Question

A moon rock collected by a U.S. Apollo mission is estimated to be 4.00 billion years old by uranium/lead dating. Assuming that the rock did not contain any lead when it was formed, what is the current mass of 206Pb per 1.595 g of 238U in the rock? The half-life of 238U is t1/2 = 4.47 × 109 years.

Answer 1

half-life of 238U t1/2 = 4.47 × 10^9 years.

decay constant k = 0.693 / t1/2

                            = 0.693 / 4.47 × 10^9

                            = 1.55 x 10^-10 yr-1

mass of 206Pb = x

mass of U238 = 1.595 g

total original mass of U238 = 1.595 + x

k = 1/t ln (Ao / At)

1.55 x 10^-10 = 1 / 4.00 x 10^9 ln (1.595 + x / 1.595)

(1.595 + x / 1.595) = 1.859

x = 1.370

mass of 206 Pb = 1.370 x (206 / 238)

mass of ²⁰⁶ Pb = 1.186 g