Chapter 25, Problem 71IAE

Interpretation Introduction

Interpretation:

The age of the earth depending on the current natural abundances of U-238 and U-235 isotopes of Uranium needs to be determined, assuming initial abundance of both be equal.

Concept introduction:

All radioactive reactions are first order thus the integrated rate law can be represented as follows:

$\ln \frac{{\left[A\right]}_t}{{\left[A\right]}_0}=-\lambda t$

Also, for first order reaction, the relation between half-life time and decay constant is as follows:

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

Here, $t_{1/2}$ for the reaction in which the concentration of reactant becomes half of its initial value.