The ratio of ²³⁸U to ²⁰⁶Pb is used to date old mineral samples.Each 1.000 g of ²³⁸U that decays eventually produces 0.866 g of ²⁰⁶Pb.If the half-life of ²³⁸U is 4.468 × 10⁹ years,what is the age of a mineral that has a ²³⁸U/²⁰⁶Pb mass ratio of 2.00?

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The age of the mineral can be calculated using the decay formula, which involves the half-life of the substance. Given the ratio of Uranium to Lead is 2.00, and knowing that 1.000 g of Uranium decays to 0.866 g of Lead, we can infer that for every 1.000 g of Uranium, there was originally 1.000 + 0.866 = 1.866 g of Uranium. With a current ratio of 2.00, this means there is now 1 g of Uranium for every 0.866 g of Lead, indicating half of the original Uranium has decayed, which corresponds to one half-life. Since the half-life of Uranium-238 is 4.468 × 10^9 years, the age of the mineral is approximately 4.468 × 10^9 years, matching choice A.

The Ratio of 238U to 206Pb Is Used to Date

The Ratio of ²³⁸U to ²⁰⁶Pb Is Used to Date