Stability of half-filled or completely filled orbitals

The orbital configuration of chromium is the fourth configuration of electrons in a given subshell, [Ar]3d54s1. This is because of symmetry, when the 5d subshell is filled, the orbitals are symmetrical. Chromium has an additional electron in the 4s subshell, this causes the “hole” to be slightly unstable because of exchange energy.

The orbital configuration of chromium is not the second configuration in a given subshell, [Ar]3d6, due to the lack of symmetry and greater stability from having the 4s subshell completely filled; even though it causes instability by adding one more electron in the 3d subshell.

The second configuration for chromium would have been [Ar]3d4 4s2, but there is lower symmetry with two electrons and the stability of these orbitals is higher than those with one electron, thus making it more stable.

The totally filled orbitals are having more energy than other partially filled configurations which are present in degenerate orbitals. The reason for this is that they have more symmetry and a greater number of nodes which makes them less reactive than other orbits that have different configurations: [Ar]3d4 4s2 and [Ar]3d6 4s1.

Electron symmetrical distribution

If you have an atom or molecule that is not in its lowest possible energy state, it can fall to a lower energy state by emitting radiation.

In particular, if the atom has more electrons than protons (it is negatively charged), it will emit photons. It does this because there are more ways of arranging the electrons than there are of arranging the protons and electrons together, and so it will pick the way that keeps the electrons most symmetrical. The half-filled and fully-filled configurations are symmetrical.

Symmetry is important in physics. A perfectly spherical pool ball is more likely to roll into a corner pocket than one that is more squashed. Symmetry explains why ice skaters spin faster when they bring their arms close to their bodies, why drops of water are round, why ballerinas twirl faster when they pull in their arms and other things like that.

As a rule, nature doesn’t like unsymmetrical things. If you have a system with something like an electron with some uncertainty about where it is, it will tend to settle into some kind of symmetrical configuration—a superposition of several different possible positions—even if only for an instant. 

The electron shells in the atom are known as valence shells, core-shell or energy levels. The orbitals which are used to accommodate electrons in the outermost shell are called valence orbitals. They are of two types, namely s and p orbitals. Based on their size, shape and orientation in space, they can be classified into three sets of orbitals.

The first set is formed by px, py, and pz orbitals which have equal energies and their orientation in space are different. Due to this symmetrical distribution, the shielding of one electron on the other is relatively small and hence the electrons are attracted more strongly by the nucleus and it increases the stability. Thus p orbital is also called a stable orbital. On the other hand, dxy and dyz orbitals have unequal energies and their orientation in space does not change when an electron is added to it. This leads to a high degree of shielding of one electron by another and hence these orbitals are not very stable. These kinds of orbitals are also known as degenerate orbitals.

Formation of new atoms from old atoms occurs due to gain or loss of total (or net) four or more electrons by an atom which results in the formation of negative or positive ions respectively. 

Exchange Energy

Exchange energy is the amount of energy required to exchange two electrons between the orbitals. It is an important concept while studying the stability of half-filled or completely filled orbitals. This exchange of electrons is possible in the case of orbitals which are half filled or fully filled. In half filled cases, one electron occupies one orbital and another electron occupies another orbital. But during the exchange process, both electrons change their position from one to another orbital. The energy required to make this transition is called exchange energy.

Totally filled and half-filled quantum-mechanical orbitals are also important in chemistry and physics. Energy levels of these orbitals depend upon the number of electrons present in them. If they are less than half-filled or fully-filled, then they are degenerate orbitals. In this type of orbitals, there is some possibility of exchanging the position of electrons present in them. When we try to exchange the position of electrons, it results in the formation of different states of matter called excitons. Carbon nanotubes and graphene sheets have such a property that they can produce excitons with high efficiency by using the applied voltage across them. Excitons are much smaller than normal molecules, but larger than atoms because they contain whole molecular orbitals from both donor and acceptor molecules. 

The 3d orbital is half filled in a lot of common metals. For example, chromium has the configuration [Ar]3d5 4s1. So do manganese, iron, and cobalt. Based on the number of possible electron exchanges, this means that 3d orbitals are more stable than 2d orbitals.

Trouble is, it’s not really true. The Hund Rule doesn’t work for all elements.

In fact, in many compounds including those mentioned above, the 4s orbital is actually lower in energy than the 3d orbital. How can that be? The answer lies in the word “exchange”. Here’s what happens. In a compound like chromium, there are five valence electrons. Three of them go into the 3d subshell and two go into the 4s subshell. But it turns out that sometimes, one of those electrons will jump back and forth between the 3d and 4s shells at room temperature and normal pressure. 

Conclusion

In this material, we discussed the stability of half filled and completely filled orbitals in detail. Along with that, we also discussed the concept of electron distribution and also the concept of energy exchange. We discussed how the stability of half-filled orbitals and stability of completely filled orbitals is different from each other.