Chapter 20, Problem 93RQ

Interpretation Introduction

Interpretation:

The percentage of cesium chloride made of cesium-137 (beta-emitter, $t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}=30.1\text{ y}$) which is left after 150 years(y), and the chemical product formed are to be discussed here.

Concept Information:

Rate expression for a first order reaction, here, radioactive decay, is given as:

$rate=-\frac{\Delta \left[\text{A}\right]}{\Delta t}=\text{k}\left[\text{A}\right]$

Solving this rate equation, we get the following relation between concentration and time,

$\left[\text{A}\right]={\left[\text{A}\right]}_0{e}^{-\text{k}t}$

Where, ${\left[\text{A}\right]}_0$ and $\left[\text{A}\right]$ denote, respectively, the initial and final concentrations of reactant A.