Question

Which relation represent the correct relationship of the radius of an atom, its cation and its anion? (1) atom $=$ cation $=$ anion (2) atom $>$ cation $>$ anion (3) atom $>$ cation $<$ anion (4) atom $<$ cation $>$ anion

Short answer

Option (3): atom > cation < anion

Step-by-step solution

Understand Atomic Radius

The atomic radius is the distance from the nucleus to the outermost electron cloud of an atom in its neutral state.

Understanding Cation

A cation is formed when an atom loses one or more electrons, resulting in a positive charge. The loss of electrons reduces electron-electron repulsion in the outer shell, pulling electrons closer to the nucleus and thus decreasing the atomic radius.

Understanding Anion

An anion is formed when an atom gains one or more electrons, resulting in a negative charge. The addition of electrons increases electron-electron repulsion among the outer electrons, pushing them further from the nucleus and thus increasing the atomic radius.

Compare Atomic Radii

By considering the changes in electron configuration and repulsion, the radius of an atom decreases when it forms a cation and increases when it forms an anion. Thus, the correct relationship of the radii is: atom > cation < anion.

Select the Correct Option

Compare the findings with the provided options. The correct relationship is represented by option (3): atom > cation < anion.

Key concepts

Atomic Radius

The atomic radius of an atom is the distance from its nucleus to the outermost boundary of the electron cloud. This distance determines how large the atom is. Understanding the atomic radius helps us to compare the sizes of different atoms and ions.
The size of the atomic radius depends on:

• The number of protons in the nucleus, which pull electrons closer
• The number of electron shells, as more shells mean a larger radius

As we move across a period (row) in the periodic table, the atomic radius generally decreases because more protons pull the same electron shell closer to the nucleus. Conversely, as we move down a group (column), the atomic radius increases due to the addition of electron shells.

Cation Size

A cation is an atom that has lost one or more electrons, resulting in a positive charge. When an atom loses electrons to form a cation, the loss occurs from the outermost electron shell.
This loss of electrons has two main effects on the size of the cation:

• Reduction in electron-electron repulsion: With fewer electrons in the outer shell, there is less repulsion pushing the electrons apart, allowing the shell to contract closer to the nucleus.
• Greater effective nuclear charge: The nucleus' positive charge has a stronger pull on the remaining electrons, pulling them inward.

Because of these factors, a cation is always smaller than its parent atom.

Anion Size

An anion is an atom that has gained one or more electrons, resulting in a negative charge. When an atom gains electrons to form an anion, these extra electrons are added to the outermost electron shell.
This gain of electrons causes the following changes:

• Increased electron-electron repulsion: The additional electrons increase repulsion among the electrons in the outer shell, which causes the shell to expand.
• Lower effective nuclear charge per electron: The same nuclear charge is shared among more electrons, weakening the pull on each individual electron.

As a result, anions are always larger than their parent atoms due to the increase in electron repulsion.

Electron Configuration

The electron configuration of an atom or ion describes how electrons are arranged in shells and subshells around the nucleus.
When an atom becomes a cation or anion, its electron configuration changes to reflect the loss or gain of electrons. Here's how:

• Cations: Electrons are removed from the outermost shell, reducing the overall size and leading to a more compact electron configuration.
• Anions: Electrons are added to the outermost shell, resulting in a larger electron cloud and an expanded configuration.

Understanding electron configuration is essential for predicting the physical and chemical properties of elements and their ions.