Chapter 18, Problem 1RQ

Interpretation Introduction

Interpretation: The given terms are to be defined.

Concept introduction: Nuclei of radioactive element decompose in various ways.  There are two major categories.  One involves a change in mass number of the decaying nucleus while others do not.  Types of radioactive processes include $\text{α}$ particle production, $\text{β}$ particle production, $\text{γ}$ ray production, electron capture and many others.

Explanation of Solution

Explanation

(a)

To define: The term thermodynamic stability.

The thermodynamic stability is related with neutron to proton ratio in a nucleus of an atom.

Thermodynamic stability is defined as the potential energy of a nucleus which is formed from its constituent protons and neutrons. Higher the nuclear binding energy, higher will be the thermodynamic stability of a nuclide.

(b)

To define: The term kinetic stability.

Kinetic stability is obtained by radioactive decay.

Kinetic stability of a nucleus indicates the probability of a particular unstable nucleus to undergo decomposition through a process called radioactive decay to form a relatively stable nuclide.

(c)

To define: The term radioactive decay.

The unstable nucleus loses energy by the emission of ionizing particles and radiation.

All the nuclides with protons greater than or equal to $84$ are unstable. They decompose forming another nucleus and one or more particles and this process is known as radioactive decay. As the nuclei get larger, more neutrons are required for the stability.

(d)

To determine: The term beta particle production.

Beta particle production is characterized by the increase in the atomic number of the product nuclide.

The decay process in which the mass number of the decaying nucleus remains constant while atomic number increases by one unit is known as beta particle production decay. The decay of carbon- $14$ is an example of beta particle production decay.

${}_6^{14}\text{C}\to {}_7^{14}\text{N}+{}_{-1}^0\text{e}$

Where,

• ${}_{-1}^0\text{e}$ is a beta particle.

(e)

To determine: The term alpha particle production.

Alpha particles are positively charged helium nucleus.

When the atomic number of the decaying nuclide decreases by $2$ and mass number decreases by $4$ units, then the type of decay is alpha particle production. Its example is decay of ${}_{\text{92}}^{\text{238}}\text{U}$.

${}_{\text{92}}^{\text{238}}\text{U}\to {}_{\text{90}}^{\text{234}}\text{Th}+{}_2^4\text{He}$

Where,

• ${}_2^4\text{He}$ is a beta particle.

(f)

To define: The term positron production.

It is the decay mode for nuclides that are below the zone of stability.

The nuclides that have neutrons to protons ratio too small undergoes a decay known as positron production. Its example is decay of ${}_{\text{11}}^{\text{22}}\text{Na}$.

${}_{\text{11}}^{\text{22}}\text{Na}\to {}_{\text{10}}^{\text{22}}\text{Ne}+{}_1^0\text{e}$

Where,

• ${}_1^0\text{e}$ is a positron particle.

(g)

To define: The term electron capture.

An inner shell electron is captured by the nucleus.

In the electron capture decay, the atomic number of the decaying nuclide decreases by one and the mass number remains constant. Its example is decay of ${}_{80}^{201}\text{Hg}$.

${}_{80}^{201}\text{Hg}+{}_{-1}^0\text{e}{\to }_{79}^{201}\text{Au}+{}_0^0\text{γ}$

(h)

To define: The term gamma-ray production.

High energy photon is known as gamma ray.

Gamma-ray production accompanies nuclear decays and particle production, such as in alpha particle decay of ${}_{\text{92}}^{\text{238}}\text{U}$.

${}_{\text{92}}^{\text{238}}\text{U}\to {}_{\text{2}}^{\text{4}}\text{He}{+}_{90}^{234}\text{Th}+2_0^0\text{γ}$

Where two gamma rays are produced along with alpha particles, the nuclides with excess energy comedown to their ground state by gamma particle production.

Explanation

To determine: The meaning of the given statement.

The atomic number and mass number in radioactive decay process are conserved.

This means that sum of the atomic number of the decaying nuclides is equal to the sum of atomic number of products nuclides.

Similarly, sum of the mass number of the decaying nuclides is equal to the sum of mass number of products nuclides.

Conclusion

Conclusion

The given terms have been rightfully defined and the atomic number and mass number in radioactive decay process are conserved.