Chapter 15, Problem 27QP

(a)

Interpretation Introduction

Interpretation:

The balanced nuclear reaction for the given nuclear reaction is to be determined

Explanation of Solution

A nuclear reaction involves changes at the subatomic level such as, the changes in the number of protons, the number of neutrons, and the energy state. To balance a nuclear reaction, two conservation conditions can be used, conservation of mass number and conservation of charges (atomic number).

The given reaction is as follows.

$\text{U}\to \text{T}\text{h + }\text{X}$

Where, $\text{A}$ is mass number and $\text{Z}$ 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.

The sum of mass numbers of reactants is equal to the sum of mass numbers of the products.

$\begin{array}{c}238=234+\text{A}\\ \text{A = 4}\end{array}$

Similarly, balance the atomic numbers. The sum of atomic numbers of reactants is equal to the sum of atomic numbers of the products.

$\begin{array}{c}92=90+\text{Z}\\ \text{Z = 2}\end{array}$

The element with atomic number $2$ is Helium, denoted by $\text{H}\text{e}$ . It is an alpha particle. Therefore, the product, $\text{X}$ is $\text{α}$ . Hence, the balanced reaction can be written as,

$\text{U}\to \text{T}\text{h + }\text{α}$

(b)

Interpretation Introduction

Interpretation:

The balanced nuclear reaction for the given nuclear reaction is to be determined

Explanation of Solution

The given reaction is as follows.

$\text{T}\text{h}\to \text{P}\text{a + }\text{X}$

Where, $\text{A}$ is mass number and $\text{Z}$ 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. The sum of mass number of reactants is equal to the sum of mass number of the products.

$\begin{array}{c}234=234+\text{A}\\ \text{A = 0}\end{array}$

Similarly, balance the atomic numbers. The sum of atomic numbers of reactants is equal to the sum of atomic numbers of the products.

$\begin{array}{c}90=91+\text{Z}\\ \text{Z = }-\text{1}\end{array}$

As the charge is $-1$ , product $\text{X}$ is a beta particle.

Hence, the balanced reaction can be written as,

$\text{T}\text{h}\to \text{P}\text{a + }\text{β}{}^{\text{-}}$

(c)

Interpretation Introduction

Interpretation:

The balanced nuclear reaction for the given nuclear reaction is to be determined

Explanation of Solution

The given reaction is as follows.

$\text{U}\to \text{α}\text{ + }\text{X}$

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

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

Balance the mass numbers.

The sum of mass numbers of reactants is equal to the sum of mass numbers of the products.

$\begin{array}{c}234=4+\text{A}\\ \text{A = 230}\end{array}$

Similarly, balance the atomic numbers. The sum of atomic numbers of reactants is equal to the sum of atomic numbers of the products.

$\begin{array}{c}92=2+\text{Z}\\ \text{Z = 90}\end{array}$

The element with atomic number $90$ is Thorium. Therefore, the product, $\text{X}$ , is $\text{T}\text{h}$ .

Hence, the balanced reaction can be written as,

$\text{U}\to \text{α}\text{ + }\text{T}\text{h }$

(d)

Interpretation Introduction

Interpretation:

The balanced nuclear reaction for the given nuclear reaction is to be determined

Explanation of Solution

The given reaction is as follows.

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

Where, $\text{A}$ is mass number and $\text{Z}$ 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. The sum of mass numbers of reactants equal to the sum of mass numbers of the products.

$\begin{array}{c}210+0=\text{A}\\ \text{A = 210}\end{array}$

Similarly, balance the atomic numbers.

The sum of atomic numbers of reactants is equal to the sum of atomic numbers of the products.

$\begin{array}{c}83+\left(-1\right)=\text{Z}\\ \text{Z = 82}\end{array}$

The element with atomic number $82$ is Lead. Therefore, the product, $\text{X}$ , is $\text{P}\text{b}$ . Hence, the balanced reaction can be written as,

$\text{B}\text{i + }\text{e}{}^{-}\to \text{P}\text{b}$