Degenerate Orbitals

Introduction

Degenerate orbitals are the same subshell electron orbitals with the same energy level. These degenerate orbitals always exist if the magnetic field does not interfere with them. The degeneracy interferes with how the magnetic field is used.

Learning about matter and chemical compounds through visualisation is a key component of the chemistry curriculum. Here, through comprehending the meaning of degenerate orbitals and the related concepts of the Aufbau Principle and Hund's Rule, we will learn the fundamental structure of the atom.

Hund's Maximum Multiplication Rule

• According to Hund's Rule of Maximum Multiplicity, the phrase with the greatest number of multiplicities has the lowest energy for a certain electronic configuration. According to the rule, electrons in the p, d, & f orbitals must couple up only if one electron is present in each orbital or if it is solely filled.

• The degenerate orbitals are filled by electrons.

• In a subshell, 1 electron is introduced to each before 2 electrons are transferred to any orbital, as per Friedrich Hund's Hund's law of Multiplicity.

• Electrons are consistently introduced to a subshell with the identical quantum spin no. until at least 1 electron is present in each of its orbitals.

• Till every electron in a subshell has one electron, Hund's rule of multiplicity states that electron pairing in the f, p & d orbitals will never take place in a particular electron configuration. Assume that an atom of carbon has the electron configuration 1𝑠22𝑠22𝑝2 . As per Hund's rule, 2 2s electrons will fill the orbital, and 2 2p electrons will fill each of the other orbitals.

What is Hund's Rule?

According to Hund's rule of electrons, degenerate orbitals occupy uniformly before electrons in the upper energy state do. The Aufbau Principle, Pauli-exclusion Principle, & Hund's Rule are the 3 concepts that explain the filling of electrons in succeeding energy levels.

Postulates of Hund's Rule

• One orbital at a subshell is filled before it can be taken up by another orbital, as per the report.

• The spin of an electron in each orbital is the same as that of an electron across several orbitals.

A description of Hund's Rule

Electrons pair up with one another whenever they approach an orbital. These negatively charged atoms are attracted to one another. The repulsion between electrons is less since they do not share orbitals.

When we analyse the 2nd rule, the spins of unpaired electrons in individually filled orbitals are identical. The spin of all the other electrons in a subshell is governed by the spin of the initial electron at that level. The electronic configuration of a 𝐶 atom, which would be 1𝑠22𝑠22𝑝2 , is one instance in which this would be accurate. According to Hund's rule, the 2 2s electrons will occupy the identical orbital, but the 2 2p electrons will fill distinct orbitals.

What is the Aufbau Principle?

According to Aufbau's principle, electrons fill up in the order of lower energy state to upper energy state, starting with the lower energy states. The electrons are filled in with increasing n+l value where n is principal quantum no. and l is angular quantum no. This idea aids in foretelling the kind of chemical bond that an atom could make.

Goodphy, Picture of Madelung rule, CC BY-SA 4.0

Degenerate Orbitals Example

Here is an illustration of degenerate orbitals.

Example − s, p, d & f are the 4 orbitals that make up an atom. There are 3 orbitals in the p orbital: 𝑝𝑥, 𝑝𝑦& 𝑝𝑧. These 3 orbitals are referred to as degenerate molecular orbitals since they are all identical in energy and correspond to the identical orbital (p). Every orbital starts with a single electron, which is followed by the subsequent electron with the opposite spin filling the equivalent orbital. In the end, the p orbital is occupied and 3 orbitals each contain six electrons.

Explanation of Degenerate Orbitals with Diagram

To visualise this concept, let's move through a thorough explanation of degenerate orbitals using a diagram. A 2p orbital electron filling process requires 2𝑝𝑥, 2𝑝𝑦& 2𝑝𝑧. These orbitals are all equally energetic with one another. A 3p orbital electron filling process also incorporates 3𝑝𝑥, 3𝑝𝑦& 3𝑝𝑧. Degenerate molecular orbitals are those orbitals that have identical energy levels. Since the 4𝑝𝑥, 4𝑝𝑦& 4𝑝𝑧 electrons in 4p have identical energy levels to one another, they are similarly degenerate. Let's now use a graphical depiction to evaluate these energy subshell degeneracies.

CK-12 Foundation, Orbital representation diagram potassium, CC BY-SA 3.0

Conclusion

It can be concluded that Degenerate orbitals are electronic orbitals with identical energy states. Any exterior influences, such as an electric/magnetic field, do not affect the electrons of the orbitals. The degeneracy of these orbitals interferes with the application of the magnetic field. The one with the identical energies is Degenerate Orbitals. The highest stable atoms and those that do not interact with other elements are those whose orbitals are filled. According to Friedrich Hund, most of the parallel electron spins in any subshell spin in the ground-level electronic configuration. The Aufbau Principle predicts that electrons will occupy lower to greater energy states. The orbitals p, d, & f have degeneracy values of 3, 5, and 7 correspondingly.

FAQs

1. Where will the next electron enter when the 3d orbital is filled?

The electron will go from a lower energy state to an upper energy state, as stated by the Aufbau Principle. The electron will go into the 4p orbital since it has a greater energy state than the 3d orbital.

2. What leads to degeneration?

The Pauli exclusion principle forbids particles from having identical energy when they are very close to one another, which causes the particles to repel one another. Degeneracy pressure is created as a result, which, contrary to thermal pressure, is solely dependent on density & not temperature.

3. In what kind of degenerate orbitals does Hund's rule break?

Each orbital with the identical energy must have 1 electron with the identical spin before 2 electrons are deposited in the same orbit, which is a contradiction of Hund's rule. Hund's law is broken by the arrangement of these electrons.

4. What orbit will the incoming electron enter once the 3d orbital is fully occupied?

According to the Aufbau Principle, the electron moves from a lower to a higher energy state as it arrives. The electron will go into the following higher state orbital, the 4p orbital, if the third orbital is finished.

5. Describe degenerate eigenvalue?

If more than 1 linearly independent eigenstate is a part of a given eigenvalue, the eigenvalue is said to be degenerate. Both classical & quantum mechanical issues can experience degeneracy, and it is virtually usually connected to the system's spatial symmetry.