What Are Degenerate Orbitals Definition Rules and Examples
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.
Hunds's Maximum Multiplication Rule
For a given electron configuration, Hund's Rule of Maximum Multiplicity states that the term with maximum multiplicity has the lowest energy. The rule states that, for p, d, and f orbitals, electrons must be paired only if each orbital contains an electron or is singly occupied.
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.
Postulates of Hund's Rule:
According to the report:
1. A sublevel consists of single orbitals that are occupied before multiple orbitals can occupy them.
2. An electron occupying single orbitals has the same spin as an electron in multiple orbitals.
A description of Hund's Rule
After entering an orbital, electrons pair with each other. These negatively charged particles repel one another. Because electrons do not share orbitals, their repulsion is minimized.
The spins of unpaired electrons in singly occupied orbitals are the same when we consider the second rule. It's determined by the spin of the first electron in a sublevel what the spin of the other electrons will be. One example in which this would be true is the electron configuration of a carbon atom, which would be 1s²2s²2p². The two 2s electrons will occupy the same orbital, which is consistent with Hund's rule, whereas the two 2p electrons will occupy different orbitals.
What is the Aufbau Principle?
Aufbau’s 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.
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.
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Solved Examples
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
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.
This is all about degenerate orbitals and the principles related to them. Understand the concepts well and study the solved examples to grab hold of the concepts.
FAQs on Degenerate Orbitals in Atomic Structure
1. What are degenerate orbitals?
Degenerate orbitals are atomic orbitals that have the same energy level within an atom.
- They differ in spatial orientation but not in energy.
- Degeneracy commonly occurs in isolated atoms.
- For example, the three 2p orbitals (2px, 2py, 2pz) are degenerate because they have equal energy.
2. Why are p orbitals considered degenerate?
The three p orbitals are degenerate because they have identical energy in an isolated atom but different orientations in space.
- They are labeled as px, py, and pz.
- Each has the same principal quantum number (n) and angular momentum quantum number (l = 1).
- Their energy equality results from the symmetrical environment around the nucleus.
3. What is the difference between degenerate and non-degenerate orbitals?
Degenerate orbitals have equal energy, while non-degenerate orbitals have different energy levels.
- Example of degenerate orbitals: 3px, 3py, 3pz in a free atom.
- Example of non-degenerate orbitals: 3s and 3p orbitals, which have different energies.
- Energy differences arise due to shielding, penetration, or external fields.
4. Are d orbitals degenerate?
Yes, the five d orbitals are degenerate in an isolated atom because they have equal energy.
- The five orbitals are dxy, dyz, dxz, dx²−y², and dz².
- All have the same principal quantum number (n) and angular momentum quantum number (l = 2).
- In complexes, this degeneracy is often split due to crystal field splitting.
5. What causes degeneracy to be removed in orbitals?
Degeneracy is removed when orbitals experience an external electric or magnetic field or chemical bonding interactions.
- In transition metal complexes, ligands cause crystal field splitting.
- This splits d orbitals into groups with different energies (e.g., t2g and eg).
- The phenomenon is known as lifting of degeneracy.
6. How do degenerate orbitals relate to Hund’s rule?
Hund’s rule states that electrons fill degenerate orbitals singly first with parallel spins before pairing.
- This minimizes electron–electron repulsion.
- Example: Nitrogen (atomic number 7) has electron configuration 1s2 2s2 2p3.
- The three 2p electrons occupy three separate degenerate 2p orbitals before pairing.
7. Are s orbitals degenerate?
No, s orbitals within the same shell are not multiple and therefore are not degenerate with each other.
- Each energy level has only one s orbital.
- Since degeneracy requires two or more orbitals of equal energy, a single s orbital has no degenerate partner.
- However, different subshells like 2s and 2p are not degenerate because they have different energies.
8. What are examples of degenerate orbitals in the second energy level?
In the second energy level (n = 2), the three 2p orbitals (2px, 2py, 2pz) are degenerate.
- They have the same energy in an isolated atom.
- The 2s orbital is not degenerate with 2p because it has lower energy.
- Degeneracy depends on having the same n and l values.
9. What is meant by lifting of degeneracy?
Lifting of degeneracy refers to the splitting of orbitals that originally had equal energy into orbitals with different energies.
- Occurs in electric or magnetic fields.
- Common in transition metal complexes due to ligand interaction.
- Example: In an octahedral field, five d orbitals split into t2g (lower energy) and eg (higher energy).
10. Why are degenerate orbitals important in chemistry?
Degenerate orbitals are important because they determine electron configuration, magnetic properties, and chemical reactivity.
- They explain Hund’s rule and electron spin arrangement.
- They influence bonding and hybridization.
- Splitting of degenerate orbitals explains color and magnetism in coordination compounds.
