Question

Uranium-lead (U-Pb) dating of geological samples is one of the oldest and most refined radiometric dating methods, able to determine ages of about 1 million years to over 4.5 billion years with precision in the 0.1–1% range. The U-Pb dating method relies on two separate decay chains, one of which is the uranium series from 238U to 206Pb, with a half-life of 4.47 billion years.

Geologists unearth a sample of zircon that appears to be a closed system. They find 0.734 microgram of 206Pb for 1.000 microgram of 238U present. Approximately how old is the sample?

Answer 1

We have half life t_1/2 = 4.47 times 10^3 years we know that radi8oactivity follows 1^st order kinetics rate constant k = ln^2/t_1/2 k = 0.693/4.47 times 10^9 = 1.55 times 10^T-10 yr^-1 238 U rightarrow 206 pb for 238 g U rightarrow 206 g pb 1g pb rightarrow 238/206 g U 0.734 mu g rightarrow 238/206 times 0.734 mu g = 0.848 mu g \r\n for 1^st order reaction ln A_0/A = kt A_0 = Initial mass of U A = mass of U at any time t ln 1/0.848 = 1.55 times 10^-10 yr^-1 times 1 t = 1.063 times 10^9 years