Question

Why are half-filled and completely filled orbitals more stable? Justify your answer with the help of suitable examples.

Short answer

Half-filled and completely filled orbitals are more stable because of reduced electron-electron repulsion, increased symmetry, and increased exchange energy. Examples include Carbon preferring a half-filled configuration for increased stability and maximum bonding.

Step-by-step solution

Understand Orbital Filling

Orbitals are filled according to the Aufbau principle which states that an electron populates orbitals in a way that it will have the lowest possible total energy. The orbitals filling starts from the lower energy level to the higher energy level.

Electron-Electron Repulsion

Inside an atom, electrons stay as far apart as possible due to electron-electron repulsion. So, the farther the electrons, the less is the repulsion and more stable the atom.

Symmetry

Fully filled and half filled orbitals offer symmetrical distribution of electrons, thereby maintaining stability. For example, in the case of carbon (C) in its ground state, it has electronic configuration of 1s² 2s² 2p² . But Carbon prefers to be in the 1s² 2s¹ 2p³ configuration - a half filled stable configuration. This also creates 4 unpaired electrons available for bonding.

Exchange Energy

In half filled and fully filled degenerate orbitals, any two electrons can exchange their positions, and the energy released during this process is called Exchange Energy. Greater the exchange energy, greater will be the stability of the atom.

Key concepts

Aufbau Principle

The Aufbau Principle plays a crucial role in determining how electrons are distributed within an atom. According to this principle, electrons fill atomic orbitals starting from the lowest energy levels to higher ones. This ordering helps to minimize the total energy of the atom, leading to increased stability.

When visualizing how electrons populate these orbitals, imagine a building being constructed from the ground up. The lower levels, or energy levels in this case, must be fully completed before moving to the next level. For instance:

• Electrons fill the 1s orbital before 2s because 1s is closer to the nucleus and has lower energy.
• This pattern continues with electrons filling the 2p orbital after the 2s orbital.

The systematic way in which electrons are filled according to their energy levels helps maintain an orderly electron distribution. This orderly pattern contributes to the stability of atoms, particularly evident in elements with half-filled or completely filled orbitals.

Electron-Electron Repulsion

Electron-electron repulsion is a phenomenon where electrons repel each other due to their like charges. This repulsion plays a significant part in the distribution and stability of electrons in an atom.

Electrons naturally tend to keep as far apart as possible to minimize this repulsion. This inherent behavior leads to configurations that are energetically favorable and more stable. Some points to consider:

• When electrons occupy the same orbital, their repulsion increases, resulting in less stability.
• Electrons occupying different orbitals spread out, reducing repulsion and fostering stability.

In summary, understanding how electron-electron repulsion impacts atom stability gives insight into why certain electron configurations, particularly those that maximize spacing, are preferred.

Symmetrical Distribution of Electrons

Symmetrical distribution of electrons within orbitals contributes to an atom's stability. Fully and half-filled orbitals inherently possess such symmetry, offering a configuration that reduces potential energy and enhances stability.

An example is the element carbon, which tends to rearrange its electrons to achieve a symmetrical half-filled configuration. Initially, carbon's ground state configuration is 1s² 2s² 2p². However, it often adopts 1s² 2s¹ 2p³, achieving half-filled p orbitals for greater symmetry and stability.

• Half-filled orbitals, such as 2p³, have evenly distributed electrons.
• This configuration provides more potential for bonding, as seen in carbon's ability to form four bonds.

Symmetry provides a means for the electrons to maintain stability through balanced distribution, reducing elevated energy levels caused by crowded electron arrangements.

Exchange Energy

Exchange energy is a crucial concept in understanding atomic stability, especially in contexts of half-filled and fully filled orbitals. Exchange energy refers to the energy released when electrons in degenerate orbitals swap positions.

The swapping of electrons can occur because these electrons are indistinguishable, allowing them to exchange their positions without influencing the overall energy configuration. As more exchanges take place, the stability of the atom increases due to the release of exchange energy.

• Greater the number of possible exchanges, higher the exchange energy.
• Exchange energy contributes significantly to the stability of electron configurations.

Thus, the concept of exchange energy helps explain why atoms with half-filled and fully filled orbitals exhibit increased stability by capitalizing on the energy release from these exchanges.