Stability Of Orbitals: Half-Filled And Completely-Filled

Stability Of Orbitals: Half-Filled And Completely-Filled

Shivani PooniaUpdated on 02 Jul 2025, 06:32 PM IST

Stability of Filled and Half-Filled Subshells

This Story also Contains

  1. Stability of filled and half-filled subshell: arrangement of elements
  2. Rules for filling the electrons in shells and sub-shells:
  3. Solved Examples Based On-Stability of filled and half-filled subshell: arrangement of elements
  4. Conclusion
Stability Of Orbitals: Half-Filled And Completely-Filled
Stability Of Orbitals

The idea of stability of the filled and the half-filled shells is one of the fundamental principles in chemistry that has its genesis in the behavior of electrons of the atoms. Electrons orbit in desirability around the nucleus of the atoms to fill the shells following rules that have been derived from quantum mechanics. The stability characteristic of filled and half-filled subshells is explained by the electron configuration, concerning the Pauli exclusion principle & Hund’s rule. The distribution of electrons in the atomic orbitals within a subshell is done in such a manner that the energy is at its minimum. The Pauli exclusion principle is a principle that states that no two electrons in an atom can have the same quantum numbers that is, every electron must occupy a different orbital in every subshell. Hund’s rule also postulates that electrons are filled singly in an orbital before they are accommodated in pairs thus giving the lowest possible energy configuration for the atom. When the shells are full or half full, then this is the answer because the electrons are symmetrically placed in Subshells. This stability is because the filled subshells have all the orbitals being filled with the electrons of opposite spins, with an opposing force of repulsion hence they have lower energy than the single occupied subshells. This is the same as half-filled subshells that contain unpaired electrons whose distribution which results in the lowest possible repulsion that enhances stability is uneven.
To one’s mind, the stability of the filled and half-filled subshells offers a good insight into the explanation of their chemical characteristics. When subshells are filled to the brim or intermediate, elements display special features like innerness or higher reactivity as located on the periodic table. This process also applies to the ion's stability and chemical bonds since atoms look for full octets by sharing, accepting, or donating electrons. Finally, it will help to understand the atomic and molecular interaction in chemical reactions or any material science and even in factoring filled and half-filled subshells to predict the coherence or incoherence of a set atomic or molecular structure.

In this article, we will cover the concept of the stability of filled and half-filled subshells. This concept falls under the broader category of Atomic structure, which is a crucial chapter in Class 11 chemistry. It is not only essential for board exams but also for competitive exams like the Joint Entrance Examination (JEE Main), National Eligibility Entrance Test (NEET), and other entrance exams such as SRMJEE, BITSAT, WBJEE, BCECE, and more.

Let us study the Stability of filled and half-filled subshells in detail to gain insights into this topic and solve a few related problems.

Stability of filled and half-filled subshell: arrangement of elements

The concept of filled and half-filled subshells in atoms is a core aspect of chemistry due to its impact on the characteristics of elements in the periodic table. Electrons stay stable in an atom by completing the shells in an order that is dictated by the Pauli exclusion theory which says that two electrons in an atom cannot occupy the same 4-digit numbers or spin. This eventually leads them to arrange themselves in the orbitals provided by subshells in a manner that will allow them to repel each other and bring the energy level of the atom down.
Shells that are fully loaded for example noble gas expansions like helium with 1s², and neon with [He] 2s²2p⁶ are very stable. In this configuration, the orbitals of the subshell are filled with electrons each with opposite spin and thereby arranged in such a manner that an equal amount of repulsion between two electrons is achieved. This makes noble gases chemically inactive at standard conditions because they do not readily engage in the loss, gain or sharing of electrons.
In the same regard, semi-filled subshells are also rather stable, for instance, chromium with the configuration 3d⁵4s¹ or copper with the configuration 3d¹⁰4s¹. In these cases, electrons share orbitals one at a time before they pair up; according to Hund’s rule, electrons in degenerate orbitals will share the orbitals while having parallel spins. As such, the half-filled configuration is characterized by a more extended separation of electrons with opposite spin states which results in less electron-electron interchange repulsion as compared to the case with less or more electrons.
The filled and half-filled subshells in particular relate to the reactivity and the bonding properties of the elements and thereby influence their stability. At times the elements undergo transfers of electrons to and from other elements in an attempt to acquire the electron number that is characteristic of the noble gases, hence achieving the state of stability. Transition metals are known to have partially filled d-orbitals, and are capable of variable oxidation and complex ion/compound formation because of their stable electronic configuration.

Rules for filling the electrons in shells and sub-shells:

The filled or half-filled subshells have a symmetrical distribution of electrons in them and are therefore more stable.

