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.
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
1. What are degenerate orbitals in Chemistry?
Degenerate orbitals are a set of orbitals within the same subshell of an atom that have the exact same energy level. This means electrons in any of these orbitals possess identical energy. This condition holds true for an isolated atom in the absence of any external electric or magnetic fields.
2. What are some examples of degenerate orbitals in an atom?
Examples of degenerate orbitals are found in any subshell that contains more than one orbital. Common examples include:
- The p-subshell, which has three degenerate orbitals: pₓ, pᵧ, and p₂.
- The d-subshell, which has five degenerate orbitals: dₓᵧ, dᵧ₂, d₂ₓ, dₓ²₋ᵧ², and d₂².
- The f-subshell, which has seven degenerate orbitals.
3. What is the difference between degenerate and non-degenerate orbitals?
The key difference lies in their energy levels. Degenerate orbitals belong to the same subshell (e.g., all three 3p orbitals) and have identical energy. In contrast, non-degenerate orbitals have different energy levels. This occurs when orbitals are in different subshells (like 2s and 2p) or different principal energy shells (like 2p and 3p).
4. How do Hund's Rule and the Aufbau Principle relate to the filling of degenerate orbitals?
Both principles govern how electrons fill orbitals, but they apply at different stages:
- The Aufbau Principle dictates the overall filling order from lower to higher energy subshells (e.g., 1s, then 2s, then 2p).
- Hund's Rule of Maximum Multiplicity specifically applies when filling a set of degenerate orbitals. It states that every orbital in the subshell must be singly occupied with an electron of the same spin before any orbital is doubly occupied.
5. Why are the three 2p orbitals considered degenerate, but the 2s and 2p orbitals are not?
This is due to their quantum numbers. The three 2p orbitals (2pₓ, 2pᵧ, 2p₂) all share the same principal quantum number (n=2) and the same azimuthal quantum number (l=1), giving them identical energy. However, the 2s orbital (n=2, l=0) has a lower energy than the 2p orbitals (n=2, l=1). Because their energy values are different, the 2s and 2p orbitals are non-degenerate.
6. How can you determine the number of degenerate orbitals in a given subshell?
The number of degenerate orbitals in any subshell is determined by its azimuthal quantum number (l) using the formula (2l + 1).
- For a p-subshell (l=1), there are 2(1) + 1 = 3 degenerate orbitals.
- For a d-subshell (l=2), there are 2(2) + 1 = 5 degenerate orbitals.
- For an f-subshell (l=3), there are 2(3) + 1 = 7 degenerate orbitals.
7. Under what conditions can the degeneracy of orbitals be removed or 'lifted'?
The degeneracy of orbitals is 'lifted' or removed when an atom is subjected to an external magnetic or electric field. In the presence of a magnetic field, for instance, the three p-orbitals will split into three slightly different energy levels. This splitting of spectral lines due to a magnetic field is known as the Zeeman effect.
8. How does understanding degenerate orbitals help in writing the electronic configuration of an element?
Understanding degeneracy is crucial for correctly applying Hund's Rule. When writing the electronic configuration for an element like Carbon (Z=6), which is 1s²2s²2p², you know the two p-electrons must occupy separate degenerate orbitals (2pₓ¹ 2pᵧ¹) rather than pairing up in one (2pₓ²). This ensures the most stable, lowest-energy configuration is represented.
9. Why is the concept of degeneracy important for explaining the stability of half-filled and fully-filled subshells?
The special stability of half-filled (p³, d⁵) and fully-filled (p⁶, d¹⁰) subshells arises from two effects within degenerate orbitals:
- Symmetrical Electron Distribution: These configurations have a perfectly symmetrical arrangement of electrons around the nucleus, which minimizes repulsion and increases stability.
- Maximum Exchange Energy: Electrons with parallel spins in different degenerate orbitals can exchange their positions. This exchange releases energy. Half-filled subshells maximise the number of parallel spins, thus maximising the stabilising exchange energy.
