Chapter 25, Problem 71A

(a)

Interpretation Introduction

Interpretation: Complete the equations using the balanced nuclear reaction.

Concept Introduction: When an atomic nucleus or more atomic nucleus and a subatomic particle collide, one or more nuclides also known as nuclear reactions are created.

Answer to Problem 71A

The complete nuclear reaction is as follows:

  ${}_{\text{19}}^{\text{38}}\text{K}{\to }_{\text{20}}^{\text{38}}\text{Ca}{+}_{-1}^0\text{e}$

Explanation of Solution

According to nuclear reactions, the sum of the atomic number and mass number on the reactant side is equal to the sum of the atomic number and mass on the product side.

In the given reaction, let $x$ be the unknown’s atomic number and $y$ be the unknown’s mass number.

Equate the values of the atomic number of the reactants and products.

  $\begin{array}{l}19=20+x\\ x=19-20\\ x=-1\end{array}$

Equate the values of the mass number of the reactants and products.

  $\begin{array}{l}38=38+y\\ y=38-38\\ y=0\end{array}$

The particle with $-1$ atomic number and zero mass number is a beta particle.

The complete balanced nuclear equation is as follows:

  ${}_{\text{19}}^{\text{38}}\text{K}{\to }_{\text{20}}^{\text{38}}\text{Ca}{+}_{-1}^0\text{e}$

(b)

Interpretation Introduction

Interpretation: Complete the equations using the balanced nuclear reaction.

Concept Introduction: When an atomic nucleus or more atomic nucleus and a subatomic particle collide, one or more nuclides also known as nuclear reactions are created.

Answer to Problem 71A

The complete nuclear reaction is as follows:

  ${}_{94}^{242}\text{Pu}{\to }_{92}^{238}\text{U}{+}_2^4\text{He}$

Explanation of Solution

According to nuclear reactions, the sum of the atomic number and mass number on the reactant side is equal to the sum of the atomic number and mass on the product side.

In the given reaction, let $x$ be the unknown’s atomic number and $y$ be the unknown’s mass number.

Equate the values of the atomic number of the reactants and products.

  $\begin{array}{l}94=x+2\\ x=94-2\\ x=92\end{array}$

Equate the values of the mass number of the reactants and products.

  $\begin{array}{l}242=y+4\\ y=242-4\\ y=238\end{array}$

The element with $92$ atomic number is Uranium.

The complete balanced nuclear equation is as follows:

  ${}_{94}^{242}\text{Pu}{\to }_{92}^{238}\text{U}{+}_2^4\text{He}$

(c)

Interpretation Introduction

Interpretation: Complete the equations using the balanced nuclear reaction.

Concept Introduction: When an atomic nucleus or more atomic nucleus and a subatomic particle collide, one or more nuclides also known as nuclear reactions are created.

Answer to Problem 71A

The complete nuclear reaction is as follows:

  ${}_{31}^{\text{68}}\text{Ga}{\to }_{32}^{\text{68}}\text{Ge}{+}_{-1}^0\text{e}$

Explanation of Solution

According to nuclear reactions, the sum of the atomic number and mass number on the reactant side is equal to the sum of the atomic number and mass on the product side.

In the given reaction, let $x$ be the unknown’s atomic number and $y$ be the unknown’s mass number.

Equate the values of the atomic number of the reactants and products.

  $\begin{array}{l}31=x-1\\ x=31+1\\ x=32\end{array}$

Equate the values of the mass number of the reactants and products.

  $\begin{array}{l}68=y+0\\ y=68\end{array}$

The element with $32$ atomic number is Germanium.

The complete balanced nuclear equation is as follows:

  ${}_{31}^{\text{68}}\text{Ga}{\to }_{32}^{\text{68}}\text{Ge}{+}_{-1}^0\text{e}$

(d)

Interpretation Introduction

Interpretation: Complete the equations using the balanced nuclear reaction.

Concept Introduction: When an atomic nucleus or more atomic nucleus and a subatomic particle collide, one or more nuclides also known as nuclear reactions are created.

Answer to Problem 71A

The complete nuclear reaction is as follows:

  ${}_{32}^{\text{68}}\text{Ge}{\to }_{31}^{\text{68}}\text{Ga}{+}_{+1}^0\text{e}$

Explanation of Solution

According to nuclear reactions, the sum of the atomic number and mass number on the reactant side is equal to the sum of the atomic number and mass on the product side.

In the given reaction, let $x$ be the unknown’s atomic number and $y$ be the unknown’s mass number.

Equate the values of the atomic number of the reactants and products.

  $\begin{array}{l}32=31+x\\ x=32-31\\ x=1\end{array}$

Equate the values of the mass number of the reactants and products.

  $\begin{array}{l}68=68+y\\ y=68-68\\ y=0\end{array}$

The particle with $+1$ atomic number and zero mass number is a positron.

The complete balanced nuclear equation is as follows:

  ${}_{32}^{\text{68}}\text{Ge}{\to }_{31}^{\text{68}}\text{Ga}{+}_{+1}^0\text{e}$