Chapter 18, Problem 35QAP

Interpretation Introduction

Interpretation:

The age of the cypress beam needs to be determined, if half life of the carbon-14 isotope is 5790 years.

Concept introduction:

All the radioactive reactions are first order reactions. For first order reaction, the relation between rate constant, k and half-life time is as follows:

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

Also, the integrated rate expression can be written as follows:

$t=\frac{2.303}{k}\log \frac{A_o}{A_t}$

Here, t is time required to decrease the amount of substance from $A_o$ to $A_t$ and k is rate constant for the reaction.