Chapter 19, Problem 19.21A

Interpretation Introduction

Interpretation:

To calculate how long ago the rock cooled and also to calculate the age of the painting from Lascaux cave

Concept Introduction:

Half-life is defined as the time taken for a radioactive substance to decay to half of its original amount.

When the amount of radioactive reactant and product are given, then the ratio of amount of product: amount of reactant remaining gives the fraction of the amount remaining.
This fraction can be used to calculate how many half-lives have elapsed from the formula:

  $fraction={(\frac{1}{2})}^n$ where n= number of half lives elapsed
This n when multiplied by the half life provides the age of the substance.