Chapter 11, Problem 41P

Interpretation Introduction

Interpretation: It is required to find the rate constant with the available information then the half-life time can be determined using an equation.

Concept Introduction:The half-life time is the time it takes for a sample to decay by 50%. A radioactive decay can be described using first order reaction kinetics.

All radioactive reaction follow first order kinetics thus, rate constant and half-life time are related to each other as follows:

  

Also, the rate equation for first order reaction is as follows:

  

where:

is the initial amount.
is the final amount
t is the time elapsed
k is the rate constant