Chapter 25, Problem 32E

Interpretation Introduction

Interpretation:

The age of the piece of the volcanic rock needs to be determined.

Concept introduction:

All radioactive reactions follow the first order kinetics thus;decay constant is related to half-life time of the reaction as follows:

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

Here, k is decay constant and $t_{1/2}$ is half lifetime.

For the given radioactive decay, the age of the rock can be calculated using the following formula:

$t=\frac{1}{\lambda }\ln \left(\frac{\text{Ar}-40}{\text{K}-40}\left(\frac{\lambda }{{\lambda }_e}\right)+1\right)$

Here, $\lambda$ is decay constant from beta decay and ${\lambda }_e$ from electron capture.