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:
[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:
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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