Stability Of Orbitals: Half-Filled And Completely-Filled

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.

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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. However in certain elements when the two subshells differ slightly in their energies, an electron may shift from a subshell of lower energy to a subshell of higher energy only if such a shift results in the symmetrical distribution (either completely filled or exactly half-filled) of the electrons in the various orbitals of the subshell of higher energy. This is due to the following two reasons:

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. For example, the expected electronic configuration of chromium (Z = 24) is as follows:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s² 3d⁴ or 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁴ 4s²

But if one of the 4s electrons shifts to the vacant 3d-orbital, the distribution of the electrons will become more symmetrical and this will impart extra stability. Therefore, the electronic configuration of Cr, as given above, is wrong and the actual configuration is as follows:

1s² 2s² 2p⁶ 3s² 3p⁶ 4s¹ 3d⁵ or 1s² 2s² 2p⁶ 3s² 3p⁶ 3d⁵ 4s¹

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.

The number of exchanges that can take place in d⁴ configuration are as follows:

Total number of exchanges = 3 + 2 + 1 = 6

The number of exchanges that can take place in d⁵ configuration are as follows:

Total number of exchanges = 4 + 3 + 2 + 1 = 10

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

Related Topics,

• Electronic Configuration Of Elements
• Quantum Numbers
• Frequency, Time Period And Angular Frequency
• Radial Nodes And Planar Nodes

Recommended topic video on (Stability Of Orbitals: Half-filled And Completely-filled)

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) 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) 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) $4 s^1 3 d^5$ 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) $K=4 s^1, C r=3 d^5 4 s^1, C u=3 d^{10} 4 s^1$

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: The electronic configuration of $\mathrm{Cu}(\mathrm{II})$ is $3 \mathrm{~d}^9$ whereas that of $\mathrm{Cu}(\mathrm{I})$ is $3 \mathrm{~d}^{10}$. Which of the following is correct?

1) $\mathrm{Cu}(\mathrm{II})$ is less stable

2) Stability of $\mathrm{Cu}(\mathrm{I})$ and $\mathrm{Cu}$ (II) depends on nature of copper salts.

3) $\mathrm{Cu}($ II) is more stable.

4) $\mathrm{Cu}(\mathrm{I})$ and $\mathrm{Cu}$ (II) are equally stable.

Solution:

$\mathrm{Cu}(\mathrm{II})$ is more stable than $\mathrm{Cu}(\mathrm{I})$ because hydration energy of $\mathrm{Cu}^{+2}$ ion compensate $\mathrm{I.E}_2$ of $\mathrm{Cu}$.

Hence, the answer is the option (3)

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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.

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