Chapter 20, Problem 20.30QP

Interpretation Introduction

Interpretation: The age of the rock & the ratio between ${\text{U}}^{\text{238}}$ to ${\text{Pb}}^{\text{206}}$ should be determined.

Concept Introduction:

• Half-life period: The time required to the reduce to half of its original value.
• This is denoted by: ${\text{t}}_{\text{1/2}}$
• This term is popularly use in nuclear chemistry, to describe the stability & instability of atoms or radioactive decay.
• For determination of first order rate constant K in half –life period we use

  $\text{K=}\frac{\text{0}\text{.693}}{{\text{t}}_{\text{1/2}}}$ Equation.

• The half-life in first order does not depend upon the initial concentration.

To determine: The age of the rock and the ratio between ${\text{U}}^{\text{238}}$ to ${\text{Pb}}^{\text{206}}$ in a rock is $\text{1}{\text{.7×10}}^{\text{8}}\text{yr}$

Given:

Half-life of ${\text{U}}^{\text{238}}$= $\text{4}{\text{.51×10}}^{\text{9}}\text{yr}$&.the age of the rock is found to contain=1.09mg ${\text{U}}^{\text{238}}$&0.08mg ${\text{Pb}}^{\text{206}}$.