Chapter 15, Problem 30QP

(a)

Interpretation Introduction

Interpretation:

The balanced equation of beta emission by $\text{A}\text{g}$ is to be determined.

Explanation of Solution

A nuclear reaction involves changes at the subatomic level such as changes in the number of protons, number of neutrons or energy state. A nuclear reaction is balanced by two conservation laws. That are,

1. conservation of mass number that conserves the mass number of the elements.

2. conservation of charges that conserves the atomic number of the elements.

The reaction can be written as follows:

$\text{A}\text{g}\to \text{X}+\text{e}{}^{-}$

Where, $\text{A}$ is mass number, $\text{Z}$ is the atomic number of the unknown product, $\text{X}$ .

Apply the conservation conditions for mass numbers and atomic numbers to identify the product, $\text{X}$ .

Balance the mass numbers according to the law of conservation of mass numbers. The mass number of the reactant is equal to the sum of mass numbers of the products.

$\begin{array}{c}114=\text{A + 0}\\ \text{A = 114}\end{array}$

Similarly, balance the atomic numbers according to the law of conservation of charges. The atomic number of the reactant is equal to the sum of atomic numbers of the products.

$\begin{array}{c}47=\text{Z + }\left(-1\right)\\ \text{Z = 48}\end{array}$

The element with atomic number $48$ is cadmium. Therefore, the product, $\text{X}$ is $\text{C}\text{d}$ .

Hence, the balanced equation for the reaction is,

$\text{A}\text{g}\to \text{C}\text{d }+\text{e}{}^{-}$

(b)

Interpretation Introduction

Interpretation:

The balanced equation of alpha emission by $\text{P}\text{o}$ is to be determined.

Explanation of Solution

The given reaction can be written as follows:

$\text{P}\text{o}\to \text{X}+\text{α}$

Where, $\text{A}$ is mass number, $\text{Z}$ is the atomic number of the unknown product, $\text{X}$ .

Apply the conservation conditions for mass numbers and atomic numbers to identify the product, $\text{X}$ .

Balance the mass numbers according to the law of conservation of mass numbers. The mass number of the reactant is equal to the sum of mass numbers of the products.

$\begin{array}{c}210=\text{A + 4}\\ \text{A = 206}\end{array}$

Similarly, balance the atomic numbers according to the law of conservation of charges. The atomic number of the reactant is equal to the sum of atomic numbers of the products.

$\begin{array}{c}84=\text{Z + 2}\\ \text{Z = 82}\end{array}$

The element with atomic number $82$ is lead. Therefore, the product, $\text{X}$ is $\text{P}\text{b}$ .

Hence, the balanced equation for the reaction is,

$\text{P}\text{o}\to \text{P}\text{b +}\text{α}$

(c)

Interpretation Introduction

Interpretation:

The balance equation of electron capture by $\text{B}\text{a}$ is to be determined.

Explanation of Solution

The reaction can be written as follows:

$\text{B}\text{a }+\text{e}{}^{-}\to \text{X}$

Where, $\text{A}$ is mass number, $\text{Z}$ is the atomic number of the unknown product, $\text{X}$ .

Apply the conservation conditions for mass numbers and atomic numbers to identify the product, $\text{X}$ .

Balance the mass numbers according to the law of conservation of mass numbers. The mass number of the reactant is equal to the sum of mass numbers of the products.

$\begin{array}{c}133+0=\text{A}\\ \text{A = 133}\end{array}$

Similarly, balance the atomic numbers according to the law of conservation of charges. The atomic number of the reactant is equal to the sum of atomic numbers of the products.

$\begin{array}{c}56-1=\text{Z}\\ \text{Z = 55}\end{array}$

The element with atomic number $55$ is caesium. Therefore, the product, $\text{X}$ is $\text{C}\text{s}$ .

Hence, the balanced equation for the reaction is,

$\text{B}\text{a}+\text{e}{}^{-}\to \text{C}\text{s}$