Orbitals That Have The Same Energy Are Called

Orbitals That Have the Same Energy Are Called Degenerate Orbitals: A Deep Dive into Atomic Structure

Orbitals are regions of space around an atom's nucleus where there's a high probability of finding an electron. But what happens when multiple orbitals share the same energy level? They're called degenerate orbitals. Understanding degeneracy is crucial for comprehending atomic structure, chemical bonding, and the behavior of atoms and molecules. This article delves deep into the concept of degenerate orbitals, exploring their characteristics, causes, and implications.

What are Degenerate Orbitals?

The term "degenerate" in this context means having the same energy. Degenerate orbitals are orbitals within the same subshell that possess identical energy levels. This means electrons occupying these orbitals experience the same attraction to the nucleus and have the same probability distribution in space. It's important to note that this degeneracy is a simplification – in reality, subtle differences in energy often exist due to factors like external magnetic fields or interactions with other electrons. However, for many purposes, the assumption of degeneracy provides a useful and accurate model.

Examples of Degenerate Orbitals

Consider the second energy level (n=2) of a hydrogen atom. This level contains one s subshell and one p subshell.

• 2s subshell: Contains one 2s orbital. This orbital is spherically symmetrical.

• 2p subshell: Contains three 2p orbitals (2px, 2py, 2pz). These orbitals are oriented along the x, y, and z axes respectively, and have dumbbell shapes.

In the absence of any external fields, all three 2p orbitals are degenerate. They possess the same energy. Similarly, all five 3d orbitals (3dxy, 3dxz, 3dyz, 3dx²-y², 3dz²) are degenerate within the 3d subshell.

Factors Affecting Orbital Degeneracy

Several factors can influence the energy levels of orbitals and, consequently, their degeneracy.

1. Nuclear Charge (Z):

The number of protons in the nucleus (atomic number, Z) directly impacts the attraction between the nucleus and electrons. A higher nuclear charge leads to stronger attraction, lowering the energy of all orbitals. However, the relative energy difference between different subshells remains generally consistent for atoms of the same element.

2. Shielding Effect:

Inner electrons shield outer electrons from the full positive charge of the nucleus. This reduces the effective nuclear charge experienced by outer electrons. The extent of shielding varies depending on the subshell, influencing the energy of the orbitals. s orbitals, being closer to the nucleus, penetrate the electron cloud better and experience less shielding than p, d, and f orbitals.

3. Electron-Electron Repulsion:

Interactions between electrons within the same atom also affect orbital energies. Repulsion between electrons increases the energy of the orbitals. This effect is particularly significant in polyelectronic atoms where electron-electron interactions are not negligible.

4. External Magnetic and Electric Fields:

Applying external magnetic or electric fields removes the degeneracy of orbitals. This phenomenon is called the Zeeman effect (for magnetic fields) and the Stark effect (for electric fields). The energy levels of the degenerate orbitals are split into closely spaced levels in the presence of these external fields, leading to a change in the spectral lines observed. This effect is frequently used in spectroscopic techniques to investigate atomic and molecular structures.

5. Shape and Penetration of Orbitals:

The shapes and penetration abilities of orbitals also contribute to their energies. For example, s orbitals have greater penetration towards the nucleus compared to p orbitals, leading to lower energies for s orbitals in the same shell. The different orientations of p, d, and f orbitals also result in slight energy variations, though often negligible compared to other factors.

Breaking Degeneracy: The Jahn-Teller Effect

In molecules with degenerate orbitals containing unpaired electrons, a phenomenon known as the Jahn-Teller effect can occur. The molecule distorts its geometry to remove the orbital degeneracy, leading to a lower energy state. This distortion is a consequence of the interplay between electron-electron repulsion and the molecule's vibrational modes. The Jahn-Teller effect has implications in various fields, including material science and coordination chemistry.

Implications of Degenerate Orbitals

The concept of degenerate orbitals has significant implications across various areas of chemistry and physics:

1. Electronic Configuration:

Degeneracy dictates how electrons are distributed among orbitals. According to Hund's rule, electrons first singly occupy degenerate orbitals before pairing up, maximizing the total spin. This configuration is lower in energy due to reduced electron-electron repulsion.

2. Spectroscopy:

The energy differences between degenerate orbitals and non-degenerate orbitals determine the wavelengths of light absorbed or emitted during electronic transitions. Spectroscopic techniques exploit these transitions to gain insights into the electronic structure of atoms and molecules.

3. Chemical Bonding:

The involvement of degenerate orbitals in bonding profoundly influences the properties of molecules. The formation of sigma and pi bonds, for instance, involves the interaction between different types of atomic orbitals. Understanding the degeneracy of atomic orbitals helps to predict the geometry and reactivity of molecules.

4. Magnetic Properties:

The presence of unpaired electrons in degenerate orbitals leads to paramagnetic behavior. Materials with unpaired electrons are attracted to external magnetic fields. Understanding orbital degeneracy is thus important in predicting and interpreting the magnetic properties of substances.

5. Catalysis:

Degenerate orbitals in transition metal complexes play a vital role in catalysis. The ability of these orbitals to accept or donate electrons facilitates many catalytic reactions, making them important in various industrial processes.

Degeneracy in Polyelectronic Atoms

In hydrogen and hydrogen-like atoms (atoms with only one electron), the energy of an orbital depends solely on the principal quantum number (n). However, in polyelectronic atoms (atoms with multiple electrons), the energy also depends on the azimuthal quantum number (l) and sometimes on the magnetic quantum number (ml). This is due to electron-electron interactions and the shielding effect.

While the orbitals within the same subshell are often considered degenerate as a first approximation, subtle energy differences exist due to the complex interactions between electrons. These differences become more pronounced as the atomic number increases.

Beyond the Basics: Relativistic Effects

At higher atomic numbers, relativistic effects become significant. These effects stem from the very high speeds of inner electrons, resulting in a contraction of s and p orbitals. This contraction influences the energies of the orbitals, impacting the observed electronic configurations and chemical properties of heavy elements. The relativistic effects can even lead to changes in the expected ordering of orbital energies.

Conclusion

Degenerate orbitals, orbitals with the same energy level, are a fundamental concept in atomic structure and quantum mechanics. While the idealized picture of perfect degeneracy often serves as a useful model, factors like nuclear charge, shielding, electron-electron repulsion, external fields, and relativistic effects can all perturb orbital energies and lift degeneracy. Understanding these factors is vital for interpreting the electronic structure, spectroscopic properties, chemical bonding, and reactivity of atoms and molecules. The concept of degeneracy and the conditions that break or preserve it are central to a deeper understanding of the chemical world around us. Further research into these areas continues to reveal subtle nuances and important applications in diverse scientific fields.