Which Of The Following Atoms Is Diamagnetic In Its Ground-state

The property of diamagnetism in atoms is intricately linked to their electronic configuration, specifically the pairing of electrons within their orbitals. An atom is considered diamagnetic if all of its electrons are paired, resulting in no net magnetic dipole moment. Understanding this concept requires a journey into the quantum realm of atomic structure and electron behavior.

Understanding Diamagnetism

Diamagnetism is a fundamental property of matter arising from the response of a material to an applied magnetic field. When an external magnetic field is applied, diamagnetic materials create an induced magnetic field in the opposite direction, causing them to be repelled by the external field. This behavior is a result of the realignment of electron orbits within the atoms of the material.

Atomic Orbitals and Electron Configuration

To determine whether an atom is diamagnetic in its ground state, we must first understand the basics of atomic orbitals and electron configurations.

• Atomic Orbitals: These are mathematical functions that describe the probability of finding an electron in a specific region around the nucleus. They are characterized by a set of quantum numbers:

  • Principal Quantum Number (n): Determines the energy level of the electron (n = 1, 2, 3, ...).
  • Azimuthal Quantum Number (l): Determines the shape of the orbital (l = 0, 1, 2, ..., n-1), corresponding to s, p, d, and f orbitals, respectively.
  • Magnetic Quantum Number (ml): Determines the orientation of the orbital in space (ml = -l, -l+1, ..., 0, ..., l-1, l).
  • Spin Quantum Number (ms): Determines the intrinsic angular momentum of the electron, which is quantized and referred to as spin. It can be either +1/2 or -1/2, often referred to as "spin up" and "spin down."

• Electron Configuration: This describes the arrangement of electrons within the various energy levels and orbitals of an atom. It follows specific rules:

  • Aufbau Principle: Electrons first fill the lowest energy orbitals available.
  • Hund's Rule: Within a subshell (e.g., p, d, or f), electrons individually occupy each orbital before any orbital is doubly occupied, and all electrons in singly occupied orbitals have the same spin (maximize total spin).
  • Pauli Exclusion Principle: No two electrons in an atom can have the same set of all four quantum numbers. This implies that each orbital can hold a maximum of two electrons, with opposite spins.

Diamagnetism vs. Paramagnetism

It's helpful to contrast diamagnetism with paramagnetism to fully grasp the concept.

• Diamagnetism: Occurs when all electrons in an atom or molecule are paired. The magnetic fields produced by each pair of electrons cancel each other out, resulting in no net magnetic moment. When an external magnetic field is applied, the electron orbits distort slightly, creating a small opposing magnetic field.

• Paramagnetism: Occurs when an atom or molecule has one or more unpaired electrons. These unpaired electrons possess a net magnetic moment. In the absence of an external magnetic field, these magnetic moments are randomly oriented. However, when a magnetic field is applied, the magnetic moments tend to align with the field, resulting in a net attraction to the magnetic field.

Identifying Diamagnetic Atoms: A Step-by-Step Approach

To determine whether a given atom is diamagnetic in its ground state, follow these steps:

1. Determine the Number of Electrons: This is equal to the atomic number of the element.

2. Write the Ground State Electron Configuration: Use the Aufbau principle, Hund's rule, and the Pauli exclusion principle to determine how the electrons are distributed among the various atomic orbitals.

3. Check for Unpaired Electrons: Examine the electron configuration. If all the electrons are paired within their respective orbitals, the atom is diamagnetic. If there is at least one unpaired electron, the atom is paramagnetic.

Examples of Diamagnetic Atoms

Let's consider some examples to illustrate the process:

• Helium (He): Atomic number 2. Its electron configuration is 1s². Both electrons occupy the 1s orbital and are paired (one with spin up, one with spin down). Therefore, Helium is diamagnetic.

• Beryllium (Be): Atomic number 4. Its electron configuration is 1s² 2s². All four electrons are paired in the 1s and 2s orbitals. Therefore, Beryllium is diamagnetic.

• Neon (Ne): Atomic number 10. Its electron configuration is 1s² 2s² 2p⁶. The 1s, 2s, and 2p orbitals are all fully filled with paired electrons. Therefore, Neon is diamagnetic.

