Chapter 19, Problem 19.100CP

Interpretation Introduction

Interpretation:

The age of the elements should be determined.

Concept introduction:

Here, ratio of isotopes is given. By using this we can determine the age of the elements.

$\frac{{\text{N}}_{\text{1}}}{{\text{N}}_{\text{2}}}{\text{=e}}^{\text{0}\text{.693t}\left[\frac{\text{1}}{{{\text{(t}}_{\text{1/2}}\text{)}}_{\text{2}}}-\frac{\text{1}}{{{\text{(t}}_{\text{1/2}}\text{)}}_{\text{1}}}\right]}$

${\text{N}}_{\text{1}}$and ${\text{N}}_{\text{2}}$ is rate 1 and 2
$t_{1/2}$ is half-life

Given:

Isotopes of Uranium = $U$ and $U$

Ratio of isotopes = $\frac{U}{U}=7.25\times {10}^{-3}$

Half-life of $U$ = $7.04\times {10}^8$ y
Half-life of $U$ = $4.47\times {10}^9$ y