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

first order kinetics,

K = 0.693/t1/2

K = 0.693/(4.47*10^9) = 1.55*10^-10 Y-1

k = (1/t)ln(a/x)

a = initial amount 238-U = 1.0 g

x = amount of isomer after t, time = x g

t= time = 4*10^9 years

(1.55*10^-10) = (1/(4*10^9))ln(1/x)

x = 0.54 g

mass of 238-U converted = 1.0 - 0.54 = 0.46 g

no of mol of 238-U converted = 0.46/238 = 0.00193 mol

no of mol of 206-Pb FORMED = 0.00193*206 = 0.4 g

current mass of 206Pb per 1.595 g of 238U in the rock = 1.595*0.4/1 = 0.638 g