Chapter 9, Problem 26P

Interpretation Introduction

Interpretation:

The percentage of polonium-218 left in the lung after 9 min of its inhalation should be determined.

Concept Introduction:

The nuclear disintegration is a first order reaction and following first order kinetics.

The rate law expression for it will be.

$\text{ln}\frac{{\text{N}}_{\text{0}}}{{\text{N}}_{\text{t}}}\text{= kt}$

Where,

$\begin{array}{l}{\text{N}}_{\text{0}}\text{= initial amount}\\ {\text{N}}_{\text{t}}=\text{ final amount after time "t"}\\ \text{k = rate constant}\\ \text{t = time = 1 year = 1 }\times \text{ 365 days}\end{array}$

Rate constant for first order reaction is related to half life as.

$\text{k = }\frac{0.693}{{\text{t}}_{1/2}}$.