1. Symmetrical distribution of electrons: It is well known that symmetry leads to stability. The filled or half-filled subshells have a symmetrical distribution of electrons in them and are therefore more stable.

2. Exchange Energy: The stabilizing effect arises whenever two or more electrons with the same spin are present in the degenerate orbitals of a subshell. These electrons tend to exchange their positions and the energy released due to this exchange is called exchange energy. The number of exchanges that can take place is maximum when the subshell is either half-filled or filled. As a result, the exchange energy is maximum and so is the stability.

For eg: The valence electronic configurations of Cr and Cu are 3d54s1 and 3d104s1 respectively and not 3d44s2 and 3d94s2.

For a better understanding of the topic and to learn more about Stability Of Orbitals: Half-Filled And Completely-Filled with video lesson we provide the link to the

Solved Examples Based On-Stability of filled and half-filled subshell: arrangement of elements

Example 1: Which of the following configurations is correct in the first excited state?

1) Cr: [Ar] 3d5 4s1

2) Mn2+: [Ar] 3d5

3) (correct) Fe2+: [Ar] 3d5 4s1

4) Co3+: [Ar] 3d5

Solution: Stability of filled and half-filled subshells

It is well known that symmetry leads to stability. The filled or half-filled subshells have a symmetrical distribution of electrons in them and are therefore more stable.

For eg: the valence electronic configurations of Cr and Cu, therefore, are 3d54s1 and 3d104s1 respectively, and not 3d44s2 and 3d94s2.

As we learned,

Stability of Half-Filled Subshells of Cr -

The valence electronic configurations of Cr is 3d5 4s1 and not 3d4 4s2.

Cr: [Ar] 3d5 4s1 ground state

Mn2+: [Ar] 3d5 ground state

Fe2+: [Ar] 3d6 ground state

[Ar] 3d5 4s1 excited state

Co3+: [Ar] 3d5 ground state

Hence, the answer is the option (3).

Example 2: In Cu (atomic number = 29)

1) 13 electrons have a spin in one direction and 16 electrons in the other direction

2) (correct) 14 electrons have a spin in one direction and 15 electrons in the other direction

3) One electron can have spin only in the clockwise direction

4)None of these

Solution: As we learn, the Stability of Filled Subshells of Cu -

The valence electronic configurations of Cu are 3d10 4 s1 respectively and not 3d9 4s2.

Cu (29) = [Ar]18.3d10.4s1

All electrons are paired except 4s1. Hence 14 electrons have spin in one direction and 15 electrons in the other.

Hence, the answer is the option (2).

Example 3: Chromium has the electronic configuration $4 s^1 3 d^5$ rather than $4 s^2 3 d^4$ because
1) $4 s$ and $3 d$ have the same energy
2) $4 s$ has a higher energy than $3 d$
3) $4 s^1$ is more stable than $4 s^2$
4) (correct) $4 s^1 3 d^5$ is more stable than $4 s^2 3 d^4$

Solution: The electronic configuration of $\mathrm{Cr}$ is $[A r] 4 s^1 3 d^5$.
This is because the half-filled d orbital configuration is more stable than the corresponding $[A r] 4 s^2 3 d^4$.
The half-filled orbital configuration is generally more stable due to more exchanges in the electrons which leads to more exchange energy and also due to symmetrical distribution of electrons.
Hence, the answer is the option (4).
Example 4: Correct valence shell electronic configuration of the given element is correctly represented in
1) $K=4 s^1, C r=3 d^4 4 s^2, C u=3 d^{10} 4 s^2$
2) $K=4 s^2, C r=3 d^4 4 s^2, C u=3 d^{10} 4 s^2$
3) $K=4 s^2, C r=3 d^5 4 s^1, C u=3 d^{10} 4 s^2$
4) (correct) $K=4 s^1, C r=3 d^5 4 s^1, C u=3 d^{10} 4 s^1$

Solution: The correct configurations are given as

$\begin{aligned} & K(19):[A r] 4 s^1 \\ & C r(24):[A r] 4 s^1 3 d^5 \\ & C u(29):[A r] 4 s^1 3 d^{10}\end{aligned}$

The anomalous configuration of Cr and Cu is attributed to the extra stability of the half-filled and the filled d orbital configuration respectively.

Hence, the answer is the option (4).

Example 5: In Cu (atomic number = 29):

1) 13 electrons have a spin in one direction and 16 electrons in the other direction

2) (correct) 14 electrons have a spin in one direction and 15 electrons in the other direction

3) One electron can have spin only in the clockwise direction

4) None of these

Solution Stability of filled and Half-filled Subshells - Stability of filled and half-filled subshells

It is well known that symmetry leads to stability. The filled or half-filled subshells have a symmetrical distribution of electrons in them and are therefore more stable.

