Chapter 22, Problem 22.47CHP

a)

Interpretation Introduction

Interpretation:

The balanced equations for the decay of ${}^{\text{226}}\text{Ac}$ by $\text{α-}$ emission, $\text{β-}$ emission and electron capture has to be written.

Concept Introduction:

Nuclear reaction: In the nuclear reaction, fusion of two lighter nuclei to produce stable nuclei or the heavier nuclei splits into stable daughter nuclei generates the excess amount of energy.

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:

The days required for $80.0\%$ of a sample of ${}^{\text{226}}\text{Ac}$ to decay has to be calculated.

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:

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