Which relation represent the correct relationship of the radius of an atom, its cation and its anion?

atom > cation < anion

The correct answer is option 3. atom > cation < anion.

To understand the relationship between the radius of an atom, its cation, and its anion, let's delve into the atomic and ionic radii, and how changes in the electron configuration and effective nuclear charge affect these sizes.

Atomic Radius

The atomic radius is the distance from the nucleus of an atom to the outermost electrons in its electron cloud. In a neutral atom, this size is determined by the balance between the positive charge of the nucleus, which attracts the electrons, and the repulsive forces between the electrons themselves.

Cation Radius

A cation is formed when an atom loses one or more electrons, resulting in a positively charged ion. The formation of a cation affects its size in several ways:

Loss of Electrons: When an atom loses electrons, it often loses an entire electron shell if the electrons are removed from the outermost shell. This results in a significant decrease in size.

Reduced Electron-Electron Repulsion: With fewer electrons, the repulsive forces between electrons are reduced, allowing the remaining electrons to be drawn closer to the nucleus.

Increased Effective Nuclear Charge: The loss of electrons increases the effective nuclear charge \((Z_{eff})\), which is the net positive charge experienced by the remaining electrons. With fewer electrons to shield each other from the nucleus, the effective nuclear charge felt by the remaining electrons is stronger, pulling them closer to the nucleus.

As a result, the radius of a cation is smaller than that of the neutral atom from which it was formed.

Anion Radius

An anion is formed when an atom gains one or more electrons, resulting in a negatively charged ion. The formation of an anion affects its size in the following ways:

Gain of Electrons: Adding extra electrons increases the electron cloud size as these additional electrons add to the existing shells or create new ones.

Increased Electron-Electron Repulsion: The addition of more electrons increases repulsive forces among the electrons, causing the electron cloud to expand.

Decreased Effective Nuclear Charge per Electron: Although the nuclear charge remains the same, the increased number of electrons means that the effective nuclear charge per electron decreases. The nucleus's pull on each individual electron is weaker because of increased shielding by other electrons.

As a result, the radius of an anion is larger than that of the neutral atom from which it was formed.

Summary of Relationships

Given these changes:

Neutral Atom: Baseline size.

Cation: Smaller than the neutral atom due to loss of electrons, reduced repulsion, and increased effective nuclear charge.

Anion: Larger than the neutral atom due to gain of electrons, increased repulsion, and decreased effective nuclear charge per electron.

Therefore, the correct relationship between the radius of an atom, its cation, and its anion is: atom > cation < anion

This relationship correctly reflects that the neutral atom's size is greater than that of its cation and smaller than that of its anion. Hence, the correct answer is: (3) atom > cation < anion