Question

Generally half-filled or completely filled degenerate orbitals have lower energy because (1) of their symmetry and possible larger exchanges (2) they cannot participate in bonding (3) such orbitals have only paired electrons (4) such orbitals have only unpaired electrons

Short answer

Symmetry and larger exchange energies lower the energy of half-filled or completely filled degenerate orbitals.

Step-by-step solution

- Understanding Degenerate Orbitals

Degenerate orbitals are orbitals that have the same energy level. In an atom, these orbitals can be half-filled or completely filled, and their energy can be influenced by their electron configurations.

- Symmetry and Exchange Energy

Half-filled and fully filled orbitals have a symmetrical distribution of electrons. This symmetry leads to increased exchange energy, which stabilizes the atom by reducing its overall energy.

- Identify the Correct Option

Review each option: (1) Symmetry and exchange energy reduce energy. (2) Incorrect, these orbitals can still participate in bonding. (3) Incorrect, half-filled orbitals have unpaired electrons. (4) Incorrect, full-filled orbitals have paired electrons, half-filled have unpaired electrons. The correct answer is because of their symmetry and possible larger exchanges.

Key concepts

Symmetry in Orbitals

Degenerate orbitals refer to orbitals that have the same energy levels within an atom. The symmetry in these orbitals is a crucial concept as it significantly affects the atom's stability. Symmetrical distribution of electrons in these orbitals contributes to the atom's lower energy state.
When orbitals are either half-filled or completely filled, they exhibit this symmetry. The electrons are arranged in a way that makes the atom more balanced. This balance is essential because it leads to increased stability. The symmetrical arrangement ensures that the repulsion between electrons is minimized, further stabilizing the atom. Another important aspect is that this symmetry results in uniform energy distribution around the nucleus of the atom.
For students, recognizing the importance of symmetrical electron distribution helps in understanding why certain electron configurations are more stable than others. So remember, symmetry in half-filled or fully filled degenerate orbitals helps in achieving a lower and more stable energy state.

Exchange Energy

Exchange energy is a term that describes the energy stabilization that occurs as a result of the symmetrical arrangement of electrons in degenerate orbitals. This is especially observed when orbitals are half-filled or completely filled.
The increased exchange energy emerges as electrons with parallel spins exchange positions within the orbitals. This exchange requires less energy and leads to further lowering of the atom's total energy. Essentially, exchange energy leverages the quantum mechanical principle of electron interchangeability, providing an additional stabilizing factor.
For example, in a half-filled set of p-orbitals, the electrons with the same spin can interchange without violating Pauli’s exclusion principle, contributing to a higher exchange energy. This means that the system is more stable when electrons can easily exchange places within these symmetric configurations.
By focusing on exchange energy, students can understand why certain electron configurations are more stable and prefer this symmetry in specific instances.

Electron Configuration

Electron configuration refers to the distribution of electrons in an atom's orbitals. The way these electrons are arranged determines many physical and chemical properties of the atom.
Let's go over the basics: electrons fill orbitals in a manner that minimizes the atom's energy, following Pauli’s exclusion principle and Hund's rule. The exclusion principle dictates that no two electrons can have the same set of quantum numbers, while Hund’s rule states that electrons prefer to occupy degenerate orbitals singly before pairing up.
This is why half-filled and fully filled degenerate orbitals are particularly stable. In these configurations, the electrons avoid pairing until necessary, minimizing repulsion and maximizing exchange energy. It's also why these configurations tend to be more common in nature.
Understanding the principles behind electron configuration helps in predicting how atoms will interact in chemical reactions and bond formations. It is a foundational concept that is critical for anyone studying chemistry or physics, as it explains why certain elements behave the way they do based on their underlying electronic structures.