Chapter 18, Problem 12QAP

Interpretation Introduction

(a)

Interpretation:

The balanced equation for the following nuclear reaction should be written.

The alpha particle is lost by Th-230.

Concept introduction:

A reaction in which a nucleus of an atom or two nuclei and a subatomic particle collide to form one or more nuclide which is different from the starting nuclide is known as nuclear reaction. Nuclear reactions can be classified as nuclear fission and nuclear fusion.

Answer to Problem 12QAP

$\text{T}\text{h}\to \text{R}{\text{a+}}_2^4\alpha$

Explanation of Solution

The reaction in which the change in atomic numbers, energy states and mass number of nuclei takes place is known as nuclear reaction.

Given that, the alpha particle is lost by Th-230.

Th-230 is the isotope of thorium, atomic number of thorium is 90.

Alpha emission is a radioactive decay in which the nucleus (unstable) emits an alpha particle

( ${}_2^4\alpha$) and thus, results in the formation of different nucleus having atomic number which is reduced by 2 and mass number which is reduced by 4.

To identify the missing species: Let the species be $\text{X}$

The reaction can be written as:

$\text{T}\text{h}{\to }_Z^A{\text{X+}}_2^4\alpha$

To balance the reaction: Mass number of the reactant must be equal to the mass number of the product.

$\begin{array}{l}230=A+4\\ A=230-4=226\end{array}$

Now, atomic number or charges must be balanced, therefore:

$\begin{array}{l}90=Z+2\\ Z=88\end{array}$

Thus, the product must have mass number and atomic number equal to 226 and 88. From the periodic table, the nucleus is $\text{R}\text{a}$.

Overall reaction is:

$\text{T}\text{h}\to \text{R}{\text{a+}}_2^4\alpha$

Interpretation Introduction

(b)

Interpretation:

The balanced equation for the following nuclear reaction should be written.

The beta particle is lost by Pb-210.

Concept introduction:

A reaction in which a nucleus of an atom or two nuclei and a subatomic particle collide to form one or more nuclide which is different from the starting nuclide is known as nuclear reaction. Nuclear reactions can be classified as nuclear fission and nuclear fusion.

Answer to Problem 12QAP

${}_{82}^{\text{210}}\text{Pb}\to \text{B}{\text{a+}}_{-1}^{0}e+\overline{\nu }$

Explanation of Solution

The reaction in which the change in atomic numbers, energy states and mass number of nuclei takes place is known as nuclear reaction.

Given that, the beta particle is lost by Pb-210.

Pb-210 is the isotope of lead, atomic number of lead is 82.

The daughter product is also known as decay product. A radioactive decay in which a neutron presents inside a nucleus is changed into a proton by emission of electron that is accompanied by antineutrino ( $\overline{\nu }$). The resulting nucleus has atomic number which is increased by one and mass number will remain same.

To identify the missing species: Let the species be $\text{X}$

The reaction can be written as:

${}_{82}^{\text{210}}\text{Pb}\to \text{X}{\text{+}}_{-1}^{0}e+\overline{\nu }$

To balance the reaction: Mass number of the reactant must be equal to the mass number of the product.

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

Now, atomic number or charges must be balanced, therefore:

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

Thus, the product must have mass number and atomic number equal to 210 and 83. From the periodic table, the nucleus is $\text{B}\text{a}$.

Overall reaction is:

${}_{82}^{\text{210}}\text{Pb}\to \text{B}{\text{a+}}_{-1}^{0}e+\overline{\nu }$

Interpretation Introduction

(c)

Interpretation:

The balanced equation for the following nuclear reaction should be written.

The production of Ba-140 with another nucleus and excess of two neutrons from the fusion of

U-235.

Concept introduction:

A reaction in which a nucleus of an atom or two nuclei and a subatomic particle collide to form one or more nuclide which is different from the starting nuclide is known as nuclear reaction. Nuclear reactions can be classified as nuclear fission and nuclear fusion.

Answer to Problem 12QAP

${}_{92}^{235}\text{U}\to \text{B}\text{a+}\text{K}{\text{r+2}}_0^{1}n$

Explanation of Solution

The reaction in which the change in atomic numbers, energy states and mass number of nuclei takes place is known as nuclear reaction.

Given that, the production of Ba-140 with another nucleus and excess of two neutrons from the fusion of U-235.

Ba-140 is the isotope of barium, atomic number of barium is 56.

U-235 is the isotope of uranium, atomic number of uranium is 92.

Now, symbol of neutron is ${}_0^{1}n$.

To identify the missing species: Let the species be $\text{X}$

The reaction can be written as:

${}_{92}^{235}\text{U}\to \text{B}\text{a+}\text{X}{\text{+2}}_0^{1}n$

To balance the reaction: Mass number of the reactant must be equal to the mass number of the product.

$\begin{array}{l}235=140+A+2\\ A=235-142=93\end{array}$, thus mass number on both sides are equal

Now, atomic number or charges must be balanced, therefore:

$\begin{array}{l}92=56+Z+0\\ Z=92-56=36\end{array}$, thus charges are equal on both sides

Thus, the product must have mass number and atomic number equal to 93 and 36. From the periodic table, the nucleus is $\text{K}\text{r}$.

Overall reaction is:

${}_{92}^{235}\text{U}\to \text{B}\text{a+}\text{K}{\text{r+2}}_0^{1}n$

Interpretation Introduction

(d)

Interpretation:

The balanced equation for the following nuclear reaction should be written.

The capture of electron or K-capture of Ar-37.

Concept introduction:

A reaction in which a nucleus of an atom or two nuclei and a subatomic particle collide to form one or more nuclide which is different from the starting nuclide is known as nuclear reaction. Nuclear reactions can be classified as nuclear fission and nuclear fusion.

Answer to Problem 12QAP

${}_{18}^{37}{\text{Ar+}}_{-1}^{0}e\to \text{C}\text{l}$

Explanation of Solution

The reaction in which the change in atomic numbers, energy states and mass number of nuclei takes place is known as nuclear reaction.

Given that, the capture of electron or K-capture of Ar-37.

Ar-37 is the isotope of argon, atomic number of argon is 18.

A radioactive decay in which an unstable nucleus captured an electron from inner shell and during this process proton is converted into a neutron and result in the emission of electron neutrino and gamma radiation is known as K-electron capture. The resultant product has atomic number which is reduced by one and mass number will remain same.

To identify the missing species: Let the species be $\text{X}$

The reaction can be written as:

${}_{18}^{37}{\text{Ar+}}_{-1}^{0}e{\to }_Z^A\text{X}$

To balance the reaction: Mass number of the reactant must be equal to the mass number of the product.

$\begin{array}{l}37+0=A\\ A=37\end{array}$

Now, atomic number or charges must be balanced, therefore:

$\begin{array}{l}18-1=Z\\ Z=17\end{array}$

Thus, the product must have mass number and atomic number equal to 37 and 17. From the periodic table, the nucleus is $\text{C}\text{l}$.

Overall reaction is:

${}_{18}^{37}{\text{Ar+}}_{-1}^{0}e\to \text{C}\text{l}$