Chapter 14, Problem 14.87PAE

Interpretation Introduction

Interpretation: The value of Avogadro’s number needs to be calculated if the molar mass of ²²⁶Ra is 226.025 g/mol and half-life of the isotope is 1600 years. (1 g of ²²⁶Ra is equals to 1 curie (Ci) and $1\text{ Ci}=\text{3}\text{.70}\times {\text{10}}^{10}$ disintegrations per second.

Concept Introduction:

All radioactive reactions follow first-order kinetics.

For a first order reaction, rate constant and half life time are related to each other as follows:

$k=\frac{0.693}{t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}}$

Here,

$t_{\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$ is half-life time

k is the decay constant of the reaction

Activity is defined as:

$A=k{N}_A$

Where,

A is the activity of the radioactive nuclei

N_A is the Avogadro’s number