Chapter 2, Problem 2.73QP

a)

Interpretation Introduction

Interpretation: The ratio of neutrons to protons along with their respective numbers in the nucleus of each atom to be identified.

Concept Introduction:

Conversion of atoms to moles: $\text{no}\text{.of moles = }\frac{\text{no}\text{.of atoms}}{\text{Avogadro's number}}.$

Nuclear stability: The nucleus is composed of protons and neutrons. The strongest nuclear force binds the particles tightly. Though the protons repel each other due to no attraction between similar charges, possess short-range attractions made the attraction possible between proton and proton, proton and neutron, neutron and neutron.

The stability of any element is determined by the difference between columbic repulsion and the short-range attraction. If repulsion outweighs the attraction, the disintegration of nucleus occurs by producing the daughter nuclides. If the attractive forces prevail, the nucleus is stable.

Answer to Problem 2.73QP

$\begin{array}{l}\text{a}{\text{. Isotope }}_2^4{\text{He }}_{10}^{20}{\text{Ne }}_{18}^{40}{\text{Ar }}_{36}^{84}{\text{Kr }}_{54}^{132}\text{Xe}\text{.}\\ \text{ No}\text{.of Protons 2 10 18 36 54}\\ \text{ No}\text{.of Neutrons 2 10 22 48 78}\end{array}$

Explanation of Solution

Predict the number of protons and neutrons of each atom.

$\begin{array}{l}{\text{The element symbol : }}_{\text{Z}}^{\text{A}}\text{X,}\\ \text{where, A (mass number) = no}\text{.of protons + no}\text{.of neutrons}\text{.}\\ \text{ Z (atomic number) = no}\text{. of protons}\text{. (electrons = protons)}\text{.}\end{array}$

• ${\text{The element symbol : }}_{\text{2}}^{\text{4}}\text{He,}$

$\begin{array}{l}\text{Z (atomic number) = no}\text{. of protons}\text{. (protons = electrons)}\\ \text{= 2}\text{.}\\ \text{No}\text{.of neutrons = A (mass number) - no}\text{.of protons}\\ \text{ = 4 - 2 = 2}\text{.}\\ \text{No}\text{.of Protons : 2}\\ \text{No}\text{.of neutrons : 2}\end{array}$

In the helium atom, the atomic number $\text{2}$ is equal to protons number and the differences between the mass number and proton number obtains the neutron number $\text{2}$.

• ${\text{The element symbol : }}_{10}^{20}\text{Ne,}$

$\begin{array}{l}\text{Z (atomic number) = no}\text{. of protons}\text{. (protons = electrons)}\\ \text{= 10}\text{.}\\ \text{No}\text{.of neutrons = A (mass number) - no}\text{.of protons}\\ \text{ = 20 - 10 = 10}\text{.}\\ \text{No}\text{.of Protons : 10}\\ \text{No}\text{.of neutrons : 10}\end{array}$

In the Neon atom, the atomic number $\text{10}$ is equal to protons number and the differences between the mass number and proton number obtains the neutron number $\text{10}$.

• ${\text{The element symbol : }}_{18}^{40}\text{Ar,}$

$\begin{array}{l}\text{Z (atomic number) = no}\text{. of protons}\text{. (protons = electrons)}\\ \text{= 18}\text{.}\\ \text{No}\text{.of neutrons = A (mass number) - no}\text{.of protons}\\ \text{ = 40 - 18 = 22}\text{.}\\ \text{No}\text{.of Protons : 18}\\ \text{No}\text{.of neutrons : 22}\end{array}$

In the Argon atom, the atomic number $\text{18}$ is equal to protons number and the differences between the mass number and proton number obtains the neutron number $\text{22}$.

• ${\text{The element symbol : }}_{36}^{84}\text{Kr,}$

$\begin{array}{l}\text{Z (atomic number) = no}\text{. of protons}\text{. (protons = electrons)}\\ \text{= 36}\text{.}\\ \text{No}\text{.of neutrons = A (mass number) - no}\text{.of protons}\\ \text{ = 84 - 36 = 48}\text{.}\\ \text{No}\text{.of Protons : 36}\\ \text{No}\text{.of neutrons : 48}\end{array}$

In the Krypton atom, the atomic number $\text{36}$ is equal to protons number and the differences between the mass number and proton number obtains the neutron number $\text{48}$.

• ${\text{The element symbol : }}_{54}^{132}\text{Xe,}$

$\begin{array}{l}\text{Z (atomic number) = no}\text{. of protons}\text{. (protons = electrons)}\\ \text{= 54}\text{.}\\ \text{No}\text{.of neutrons = A (mass number) - no}\text{.of protons}\\ \text{ = 132 - 54 = 78}\text{.}\\ \text{No}\text{.of Protons : 54}\\ \text{No}\text{.of neutrons : 78}\end{array}$

In the Xenon atom, the atomic number $\text{54}$ is equal to protons number and the differences between the mass number and proton number obtains the neutron number $\text{78}$.

Conclusion

The ratio of neutrons to protons along with their respective numbers in the nucleus of each atom is identified.

b)

Interpretation Introduction

Interpretation: The ratio of neutrons to protons along with their respective numbers in the nucleus of each atom to be identified.

Concept Introduction:

Conversion of atoms to moles: $\text{no}\text{.of moles = }\frac{\text{no}\text{.of atoms}}{\text{Avogadro's number}}.$

Nuclear stability: The nucleus is composed of protons and neutrons. The strongest nuclear force binds the particles tightly. Though the protons repel each other due to no attraction between similar charges, possess short-range attractions made the attraction possible between proton and proton, proton and neutron, neutron and neutron.

The stability of any element is determined by the difference between columbic repulsion and the short-range attraction. If repulsion outweighs the attraction, the disintegration of nucleus occurs by producing the daughter nuclides. If the attractive forces prevail, the nucleus is stable.

Answer to Problem 2.73QP

$\begin{array}{l}\text{b}\text{. neutron/proton ratio 1}\text{.00 1}\text{.00 1}\text{.22 1}\text{.33 1}\text{.44 }\\ \\ \text{The ratio increasing with increasing atomic number}\text{.}\end{array}$

Explanation of Solution

Analyze the ratio of neutrons to protons for each element.

$\begin{array}{l}\text{b}{\text{. Isotope }}_2^4{\text{He }}_{10}^{20}{\text{Ne }}_{18}^{40}{\text{Ar }}_{36}^{84}{\text{Kr }}_{54}^{132}\text{Xe}\text{.}\\ \text{ No}\text{.of Protons 2 10 18 36 54}\\ \text{ No}\text{.of Neutrons 2 10 22 48 78}\\ \text{ Neutron/proton ratio}2/2\text{ 10/10 22/18 48/36 78/54 }\\ \text{ 1}\text{.00 1}\text{.00 1}\text{.22 1}\text{.33 1}\text{.44 }\end{array}$

The ratio of neutron to proton is increasing down the group along with increasing the atomic number.

Conclusion

The ratio of neutrons to protons along with their respective numbers in the nucleus of each atom is identified.