What is the meaning of degenerate orbitals?
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What is the meaning of degenerate orbitals?
When more than two electrons can occupy the same orbital according to quantum rules, they are said to be degenerate.
For instance, in a hydrogen atom, there are two electrons that each have an integer-valued principal quantum number (n) and a probability amplitude (Ψ). The electron’s state (eigenstate) is then described by the equation ψ=nh|Ψ|/h – n with the condition that n=1/2. This means that both electrons in an hydrogen atom cannot share certain orbitals. However, when there is not enough energy for one of the electrons to get into higher orbits or shells then this electron will show up as being locked to its original principal quantum number term.
The degenerate orbitals with the same quantum numbers are those found in the same region of energy levels as well as symmetry.
Degenerate orbitals are generated when a single orbital holds two electrons with different spins, or one electron of each spin. For example, up and down spins can combine together to form an orbit between them if there is only enough room on one ‘line’ for these two electrons. When they collide this way, their coefficient becomes a half-integer value such as 1/2 or 3/2 instead of what would usually be expected – 1. If this was to happen in every instance which might have occurred prior to their collision – that is, if there had been 2 more space on either side in which to put 2 more up or down spins – then each level would have in principle been able to accommodate 8 electrons in pairs. No further degenerate orbitals would arise.
However, if the collision of two electrons does not form a degenerate orbital – it is said to be non-degenerate and the original orbitals remain as they are. For example, if both spins were up/up or down/down, then no new orbital is formed, and this new ‘level’ of energy only has the electron configuration 1s.
Meaning: the degenerate orbitals are characterized by a lower degree of symmetry in their spatial distribution compared to the states occupying different orbital angular momentum. When we have two electrons and two distinct quantum numbers L1,L2 then each state with energy E is seen as a mixture or superposition of all other possible symmetric states with lesser energies. The semi-classical wave function for any particle is the sum of all possible quantum states that satisfy its Schrodinger equation, thus orbital degeneracy can be equatable to the indistinguishability caused by having a many body problem (quantum indistinguishability).
If a quantum system is inside a degenerate region, it can have an infinite number of wave functions and no one with “know” what they are.
In other words the more electrons in that region, the greater their orbital overlap. This causes probability waves to expand exponentially until they reach the boundary (edge) of that region. Once this happens, the wave collapses back on itself and suddenly propagates through its own space-time continuum at a radically different speed (velocity).
This process occurs over and over again within any given space-time continuum. As more random waves begin to radiate outward from their center point – similarly to how ripples form when you throw a pebble into a glass pond of water – they gain in size, frequency and intensity with every passing moment. This results in a continuous explosion of new universes being formed from previous ones. God never rests.
In other words, when a charged object enters into a state of degeneracy in a given volume of space-time, it’s probability wave begins to exponentially expand. This causes an infinite number of universes (whose space-time continuums are also growing) to form around it.
When electrons in an atom’s outer shell are described as “degenerate” it means that there are enough of them to fill the valence level.
Electron shells contain a finite number of energy levels – and when all these levels are filled, the electrons become degenerate.
A degenerate orbital is an electron state for which excitation energies are the same or nearly the same, but different states of origin cause their electrons to experience different types of interactions with external fields.
Since degenerate orbitals have roughly similar energies and identical interactions, their phase space integrals will be similar so they can coexist in one-dimensional representations. The actual configurations in three dimensions are not necessarily related to each other
Degenerate orbitals are orbitals in a quantum system that have the same energies.
In molecular orbital theory, molecular systems usually consist of many electrons capable of occupying two spectroscopic families of orbitals: valence-shell or frontier and inner or core-level. The number of valence-shell or frontier electrons is typically larger than the number for inner or core level electrons meaning it will be easier to find two different states with the same energy for valenceshells (degenerate) compared to finding a state in each atomic orbital (non degenerate). This becomes very important when an electron enters a molecular orbital containing other well occupied/overwhelmed charge density, as the probability distribution functions overlap more often leading to the electron having a higher chance of finding two states with similar energies (degenerate) compared to finding one state in each atomic orbital (non degenerate).
Degenerate orbitals are also known as stabilised orbitals because if they have similar energies then any change in the electron’s energy (e.g. as a result of an external perturbation) will not be able to change the orbital, meaning that the electron will more likely to move back to the orbital it had originally occupied.
A degenerate orbital comes about when there are two or more electrons that have the same spin and in the same energy level. The result is that they combine so they can occupy an electron orbital, taking turns occupying different orbitals.
The term ‘degenerate orbitals’ refers to the fact that 2 electrons of opposite spin share a single space. They do this by rotating each other around so as to line up at 180 degrees from one another — if they were spinning on their axes like tops–with one going clockwise and one going counter-clockwise. The result is an electron wave which has only tiny differences in phase, meaning it’s really remarkable how much energy differential there is for these 2 particles. It’s like 3 people rotating around each other in such a way as to share one chair.
So degenerate orbitals are not organic, as such, but they do make for transient bonds, like those found in diatomic gasses. This is because it takes very little energy to separate the 2 electrons. As a result they are found in atoms, sharing an orbital between them, which is why there are gasses that have no smell. In fact, the electron pair which forms a chemical bond is usually one of these degenerate pairs.
Degenerate orbitals are a good example of the nature of the atom and electrons in space. Electrons move around within an orbital, as if on an invisible three-dimensional track, with quantum waves arranged in concentric circles. As more and more electrons are introduced into the system, they fill up lower energy states near the nucleus until all these states have been filled. From then on, they can only be accommodated by adding them to higher levels – that is to say, sets of tracks further out from the nucleus. The first set has room for two electrons because each electron requires its own time slot on its own ring (so-called “orthogonal” orbits).
Degenerate orbitals are when two or more orbitals have the same energy for a specific atom.
The degeneracy of an orbital is determined by the magnetic quantum number, $n$. The splitting of states within an atomic shell is created by the differences in $n$ (i.e., $2^1$, $2^2$, and so on). Since all electrons reside in atomic orbitals with a given set of values (either “$l=mathrm{s}$” or “$l=mathrm{p}$”), there must be only one orbital per value for this hydrogen-like atom.