Stability Of Orbitals: Half-Filled And Completely-Filled

Stability of Filled and Half-Filled Subshells

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.