Examples of Paramagnetic Atoms

Now, let's look at some examples of paramagnetic atoms:

• Hydrogen (H): Atomic number 1. Its electron configuration is 1s¹. It has one unpaired electron in the 1s orbital. Therefore, Hydrogen is paramagnetic.

• Lithium (Li): Atomic number 3. Its electron configuration is 1s² 2s¹. It has one unpaired electron in the 2s orbital. Therefore, Lithium is paramagnetic.

• Nitrogen (N): Atomic number 7. Its electron configuration is 1s² 2s² 2p³. According to Hund's rule, the three electrons in the 2p subshell will each occupy a separate 2p orbital with the same spin. This results in three unpaired electrons. Therefore, Nitrogen is paramagnetic.

Common Misconceptions

• Filled Shells Always Mean Diamagnetism: While elements with completely filled electron shells (noble gases) are diamagnetic, it's essential to write out the electron configuration to confirm. Just because an atom has a "filled" valence shell doesn't guarantee diamagnetism in all cases, especially when considering transition metals.

• Ions and Diamagnetism: The diamagnetic or paramagnetic nature of an ion can be different from that of its neutral atom. For example, iron (Fe) is paramagnetic, but the Fe²⁺ ion can be either paramagnetic or diamagnetic depending on the ligand field splitting in the complex it forms. Therefore, determine the electron configuration of the ion, not just the neutral atom.

Transition Metals and Diamagnetism

Transition metals present a more complex scenario due to the presence of d orbitals. These orbitals can have varying numbers of unpaired electrons, leading to diverse magnetic properties.

• Scandium (Sc): Atomic number 21. Its electron configuration is [Ar] 3d¹ 4s². It has one unpaired electron in the 3d orbital. Therefore, Scandium is paramagnetic.

• Zinc (Zn): Atomic number 30. Its electron configuration is [Ar] 3d¹⁰ 4s². The 3d orbitals are completely filled with paired electrons, and the 4s orbital is also filled. Therefore, Zinc is diamagnetic.

It's crucial to remember that the electron configuration of transition metal ions can be significantly different from the neutral atom, especially when they form complexes. The ligand field theory explains how the presence of ligands around a metal ion affects the energies of the d orbitals, leading to different electron configurations and magnetic properties.

Lanthanides and Actinides

Lanthanides and actinides involve the filling of f orbitals, further complicating the magnetic properties. These elements often have multiple unpaired electrons, leading to strong paramagnetic behavior. However, there are exceptions, and a careful analysis of the electron configuration is required to determine whether they are diamagnetic or paramagnetic.

Factors Affecting Magnetic Properties

Several factors can influence the magnetic properties of atoms and materials:

• Temperature: In paramagnetic materials, higher temperatures tend to randomize the alignment of magnetic moments, reducing the overall magnetization. Diamagnetism is generally less affected by temperature.

• External Magnetic Field Strength: The strength of the applied magnetic field directly influences the induced magnetization in diamagnetic materials and the alignment of magnetic moments in paramagnetic materials.

• Chemical Environment: The chemical environment surrounding an atom can significantly affect its electron configuration and magnetic properties. This is particularly relevant for transition metal complexes, where the ligands surrounding the metal ion influence the d orbital energies.

Practical Applications

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

• Magnetic Resonance Imaging (MRI): MRI relies on the magnetic properties of atomic nuclei, particularly hydrogen nuclei, in the presence of a strong magnetic field. The different magnetic environments of these nuclei allow for the creation of detailed images of internal organs and tissues.

• Magnetic Separation: Magnetic separation techniques are used to separate materials based on their magnetic properties. This is widely used in mining, recycling, and environmental remediation.

• Data Storage: Magnetic materials are essential for data storage in hard drives and other magnetic storage devices. The ability to control and manipulate the magnetic orientation of small regions on a magnetic disk allows for the storage and retrieval of information.

• Superconducting Magnets: Superconducting magnets, which produce extremely strong magnetic fields, are used in a variety of applications, including MRI, particle accelerators, and fusion reactors.

