Chapter 25, Problem 58IL

(a)

Interpretation Introduction

Interpretation:

An equation for the neutron capture reaction and for the reaction in which the product of this reaction decays by beta-emission has to be written.

Concept introduction:

Balancing nuclear reaction equation: The balanced nuclear reaction should conserve both mass number and atomic number.

• The sum of the mass numbers of the reactants should be equal to the sum of mass numbers of the products in the reaction.
• The sum of atomic numbers (or the atomic charge) of the reactants should be equal to the sum of atomic numbers (or the atomic charge) of the products in the reaction.

(b)

Interpretation Introduction

Interpretation:

Half-life of Sodium-23 has to be determined.

Concept introduction:

Concept Introduction:

Radiocarbon dating: The dynamic equilibrium exists in all living organism by exhaling or inhaling, maintain the same ratio of ${}^{12}\text{C}$ and ${}^{14}\text{C}$ that takes in. when the living organism dies, the intake of ${}^{14}\text{C}$ stops and it’s the ratio no longer exhibits equilibrium; undergoes radioactive decay.

Half-life period: The time required to reduce to half of its initial value.

Formula used to calculate half-life:

$\begin{array}{l}{\text{t}}_{\text{1/2}}\text{=}\frac{\text{0}\text{.693}}{\text{k}}\\ \text{where,}\text{k}\text{is rate constant}\text{.}\\ \left(\text{or}\right)\\ {\text{ln[N]}}_{\text{t}}{\text{- ln[N]}}_0\text{= -kt}\end{array}$