

Problem

A zircon grain from a granite has a measured radiogenic lead ratio 206Pb∗/238U=0.850^{206}\mathrm{Pb}^*/^{238}\mathrm{U} = 0.850 (corrected for any common, non-radiogenic lead), and this point lies on the U-Pb concordia curve. Take the decay constant of 238U^{238}\mathrm{U} as λ238=1.55125×10−10 yr−1\lambda_{238} = 1.55125\times10^{-10}\,\mathrm{yr^{-1}}. ((a)) Write down the growth equation relating 206Pb∗/238U^{206}\mathrm{Pb}^*/^{238}\mathrm{U} to time and solve it for the age tt. ((b)) Evaluate tt, in gigayears, for the measured ratio.

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