Chapter 25, Problem 55IL

Interpretation Introduction

Interpretation:

The age of the bone fragment has to be calculated.

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of ${}^{12}\text{C}$ and ${}^{14}\text{C}$ that takes in. when the living organism dies, the intake of ${}^{14}\text{C}$ stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value, given by,$\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{\text{k}}\\ \text{where,}\text{k}\text{is rate constant}\text{.}\\ \left(\text{or}\right)\\ {\text{lnA- lnA}}_0\text{= -kt}\end{array}$

According to first order reaction;

$\text{ln(}\text{A}/{\text{A}}_{\text{0}}\text{)=-kt}$, where

$\begin{array}{l}\text{A=activity}\\ {\text{A}}^{\text{0}}\text{=initial}\text{activity}\\ \text{t=time}\end{array}$