Chapter 24, Problem 24.44P

Interpretation Introduction

Interpretation:

Age of the fabric has to be determined using the given information.

Concept Introduction:

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

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

Integrated rate law for a first order reaction is given below.

  $\begin{array}{c}\ln \left(\frac{N_t}{N_0}\right)=-kt\\ \text{where,}\\ \\ \text{ln}\text{=}\text{natural}\text{logarithm}\\ \\ {\text{N}}_{\text{0}}\text{= Amount}\text{of}\text{subsatnce}\text{at}\text{time}\text{t}\text{=}\text{0}\\ \\ {\text{N}}_{\text{t}}\text{= Amount}\text{of}\text{subsatnce}\text{after}\text{time, t}\\ \\ \text{k}\text{=}\text{Rate}\text{constant}\end{array}$

Radioactive decay is a first order reaction.