• Chemical Analysis: Measuring the magnetic susceptibility of a substance can provide information about its composition and structure. This technique is used in chemistry, materials science, and other fields.

Predicting Magnetic Properties of Ions

Determining the magnetic properties of ions requires an understanding of how the electron configuration changes when an atom gains or loses electrons.

1. Determine the Number of Electrons in the Ion: For cations (positive ions), subtract the number of electrons equal to the charge from the neutral atom's electron count. For anions (negative ions), add the number of electrons equal to the charge to the neutral atom's electron count.

2. Write the Electron Configuration of the Ion: Follow the same rules (Aufbau principle, Hund's rule, and Pauli exclusion principle) as for neutral atoms, but use the new number of electrons.

3. Check for Unpaired Electrons: As with neutral atoms, if all electrons are paired, the ion is diamagnetic. If there are unpaired electrons, the ion is paramagnetic.

Examples of Predicting Ionic Magnetic Properties

• Fe²⁺ (Iron(II) ion): Iron (Fe) has an atomic number of 26 and an electron configuration of [Ar] 3d⁶ 4s². When iron loses two electrons to form Fe²⁺, it loses the 4s electrons first. Therefore, the electron configuration of Fe²⁺ is [Ar] 3d⁶. According to Hund's rule, the six d electrons will occupy the five d orbitals as follows: four orbitals will have one electron each, and one orbital will have two paired electrons. This leaves four unpaired electrons. Thus, Fe²⁺ is paramagnetic.

• Cu⁺ (Copper(I) ion): Copper (Cu) has an atomic number of 29 and an electron configuration of [Ar] 3d¹⁰ 4s¹. When copper loses one electron to form Cu⁺, it loses the 4s electron. Therefore, the electron configuration of Cu⁺ is [Ar] 3d¹⁰. All ten d electrons are paired in the five d orbitals. Thus, Cu⁺ is diamagnetic.

• O²⁻ (Oxide ion): Oxygen (O) has an atomic number of 8 and an electron configuration of 1s² 2s² 2p⁴. When oxygen gains two electrons to form O²⁻, its electron configuration becomes 1s² 2s² 2p⁶. The 2p orbitals are now fully filled with paired electrons. Thus, O²⁻ is diamagnetic.

Advanced Considerations: Ligand Field Theory

For transition metal complexes, the simple rules based on electron configurations may not be sufficient to accurately predict magnetic properties. Ligand field theory provides a more sophisticated framework for understanding how the interaction between metal ions and ligands affects the d orbital energies and electron configurations.

• Ligand Field Splitting: Ligands create an electrostatic field that splits the degeneracy of the d orbitals. The pattern of splitting depends on the geometry of the complex (e.g., tetrahedral, square planar, octahedral).

• High-Spin vs. Low-Spin Complexes: Depending on the strength of the ligand field splitting and the pairing energy (the energy required to pair two electrons in the same orbital), the d electrons will either fill the orbitals to maximize the number of unpaired electrons (high-spin) or pair up in the lower energy orbitals before occupying the higher energy orbitals (low-spin).

• Example: Octahedral Complexes of Fe²⁺: In an octahedral complex, the five d orbitals split into two sets: t₂g (lower energy, three orbitals) and eg (higher energy, two orbitals). The electron configuration of Fe²⁺ is d⁶.

  • High-Spin: If the ligand field splitting is small, the electrons will arrange as t₂g⁴ eg², resulting in four unpaired electrons (paramagnetic).

  • Low-Spin: If the ligand field splitting is large, the electrons will arrange as t₂g⁶ eg⁰, resulting in zero unpaired electrons (diamagnetic).

Conclusion

Identifying diamagnetic atoms and ions involves understanding electron configurations and applying the rules governing the filling of atomic orbitals. While simple electron configuration analysis is often sufficient for main group elements and simple ions, transition metal complexes require more advanced considerations based on ligand field theory. The principles discussed here are crucial for understanding the magnetic properties of matter and have wide-ranging applications in various scientific and technological fields. By mastering these concepts, you gain a deeper appreciation of the quantum world that governs the behavior of atoms and molecules.