Uranium-238 undergoes a slow decay step (t1/2_4.5109 yr) followed by a series of fast

Chapter 24, Problem 24.135

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Uranium-238 undergoes a slow decay step (t1/2_4.5109 yr) followed by a series of fast steps to form the stable isotope 206Pb. Thus, on a time scale of billions of years, 238U effectively decays directly to 206Pb, and the relative amounts of these isotopes are used to find the age of some rocks (see margin note, p. 1079). Two students derive equations relating number of halflives (n) since the rock formed to the amounts of the isotopes: Student 1: Student 2: (a) Which equation is correct, and why? (b) If a rock contains exactly twice as much 238U as 206Pb, what is its age in years?

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