Degenerate Orbitals

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Degenerate Orbitals And Their Concerned Principles

Chemistry is a subject of visualization and learning of concepts on matter and chemical compounds. Here we will learn the basic structure of the atom by understanding degenerate orbitals' meaning and their concerned principles like the Aufbau Principle and Hund's Rule.

The same subshell electron orbitals having the same energy level are known as degenerate orbitals. These degenerate orbitals exist at every moment until not disturbed by the magnetic field. The degeneracy disrupts the application of the magnetic field.


What is the Aufbau Principle?

Aufbau principle states that electrons are filled in order from lower energy levels to higher energy levels, where the lower energy levels are filled first. This principle helps to predict the type of chemical bond that an atom can form. 


What is Hund's Rule?

Hund's rule of electrons states that degenerate orbitals are filled evenly before electrons are filled in higher energy levels. Three principles explain the process of filling electrons in subsequent levels, namely the Pauli-exclusion Principle, Aufbau Principle, and Hund’s Rule.


Degenerate Orbitals Example

Here is a degenerate orbitals example that will help students to understand the degenerate orbital meaning more clearly.

Example: An atom has four orbitals, namely s, p, d, and f. The p orbital has three orbitals px, py, and pz. All these three orbitals have similar energy belonging to the same orbital (p), hence are called degenerate molecular orbitals. Every orbital at first obtains one electron, then the next electron of opposite spin fills in the same orbital. In the end, three orbitals possess 6 electrons, and the p orbital gets filled.


Explanation of Degenerate Orbitals with Diagram

Let us go through a detailed explanation of degenerate orbitals with a diagram, to have a 3D print of this concept in mind. Electron filling in a 2p orbital involves 2px, 2py, and 2pz. All these orbitals have the same energy level as each other. Similarly, electron filling in a 3p orbital involves 3px, 3py, 3pz. These orbitals have similar energy levels, hence are called degenerate molecular orbitals. Electrons in 4p involve 4px, 4py, and 4pz, these also have a similar energy level as one another; hence these are also degenerate. Now, let us compare these p subshell degeneracies through a graphical representation.

(Image to be added soon)


Solved Examples

  1. The arrangement of orbitals based on energy is based upon their (n+l) value. The lower the value of (n+l), the lower is the energy. For orbitals having the same values of (n+l), the orbital with a lower value of n will have lower energy.
    I. Based upon the above information, arrange the following orbitals in the increasing order of energy.
    (a) 1s, 2s, 3s, 2p
    (b) 4s, 3s, 3p, 4d
    (c) 5p, 4d, 5d, 4f, 6s
    (d) 5f, 6d, 7s, 7p

Ans. Based on the meaning of the Aufbau Principle, the solutions are:

(a) 1s < 2s < 2p < 3s
(b) 3s < 3p < 4s < 4d
(c) 4d < 5p < 6s < 4f < 5d
(d) 7s < 5f < 6d < 7p


  1. When 3d orbital is complete, the new electron will enter the
    (a) 4p-orbital
    (b) 4f-orbital
    (d) 4s-orbital
    (d) 4d-orbital

Ans. According to the Aufbau Principle definition, the electron will enter from a lower energy shell to a higher energy level. 4p orbital is the next higher energy level than 3d orbital, so the electron will enter into 4p orbital.


Did You Know?

  • An atom imparts colour in visible light due to the property of empty or incompletely filled degenerate levels.

  • Aufbau Principle helps to decide the stability of an atom, the half-filled and fulfilled electron orbitals are the most stable.

  • In the Aufbau principle, the first word is a German word that means building up. In orbitals building up means filling up.

FAQ (Frequently Asked Questions)

1. What are the Aufbau Principle and Hund’s Rule?

Aufbau Principle is one of 3 major principles that explain the electron distribution in atoms. According to this principle, electrons are filled from lower energy levels to higher energy levels. So, in simple words, the meaning of the Aufbau Principle is before filling lower energy levels, you can't jump to higher energy levels.

Hund’s rule established by Friedrich Hund provides details about the ground state of a multi-electron atom. This rule states that every orbital must be filled with at least a single electron before filling an orbital with double electrons of opposite spin.

2. What does Hund's Rule Explain with an Example?

The electron filling procedure and electronic configuration are decided with the help of Hund's principle. Hund's principle for atomic structure states that every orbital occupies a single electron before occupancy of double electrons in any orbital. Let us have an example of the quick grabbing of Hund’s rule concept.

The electronic configuration of the Boron atom is 2s2 2p3. There are two paired electrons in an s subshell, and 3 electrons singly occupied in p orbitals. This is because of Hund’s rule as all degenerate molecular orbitals have first single electrons and only then get paired electrons.