Chapter 20, Problem 99RQ

Interpretation Introduction

Interpretation:

The age of the given rock sample is to be calculated under the given conditions.

Concept Introduction:

For calculating the age of a rock sample, radiological dating is taken into consideration, which is based on the half-lives of radio nuclides. It uses radiological dating pair of isotopes that undergo ‘parent’ to ‘daughter’ radioactive disintegrations. The most commonly used isotopes for such purposes are $\text{K}-\text{40}$ and $\text{Ar}-\text{40}$. $\text{K}-\text{40}$ is a naturally occurring radio nuclide while $\text{Ar}-\text{40}$ is one of the daughter disintegrations of $\text{K}-\text{40}$.

The half-life for a first-order reaction is given as:

$t_{1/2}=\frac{\text{ln 2}}{k}$