The isotope 238U decays to 206Pb with a half-life of 4.47*10^9 years. Although t

Question

The isotope 238U decays to 206Pb with a half-life of 4.47*10^9 years. Although the decay occurs in many individual steps, the first step has by far the longest half-life; therefore, one can often consider the decay to go directly to lead, as represented below.

238U --> 206Pb + various decay products.

A particular rock is thought to be 240 million years old. If it contains 3.60 mg of 238U, how much 206Pb should it contain? Assume that the rock contained no lead at formation, so all the lead now present arose from the decay of uranium.

Explanation / Answer

t1/2=0.693/k=0.693/4.47 x 10^9=1.55 x 10^-10

k=(2.303/t)log(a/a-x)

1.55 x 10^-10=(2.303/240 x 10^6)log(3.6/3.6-x)

log(3.6/3.6-x)=1.0378

So x=0.1314 mg

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