Question

A moon rock collected by a U.S. Apollo mission is estimated to be 3.60 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 1.265 g of 238U in the rock? The half-life of 238U is t1/2 = 4.47 × 10^9 years.

Answer 1

decay constant = 0.693 / half life

                          = 0.693 / 4.47 x 10^9

                         = 1.55 x 10^-10 year-1

mass of U = 1.265 g

mass of Pb = x g

total initial mass of U = 1.265 + x

for first reaction :

k = 1/ t * ln [Ao / At ]

1.55 x 10^-10 = ( 1/ 3.60 x 10^9 ) * ln (1.265 + x / 1.265)

ln (1.265 + x / 1.265) = 0.558

(1.265 + x / 1.265)   = 1.747

1.265 + x = 2.210

x = 0.945

mass of Pb-206 = 0.945 x (206 / 238)

                          = 0.818 g

current mass of ²⁰⁶Pb   = 0.818 g