Chapter 20, Problem 115RQ

Interpretation Introduction

Interpretation:

The age of the given rock sample, in years, is to be determined.

Concept Introduction:

Radiological dating is taken into consideration for calculating the age of a rock sample that is based on the half-lives of the radionuclides. It involves radiological dating a pair of isotopes that are related as a ‘parent’ to the ‘daughter’ radioactive disintegrations. The most commonly used isotopes sought for such purposes are $\text{K}-\text{40 and Ar}-\text{40}$. $\text{K}-\text{40}$ is a naturally occurring radionuclide while $\text{Ar}-\text{40}$ is one of the daughter disintegrations of $\text{K}-\text{40}$.

Half-life for a first order reaction is given by the following equation:

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

Here, $t_{1/2}$ is the half-life and $k$ is the rate constant.