Question

Suppose that a mineral body formed in an ancient cataclysm—perhaps the formation of the earth itself— originally contained the uranium isotope 238U (which has a half-life of 4:51 109 years) but no lead, the end product of the radioactive decay of 238U. If today the ratio of 238U atoms to lead atoms in the mineral body is 0.9, when did the cataclysm occur?

Answer 1

The cataclysm occured 6.85x10^8 years ago.

Explanation:

Considering that the half-life is 4.51x10^9 years, the first step to solve this problem is finding k by the formula k=ln(0.5)/t(half-life). This constant of decay can then be replaced in the N=No x e^(-kt). Since the problem states that the ratio N/No = 0.9, solving the formula for t will give you a time of 6.85x10^8 years. The question was when did the cataclysm occured so it is safe to say that it was about 685,000,000 years ago.