Extra Stability of Half-Filled and Completely Filled Orbitals

Introduction

The Discovery of many elements in the 19th century led to the development of a classification system for elements to ease their study individually. Finally, in 1913, the modern periodic table was devised by Henry Moseley an English physicist, which states that,

” physical and chemical properties of the elements are the periodic function of their atomic numbers “. 

The basic physical properties of an element are :

• Melting point
• Boiling point
• Enthalpy of fusion
• Density
• Enthalpy of vaporization 

Other than these properties elements possess properties based on their electronic configuration these are: 

• Atomic and ionic radii
• Enthalpy of ionization
• Electronegativity
• Electron gain enthalpy

ELECTRONIC CONFIGURATION OF ELEMENTS:

An element is made up of atoms, similarly, the atom has different shells, subshells, and orbitals. The distribution of elements in these shells is known as the electronic configuration of elements.

The electronic configuration of elements is represented by Alex

Where, 

n = principal quantum number

l = represents nutshell or orbital

x = number of electrons present in specific orbital 

For example, 2p² means that the p subshell in the 2nd main shell contains 2 electrons.

To write a full electronic configuration of an atom, the notations are written one after the other in increasing order of the orbital energy. The electron filling in the orbital always begins from the lowest energy orbitals first and then continues to higher energy orbitals.

A few examples of the electronic configuration of elements are listed below:

• Helium- 1s²
• Lithium- 1s²2s¹
• Beryllium- 1s²2s²

To make it simple and convenient electronic configuration is written in such a way that the electronic configuration of noble gas precedes the valence shell electrons.

It is represented by the symbol of noble gasses using the square brackets followed by the valence shell configuration.

For example: for magnesium, the electronic configuration is written as [Ne]3s², and calcium is represented as [Ar]4s².

HALF FILLED AND FULLY FILLED ORBITALS

Half-filled orbitals or also called partially filled orbitals are the orbitals that have half the number of electrons (i.e. one electron). On the other hand, filled or filled orbitals have a full number of electrons (i.e. two electrons).

STABILITY OF COMPLETELY FILLED AND HALF-FILLED SUBSHELLS:

Almost all the elements follow the same rules for writing electronic configuration. The exactly half-filled and filled orbitals have greater stability than that of partially filled configurations in degenerate orbitals. This can be explained by the exchange of energy and based on symmetry. In case sometimes when the two sub-shells differ in energies, an electron from lower energy moves to high energy. This is because of the following main reasons:

• Symmetrical distribution: it is important to note that symmetry leads to stability. The orbitals in which the subshell is exactly half-filled or filled have more stability due to the symmetrical distribution of electrons.
• exchange energy: the electrons present in degenerate orbitals having a parallel spin tend to change their position, the energy released during this process is called exchange energy. When the electrons are half-filled or filled in the orbitals then the number of exchanges is maximum leading to maximum stability.

The two or more electrons having the same spin can exchange their positions with the degenerate orbitals. This spinning of electrons generates a new type of mechanical interaction where heat is released, called exchange energy Eex. In the case of filled or filled orbitals/subshells have the maximum energy. However, even though the electrons have the same energy, they have different spatial distributions due to this their shielding effect of one over another is relatively small and so, the electrons are more attracted to the nucleus. The state of lowest total electronic energy corresponds to the ground state electronic configuration of an element.

As the s-orbital is spherical, so the electric charge is distributed uniformly in all directions. The p-orbitals px, py, and Pz are symmetrical in the x, y, and z-axis respectively. In the case of px’, the electronic charge is concentrated along the x-axis, however, in the case of py and Pz configuration more electronic charge is concentrated in the y-axis and z-axis respectively.

In px² py’ pz’ more electronic charge is concentrated in the x-axis. In the case of px² py² pz¹ configuration more electronic charge is in-plane xy. So, the uniform charge distribution results in a symmetrical configuration.

In the other case, the distribution charge in px¹py¹pz¹ and px²py²pz² configuration is symmetrical in all directions. Hence resulting in decreased exchange energy and making the configuration higher instability. similar is in the case of d-orbitals such as d⁵ and d¹⁰ have a symmetrical distribution of electronic charge on them. The greater number of exchanges results in high energy exchange and greater stability.

So, the exchange energy forms the basis of Hund’s rule (where extra stability of half-filled and filled orbitals) is because of these reasons: 

• Relatively small shielding
• Larger exchange energies
• Low coulombic repulsion energy

The exchange energy is the basis of Hund’s rule (that allows maximum multiplicity) i.e. electron pairing is only possible when all degenerate orbitals each have one electron.

Conclusion:

As we know symmetry leads to stability so electronic configurations that have a symmetrical distribution of electrons tend to have higher stability than unsymmetrical electronic distribution. If two or more electrons having the same spin are present in a degenerate orbital then they tend to exchange their position, in the mean process the amount of energy released is called exchange energy. Most numbers of exchanges are possible in half and filled orbitals only.

Examples of elements that are symmetrically full-filled or half-filled and shows great stability:

• Chromium is an element that has half-filled electrons in its 3d subshell and shows great stability. The electronic configuration of chromium is:1s²2s²2p⁶3s²3p⁶3d⁵4s¹

• Copper has filled electrons in a 3d subshell and shows great stability. The electronic configuration of copper is: 1s²2s²2p⁶3s²3p⁶3d¹⁰4s¹

 Points to remember:

• very few elements have half or filled orbitals
• the element show greater stability due to half or filled orbitals
• the reason behind stability is the symmetry and exchange of energy
• electron having the same spin present in degenerate orbits can exchange their position, while the process they release energy called exchange energy
• if the number of exchanges is maximum then elements will have high stability.