Chapter 15, Problem 28QP

(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, or 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.

$\text{L}\text{i + }\text{X}\to 2\text{α}$

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

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

Balance the mass numbers.

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

$\begin{array}{c}7+\text{A}=2\left(4\right)\\ \text{A = 1}\end{array}$

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

$\begin{array}{c}3+\text{Z}=2\left(2\right)\\ \text{Z = 1}\end{array}$

Therefore, the reactant, $\text{X}$ , is a proton, $\text{H}$ .

Hence, the balanced reaction can be written as,

$\text{L}\text{i + }\text{H}\to 2\text{α}$

(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.

$\text{P}\text{b}\to \text{B}\text{i + }\text{X}$

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.

$\begin{array}{c}214=214+\text{A}\\ \text{A = 0}\end{array}$

Similarly, balance the atomic numbers.

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

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

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

Hence, the balanced reaction can be written as,

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

(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.

$\text{A}\text{l + }\text{n}\to \text{X + }\text{N}\text{a}$

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 products.

$\begin{array}{c}27+1=\text{A+24}\\ \text{A = 4}\end{array}$

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

$\begin{array}{c}13+0=\text{Z + 11}\\ \text{Z = 2}\end{array}$

Therefore, the product, $\text{X}$ , is $\text{α}$ . Hence, the balanced reaction can be written as,

$\text{A}\text{l + }\text{n}\to \text{α}\text{ + }\text{N}\text{a}$

(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.

$\text{C}\text{ + }\text{X}\to \text{N}$

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

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 products.

$\begin{array}{c}12+\text{A = 13}\\ \text{A = 1}\end{array}$

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

$\begin{array}{c}\text{6 + Z = 7}\\ \text{Z = 1}\end{array}$

Therefore, the reactant, $\text{X}$ is $\text{H}$ . Hence, the balanced nuclear reaction can be written as,

$\text{C}\text{ + }\text{H}\to \text{N}$