You chemically analyze a small sample of a meteorite. K-40 and Ar-40 are present in a ratio of approximately 1.65 units of K-40 atoms to 8.35 units of gaseous Ar-40 atoms. How old is the meteorite given the half-life of this decay is 1.25 billion years?

Question

Quizplus · Accepted Answer

The ratio of K-40 to Ar-40 suggests that the meteorite has gone through multiple half-lives. Initially, all atoms would have been K-40. After each half-life, the amount of K-40 halves, while the amount of Ar-40 increases. Given the current ratio, we can calculate the number of half-lives that have passed. The formula for decay is $N = N_0 \times (1/2)^{t/T}$, where $N$ is the remaining quantity of the substance, $N_0$ is the initial quantity, $t$ is the time elapsed, and $T$ is the half-life period. Here, we can use the ratio of K-40 to Ar-40 to determine $t$. The ratio indicates that for every 1.65 units of K-40, there are 8.35 units of Ar-40, which suggests that a significant portion of the original K-40 has decayed. By calculating the fraction of K-40 left (1.65 out of the total 10 units), and applying the decay formula, we find that the meteorite has undergone approximately 3.25 billion years of decay, which corresponds to a little over 2.5 half-lives. This aligns closely with option D, 3.25 billion years, as the correct answer.

You Chemically Analyze a Small Sample of a Meteorite