For eg: the valence electronic configurations of Cr and Cu, therefore, are 3d54s1 and 3d104s1 respectively and not 3d44s2 and 3d94s2.

As we have learnt,

The electronic configuration of Cu is:
1s22s22p63s23p64s23d9

Thus, Cu has 14 electrons with spin in one direction and 15 electrons in another direction.

Hence, the answer is the option (2).

Conclusion

Thus, the filled as well as the half-filled subshells in atoms possess stability, which is a critical factor in studying elements in chemical processes. The filled subshells, for instance, the noble gases, are highly stable in the sense that there is a given repulsion between similar electrons. Because of this stability, noble gases do not chemically react, which makes them chemically inert gases. The same is the case with the half-filled subshells that are evident in some of the transition metals also because it provide an equal number of unpaired electrons as supported by Hund’s rule of molecular stability for it. This forms the basis of the reactivity of elements where atoms vigorously try to mimic the electronic configuration of the nearest noble gases by either donating, receiving, or sharing electrons. By understanding the stability of filled and half-filled subshells, it is possible to predict the chemical properties, bonding behaviors, and reactivity in the periodic table and extend people’s knowledge about the materials and their applications in different spheres.

Frequently Asked Questions (FAQs)

Q: What is the relationship between orbital stability and the periodic trends in atomic and ionic radii?
A:
Orbital stability influences atomic and ionic radii trends. As orbitals are filled across a period, the increasing nuclear charge generally leads to a decrease in radius. However, half-filled or completely-filled subshells can cause slight deviations from this trend due to their enhanced stability and electron distribution.
Q: How does orbital stability influence the formation of coordination compounds?
A:
Orbital stability plays a crucial role in the formation of coordination compounds. Transition metals often form complexes that allow them to achieve more stable electronic configurations, such as 18-electron configurations or arrangements with half-filled or completely-filled d-orbitals.
Q: Why do some atoms have "anomalous" electron configurations?
A:
Some atoms have "anomalous" electron configurations because they can achieve more stable half-filled or completely-filled subshells by slightly altering the expected configuration. This stability outweighs the energy cost of deviating from the standard filling order.
Q: What is the relationship between orbital stability and crystal field theory?
A:
Crystal field theory, which explains the splitting of d-orbitals in transition metal complexes, is closely related to orbital stability. The splitting of orbitals affects their relative energies and, consequently, their stability, influencing the properties of the complex.
Q: How does the concept of orbital stability help explain the stability of certain oxidation states in transition metals?
A:
Certain oxidation states in transition metals are more stable due to the resulting electron configurations. For example, Mn2+ and Fe3+ are particularly stable because they result in half-filled d-orbitals (d5), while Cu+ and Ag+ are stable due to completely-filled d-orbitals (d10).
Q: Why is the electron configuration of lawrencium (Lr) predicted to be [Rn] 5f14 7s2 7p1 instead of [Rn] 5f14 6d1 7s2?
A:
The predicted configuration of lawrencium as [Rn] 5f14 7s2 7p1 is based on orbital stability considerations. This configuration allows for a completely-filled f-orbital and a half-filled p-orbital, which may be more stable than having a single electron in the 6d orbital.
Q: How does orbital stability affect the trends in electron affinity across the periodic table?
A:
Orbital stability influences electron affinity trends. Elements with nearly-filled shells often have high electron affinities as they can achieve stable configurations by gaining an electron. However, elements with half-filled or completely-filled orbitals may have lower electron affinities due to their inherent stability.
Q: What role does orbital stability play in the formation of metallic bonds?
A:
Orbital stability influences metallic bonding. In metals, the overlap of many atomic orbitals creates bands of molecular orbitals. The stability of these bands and the distribution of electrons within them contribute to the properties of metallic bonds.
Q: How does the concept of orbital stability relate to Jahn-Teller distortions in transition metal complexes?
A:
Jahn-Teller distortions occur when orbital degeneracy leads to an unstable state. The complex distorts to remove this degeneracy, resulting in a more stable configuration. This phenomenon is directly related to the concept of orbital stability and its influence on molecular geometry.
Q: Why do some transition metals prefer certain oxidation states in aqueous solutions?
A:
Some transition metals prefer certain oxidation states in aqueous solutions due to orbital stability. For example, Cr3+ is more stable than Cr2+ in water because the Cr3+ ion has a half-filled d-orbital (d3), which is more stable than the d4 configuration of Cr2+.