Which Of The Following Orbital Diagrams Represents A Diamagnetic Atom

Understanding the nature of magnetism at the atomic level is crucial in chemistry and physics. Diamagnetism, a fundamental property of matter, arises from the behavior of electrons in atoms and molecules when exposed to an external magnetic field. Determining whether an atom is diamagnetic or paramagnetic requires careful analysis of its electron configuration and orbital diagrams. This article provides a comprehensive exploration of diamagnetism, focusing on how to identify diamagnetic atoms from their orbital diagrams. We will delve into the underlying principles, step-by-step analysis, and practical examples to enhance your understanding.

Introduction to Diamagnetism

Diamagnetism is a property exhibited by materials that are repelled by a magnetic field. This phenomenon occurs in substances where all electrons are paired in their atomic or molecular orbitals. When an external magnetic field is applied, these paired electrons create an induced magnetic field in the opposite direction, resulting in repulsion. In contrast, paramagnetic materials are attracted to magnetic fields due to the presence of unpaired electrons.

Key Concepts

• Electron Configuration: The arrangement of electrons in the energy levels and sublevels within an atom.
• Orbital Diagram: A visual representation of the electron configuration, showing how electrons are distributed among the orbitals.
• Paired Electrons: Two electrons occupying the same orbital with opposite spins (+1/2 and -1/2).
• Unpaired Electrons: A single electron occupying an orbital.
• Hund's Rule: Electrons will individually occupy each orbital within a subshell before doubling up in any one orbital.
• Magnetic Field: A region around a magnet or electric current in which a magnetic force is exerted.

The Significance of Orbital Diagrams

Orbital diagrams are essential tools for visualizing the electronic structure of atoms. They provide a clear representation of how electrons are arranged within the various orbitals (s, p, d, and f) of an atom. By examining these diagrams, we can determine the presence of paired or unpaired electrons, which is crucial for identifying diamagnetic or paramagnetic behavior.

Understanding Orbital Diagrams

An orbital diagram illustrates the distribution of electrons within an atom's orbitals. Each orbital is represented by a box or a line, and electrons are depicted as arrows pointing either upwards or downwards, indicating their spin.

Components of an Orbital Diagram

1. Orbitals: Represented as boxes or lines, each orbital can hold a maximum of two electrons.
2. Electrons: Shown as arrows. An upward arrow (↑) indicates a spin of +1/2, while a downward arrow (↓) indicates a spin of -1/2.
3. Subshells: Groups of orbitals with the same energy level. The common subshells are s (1 orbital), p (3 orbitals), d (5 orbitals), and f (7 orbitals).

Rules for Filling Orbitals

1. Aufbau Principle: Electrons fill the lowest energy orbitals first.
2. Hund's Rule: Within a given subshell, electrons will individually occupy each orbital before any orbital is doubly occupied. All singly occupied orbitals must have the same spin (maximum multiplicity).
3. Pauli Exclusion Principle: No two electrons in an atom can have the same set of quantum numbers, which means each orbital can hold a maximum of two electrons with opposite spins.

Example of an Orbital Diagram: Oxygen (O)

Oxygen has an atomic number of 8, meaning it has 8 electrons. Its electron configuration is 1s² 2s² 2p⁴. The orbital diagram for oxygen is constructed as follows:

• 1s subshell: Contains one orbital, filled with two paired electrons (↑↓).

• 2s subshell: Contains one orbital, filled with two paired electrons (↑↓).

• 2p subshell: Contains three orbitals. According to Hund's Rule, we first fill each orbital with one electron before pairing them. This results in two unpaired electrons:

  • 2p orbitals: ↑↓ ↑ ↑

Therefore, the complete orbital diagram for oxygen is:

• 1s: ↑↓
• 2s: ↑↓
• 2p: ↑↓ ↑ ↑

Identifying Diamagnetic Atoms

To determine if an atom is diamagnetic, you must examine its orbital diagram to see if all electrons are paired. If all orbitals are filled with paired electrons, the atom is diamagnetic. If there is even one unpaired electron, the atom is paramagnetic.

Step-by-Step Guide

1. Determine the Electron Configuration: Find the atomic number of the element, which indicates the number of electrons. Write out the electron configuration using the Aufbau principle.

2. Draw the Orbital Diagram: Represent each orbital as a box or line. Fill the orbitals according to Hund's Rule and the Pauli Exclusion Principle.

3. Identify Unpaired Electrons: Look for any orbitals that contain only one electron.

4. Determine Magnetic Properties:

   • If all electrons are paired, the atom is diamagnetic.
   • If there is one or more unpaired electron(s), the atom is paramagnetic.

Examples

Example 1: Helium (He)

• Atomic number: 2
• Electron configuration: 1s²
• Orbital diagram: 1s: ↑↓

Since all electrons are paired, helium is diamagnetic.

Example 2: Nitrogen (N)

• Atomic number: 7
• Electron configuration: 1s² 2s² 2p³
• Orbital diagram:
  • 1s: ↑↓
  • 2s: ↑↓
  • 2p: ↑ ↑ ↑

Nitrogen has three unpaired electrons in the 2p orbitals, making it paramagnetic.

