The decay of ⁴⁰K has a half of 1.3 × 10⁹years. The age of Earth is estimated at 4.6 × 10⁹years. The decay of ⁴⁰K is a major heat source for Earth's interior. Relative to today, how much more heat was produced by ⁴⁰K in the early Archaeon era or 3.9 × 10⁹years ago? A) 6x B) 8x C) 4x D) 2x

Question

Quizplus · Accepted Answer

Given the half-life of $^{40}K$ is $1.3 \times 10^9$ years, and the early Archaean era was $3.9 \times 10^9$ years ago, we can calculate the number of half-lives that have passed since then by dividing the elapsed time by the half-life of $^{40}K$: $\frac{3.9 \times 10^9}{1.3 \times 10^9} = 3$ half-lives. After each half-life, the amount of $^{40}K$ (and thus the heat it produces) is halved. Therefore, after 3 half-lives, the heat production would be $2^3 = 8$ times greater than it is today.

The Decay of 40K Has a Half of 1

The Decay of ⁴⁰K Has a Half of 1