Chapter 20.3, Problem 20.3.3SR

Interpretation Introduction

Interpretation:

The number of half-lives elapsed when Iron-57 decays to cobalt via beta emission should be explained.

Concept Introduction:

• Half-life period: The time required to reduce, half of its original value.
• This is denoted by:${\text{t}}_{\text{1/2}}$
• This term is popularly use in nuclear chemistry, to describe the stability & instability of atoms or radioactive decay.
• For determination of first order rate constant k we use

$\text{k=}\frac{\text{0}\text{.693}}{{\text{t}}_{\text{1/2}}}{\text{t}}_{\frac{\text{1}}{\text{2}}}\text{=}\text{half}\text{life}$

The half-life in first order does not depend upon the initial concentration.

• Half-life can be calculated by the equation $\begin{array}{l}\text{N}\text{=}{\text{N}}_{\text{0}}{\left(\frac{\text{1}}{\text{2}}\right)}^{\text{n}}\\ \text{N}\text{=}\text{Number}\text{of}\text{radioactive}\text{atoms}\text{at}\text{a}\text{particular}\text{time}\text{'t'}\\ {\text{N}}_{\text{0}}\text{=}\text{Initial}\text{number}\text{of}\text{radioactive}\text{atoms}\\ \text{n}\text{=}\text{number}\text{of}\text{half}\text{lives}\text{passed}\end{array}$