Example 3: Neon (Ne)

• Atomic number: 10
• Electron configuration: 1s² 2s² 2p⁶
• Orbital diagram:
  • 1s: ↑↓
  • 2s: ↑↓
  • 2p: ↑↓ ↑↓ ↑↓

All electrons in neon are paired, so neon is diamagnetic.

Common Mistakes to Avoid

1. Ignoring Hund's Rule: Failing to fill orbitals individually before pairing electrons can lead to incorrect predictions of magnetic properties.
2. Incorrect Electron Configuration: An inaccurate electron configuration will result in an incorrect orbital diagram.
3. Miscounting Electrons: Always ensure the number of electrons in the orbital diagram matches the atomic number of the element.
4. Overlooking Paired Electrons: Double-check that all orbitals are filled with paired electrons before concluding that an atom is diamagnetic.
5. Assuming Full Subshells are Always Diamagnetic: While full subshells result in paired electrons, it's crucial to verify this with the orbital diagram, especially in cases involving exceptions to Hund's Rule.

Advanced Considerations

Exceptions to Hund's Rule

In some cases, exceptions to Hund's Rule occur due to complex interactions between electrons. For example, in elements with nearly filled or half-filled d subshells, electrons may rearrange to achieve a more stable configuration. Chromium (Cr) and Copper (Cu) are classic examples:

• Chromium (Cr):
  • Expected configuration: [Ar] 4s² 3d⁴
  • Actual configuration: [Ar] 4s¹ 3d⁵
  • The stability gained from having a half-filled 3d subshell outweighs the energy cost of moving an electron from the 4s to the 3d. Chromium has six unpaired electrons, making it strongly paramagnetic.
• Copper (Cu):
  • Expected configuration: [Ar] 4s² 3d⁹
  • Actual configuration: [Ar] 4s¹ 3d¹⁰
  • Similarly, copper achieves a more stable configuration by having a completely filled 3d subshell. Copper has one unpaired electron, making it paramagnetic, though less so than chromium.

Ions

When dealing with ions, remember to add or remove electrons based on the charge of the ion. Cations (positive ions) have fewer electrons than the neutral atom, while anions (negative ions) have more.

Example: Iron (Fe) and Iron(II) Ion (Fe²⁺)

• Iron (Fe):
  • Atomic number: 26
  • Electron configuration: [Ar] 4s² 3d⁶
  • Orbital diagram:
    • 4s: ↑↓
    • 3d: ↑↓ ↑ ↑ ↑ ↑
  • Iron has four unpaired electrons, making it paramagnetic.
• Iron(II) Ion (Fe²⁺):
  • The Fe²⁺ ion has lost two electrons from the 4s subshell.
  • Electron configuration: [Ar] 3d⁶
  • Orbital diagram:
    • 3d: ↑↓ ↑ ↑ ↑ ↑
  • Fe²⁺ still has four unpaired electrons, making it paramagnetic.

Molecular Orbital Theory

While this article focuses on atomic diamagnetism, it is important to note that molecular orbital (MO) theory provides a more comprehensive understanding of magnetism in molecules. In MO theory, atomic orbitals combine to form molecular orbitals, which can be bonding or antibonding. The filling of these molecular orbitals determines the magnetic properties of the molecule.

For instance, molecular oxygen (O₂) has two unpaired electrons in its π* antibonding orbitals, making it paramagnetic, despite each individual oxygen atom having paired and unpaired electrons in its atomic orbitals.

Practical Applications

Understanding diamagnetism and paramagnetism has numerous practical applications in various fields:

1. Magnetic Resonance Imaging (MRI): MRI utilizes the magnetic properties of atomic nuclei to create detailed images of internal body structures. The contrast in MRI images is often enhanced by paramagnetic contrast agents, which alter the relaxation times of nearby water molecules.

2. Data Storage: Magnetic materials are used in hard drives and other data storage devices. The orientation of magnetic domains on the disk surface is used to store binary data.

3. Catalysis: The magnetic properties of transition metal complexes play a crucial role in catalysis. Paramagnetic metal centers can activate substrates and facilitate chemical reactions.

4. Materials Science: The magnetic properties of materials are essential for designing new materials with specific functionalities. For example, diamagnetic materials are used in applications where magnetic interference must be minimized.

5. Chemical Analysis: Techniques like Electron Paramagnetic Resonance (EPR) spectroscopy are used to study paramagnetic species, providing valuable information about their electronic structure and reactivity.

Conclusion

Identifying diamagnetic atoms from their orbital diagrams involves a systematic approach that includes determining the electron configuration, drawing the orbital diagram, and identifying unpaired electrons. Atoms with all paired electrons are diamagnetic, while those with unpaired electrons are paramagnetic. A solid understanding of these principles and rules, along with the ability to avoid common mistakes, will enable you to accurately predict the magnetic properties of atoms and ions. Furthermore, awareness of advanced considerations such as exceptions to Hund's Rule and the role of molecular orbital theory will provide a more comprehensive understanding of magnetism in chemical systems. This knowledge is not only crucial for academic studies but also has broad applications in various scientific and technological fields, making it an indispensable aspect of chemistry and physics.