A rock from the moon was found to contain 1.0 $\times$ 10^-5 g of uranium-238 and 4.0 $\times$ 10^-6 g lead-206. All of the lead-206 came from the decay of uranium-238. The half-life for this decay is 4.5 $\times$ 10 ⁹ years. How old is this rock?

Question

Quizplus · Accepted Answer

The age of the rock can be determined using the ratio of the remaining parent isotope (uranium-238) to the daughter isotope (lead-206). Initially, there was 1.0 g of uranium-238, and now there is 4.0 g of lead-206, indicating that for every 1 g of uranium-238 that decays, 4 g of lead-206 are produced. This suggests that the original amount of uranium-238 was 5.0 g (1.0 g remaining + 4.0 g decayed into lead-206). Since the half-life of uranium-238 is 4.5 billion years and it takes three half-lives to reduce from 5.0 g to 1.0 g (halving from 5.0 g to 2.5 g, then to 1.25 g, and finally to approximately 1.0 g), the rock is approximately 3 x 4.5 billion years old, or 13.5 billion years. However, the correct interpretation of the half-life process and the options provided suggests a simplification or rounding in the context of the question, leading to the selection of option D as the closest correct answer.

A Rock from the Moon Was Found to Contain 1 ×\times×

A Rock from the Moon Was Found to Contain 1 $\times$