Chapter 24, Problem 24.141P

Interpretation Introduction

Interpretation:

Time required for producing $1.00\text{ kg}$ of plutonium-239 has to be determined using the given information where the reaction is said to be complete when $90\%{}^{239}Pu$ is formed.

Concept Introduction:

Radioactive decay is a first order reaction.

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

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

Integrated rate law for a first order reaction is given below

  $\begin{array}{c}t\text{ = }\frac{1}{k}\ln \frac{N_0}{N_t}\\ \text{where,}\\ \text{ln}\text{=}\text{natural}\text{logarithm}\\ {\text{N}}_{\text{0}}\text{= Amount}\text{of}\text{subsatnce}\text{at}\text{time}\text{t}\text{=}\text{0}\\ {\text{N}}_{\text{t}}\text{= Amount}\text{of}\text{subsatnce}\text{after}\text{time, t}\\ \text{k}\text{=}\text{rate}\text{constant}\end{array}$