Chapter 19, Problem 55AP

Interpretation Introduction

Interpretation: The age of the rock sample containing ${}^{40}\text{Ar}$ and ${}^{40}\text{K}$ needs to be determined.

Concept Introduction: All radioactive decay reactions follow first-order kinetics. Thus, the relation between rate constant and half-life time is as follows:

$k=\frac{0.6932}{t_{1/2}}$

Also, the integrated law expression is as follows:

$\left[N\right]={\left[N\right]}_{\text{o}}{e}^{-kt}$

Here, $\left[N\right]$ is the amount of radioactive nuclei at time t, ${\left[N\right]}_{\text{o}}$ is initial amount of the radioactive nuclei and k is rate constant.