If you obtained a sample of rock from Venus and determined the abundances of ²³⁸U and ²⁰⁷Pb in it,and found that for every one uranium atom there were three lead atoms,then what would the age of this rock be? Note that ²³⁸U decays to ²⁰⁷Pb with a half-life of 700 million years.Assume that there was no ²⁰⁷Pb in the rock when it originally formed.
A) 1.4 billion years
B) 2.8 billion years
C) 230 million years
D) 4.5 billion years

Question

Quizplus · Accepted Answer

The ratio of lead to uranium (3:1) indicates that three half-lives of uranium-238 have passed, because with each half-life, the amount of uranium-238 decreases by half while the amount of lead-207 increases. Since the half-life of uranium-238 is 700 million years, three half-lives would be 3 x 700 million years = 2.1 billion years. However, the correct interpretation of the ratio involves understanding that for every one uranium atom remaining, three have decayed to lead, which corresponds to the uranium being reduced to one-fourth of its original amount, indicating two half-lives, not three. Two half-lives of 700 million years each total 1.4 billion years.

If You Obtained a Sample of Rock from Venus and Determined