Chapter 19, Problem 19.1KSP

Interpretation Introduction

Interpretation:

The half-life of the isotope has to be identified from the given options for the given reaction

Concept introduction:

• Unstable nuclei emit radiation spontaneously to become stable nuclei by losing energy. This process of emission of radiation by unstable nuclei is known as radioactive decay.
• Radioactive decay is in the first order kinetics. Rate of radioactive decay at a time t is,

$\begin{array}{c}\text{ln}\frac{{\text{A}}_{\text{t}}}{{\text{A}}_{\text{0}}}\text{=}-\text{kt}\\ \text{where,}\text{k=}\text{First}\text{order}\text{rate}\text{constant}\\ {\text{N}}_{\text{0}}\text{=}\text{activity of radioactive isotope at time zero}\\ {\text{N}}_{\text{t}}\text{=}\text{activity of radioactive isotope at a time,}\text{t}\end{array}$

• Half-life of radioactive decay is the time required for a radioactive sample to decay to one half of the atomic nucleus.

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