Chapter 12, Problem 12.123CHP

Interpretation Introduction

Interpretation:

The decay constant of ${}^{40}K$ has to be calculated. The number of ${}^{40}{K}^{+}$ ions presents in $1.00g$ of $KCl$ and the number of disintegrations/s by $1.00g$ of $KCl$ has to be determined.

Concept introduction:

Half-life time: It is the time required for the reactant (substrate) concentration reduces to one-half of its initial concentration.

$\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{\text{k}}\\ \text{where,}\\ {\text{t}}_{\text{1/2}}\text{-}\text{half-life}\text{time}\\ \text{k}\text{-}\text{rate}\text{constant}\end{array}$

$\begin{array}{l}Decayrate=kN\\ where,\\ Nisthenumberofatoms\end{array}$