Chapter 24, Problem 24.96P

Interpretation Introduction

Interpretation:

Half-life of ${}^{226}\text{Ra}$ has to be determined using the given information.

Concept Introduction:

Radioactive decay is a first order reaction.

Decay rate can be calculated using the given equation as follows,

  $\begin{array}{c}\text{A= kN}\\ \\ \text{where, }\\ \text{A = Rate of radioactivity}\\ \text{k = Rate constant}\\ \text{N = No}\text{. of radioactive nuclei}\end{array}$

The half–life period for first order reaction is as follows:

  $\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\ln \text{ 2}}{\text{k}}\\ \text{Where,}\\ \text{k = Rate constant}\\ {\text{t}}_{\text{1/2}}\text{= half-life}\end{array}$