Problem: A moon rock collected by a U.S. Apollo mission is estimated to be 4.30 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 in grams of  206Pb per 1.260 g of  236U in the rock? The half-life of  236U is t1/2 = 4.47 x 109 years.

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We’re being asked to determine the mass of 206Pb in a moon rock with 1.260 g 236U


Recall that radioactive/nuclear decay of isotopes follows first-order kinetics, and the integrated rate law for first-order reactions is:



where:

[N]t = concentration at time t

k = decay constant

t = time

[N]0 = initial concentration


Also, recall that half-life is the time needed for the amount of a reactant to decrease by 50% or one-half


The half-life of a first-order reaction is given by:



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Problem Details

A moon rock collected by a U.S. Apollo mission is estimated to be 4.30 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 in grams of  206Pb per 1.260 g of  236U in the rock? The half-life of  236U is t1/2 = 4.47 x 109 years.

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