Why do octets lead to a stable configuration?

[Shrijit Roy]

Hey everyone!
I am currently learning about the stability of an atom. I have learnt that octet or duet rule leads to stable electronic configuration but what I do not understand is why only these two configurations make stable electronic configurations? Why can't an atom be stable with any other configurations? Can someone please break it down for me? Thank you so much for the help!

 

[Borek]

These numbers reflect internal structure of the orbitals, and as such stem from the Schroedinger's equation solutions. 2, 8 and 18 are numbers of electrons that can occupy one energy shell - and if the shell is full of electrons, it is more stable than when it is not.

Technically these numbers apply directly to atoms only, but in reality solutions of the Schroedinger's equation for molecules are often variations of the solutions for atom, so these numbers appear quite often.

 

[Shrijit Roy]

These numbers reflect internal structure of the orbitals, and as such stem from the Schroedinger's equation solutions. 2, 8 and 18 are numbers of electrons that can occupy one energy shell - and if the shell is full of electrons, it is more stable than when it is not.

Technically these numbers apply directly to atoms only, but in reality solutions of the Schroedinger's equation for molecules are often variations of the solutions for atom, so these numbers appear quite often.

I am a beginner with barely any idea of quantum physics. Could you please explain in simpler terms?

 

[Zaciekawiony]

In atoms, systems with closed electron shells have the highest stability. Elements with valence electrons in the s and p shells, i.e., from the main groups, tend to have an octet, because that is the number of electrons in the second shell. D-block elements tend to form the most stable complexes in the 18-electron system.

 

[Borek]

I am a beginner with barely any idea of quantum physics. Could you please explain in simpler terms?

I am afraid at this level you need to just accept the general picture as such, any explanation will just produce more "why" questions which are not easy to answer without delving into details. Electrons occupy orbitals, number of electrons per orbital is limited to two, these orbitals are described using four small integer numbers (there are some rules that tell which combinations of values are correct and possible), energy shell are all orbitals that have the same principal quantum number. Letters s, p and d Zaciekawiony mentioned are related to another of these quantum numbers, but as I said - they will be hardly explaining anything if you have no idea what they refer to.

 

[Shrijit Roy]

In atoms, systems with closed electron shells have the highest stability. Elements with valence electrons in the s and p shells, i.e., from the main groups, tend to have an octet, because that is the number of electrons in the second shell. D-block elements tend to form the most stable complexes in the 18-electron system.

That raises another question.Why do systems with closed electron shells have the highest stability?

 

[Shrijit Roy]

I am afraid at this level you need to just accept the general picture as such, any explanation will just produce more "why" questions which are not easy to answer without delving into details. Electrons occupy orbitals, number of electrons per orbital is limited to two, these orbitals are described using four small integer numbers (there are some rules that tell which combinations of values are correct and possible), energy shell are all orbitals that have the same principal quantum number. Letters s, p and d Zaciekawiony mentioned are related to another of these quantum numbers, but as I said - they will be hardly explaining anything if you have no idea what they refer to.

No i know about the quantum numbers. I just didnt take a deep dive into quantum mechanics yet. Like schrodinger's equation and all other things you said in your last comment

 

[mjc123]

That raises another question.Why do systems with closed electron shells have the highest stability?

They don't intrinsically. A sodium atom with a single electron in the 3rd shell is more stable than a sodium ion (with a closed shell configuration) and a free electron. Why then does sodium form ionic compounds containing the Na⁺ ion? You have to consider the total energetics of the compound formation.
This discussion might be of interest: https://www.chemicalforums.com/index.php?topic=77729.msg283639#msg283639

 

[gleem]

The solution for Schrodinger's equation gives rise to quantum numbers that determine the "space" available for electrons in each orbit or shell. Electrons are fermions, which, according to Pauli's Exclusion Principle, cannot have the same quantum numbers in a given energy level. In an atom, an orbit, energy level or shell is actually split into suborbitals that have a slightly different energy, and in each suborbit, the quantum number must be different. The numbers are n, l, m _l , and m_s. n is the primary quantum number referring to the shells or cluster of suborbitals increasing from 1 to however many are needed to place all the electrons in a given atom. l is the orbital quantum number specifying the angular momentum of the orbit and takes values from 0 to n-1. m_l is the magnetic quantum number (due to the electron circulating in the various l suborbits). m_l values run from -l to +l. m_s is the spin quantum number due to its intrinsic magnetic moment, and has values of -1/2 and =1/2.

Using these quantum numbers and the exclusion rule, you find for n=1, the total available places for electrons are 2. For n=2, it is 8. For n=3, it is 18, etc.

The following video demonstrates this and includes the standard orbit (spectroscopic) nomenclature used for specifying specific suborbitals.

 

[James Demers]

You're getting what probably comes across as a lot of mumbo-jumbo about quantum numbers and "stability", language which chemists use to describe what's going on, but none of which answers your fundamental question of "why?" ("Closed electron shells have the highest stability" is an observation, not an explanation.)

For starters, you should be familiar with the notion of "lowering the energy" as a driving force for physical change. Balls roll downhill, exothermic reactions proceed in the forward direction, ink diffuses throughout a solution. By "energy" we mean the Gibbs free energy "G" of the system, which changes according to the equation ΔG = ΔH - TΔS. (You may want to review the part of your p-chem or thermodynamics textbook that covers this ... having a solid understanding of it is essential to making sense of physical and chemical processes.)

Electrons in an atom can only occupy specific orbitals, having specific energies - i.e., the energy levels are quantized. This is nicely described by the Schroedinger equation, a type of equation that produces only specific numbers ("eigenvalues", to a mathematician) for the energy of the system, which depend on the integer values of a set of quantum numbers. (We give names to the quantum numbers to help us think about and visualize them, but nobody knows what "spin" or "angular momentum" actually are to a subatomic particle/wave.) If you do the math, you find that the nth electron shell (n being the "principal quantum number") has solutions only for 2n² electrons - which is where we get 2, 8 and 18. (We also get 32 and 50, but things get complicated.) Very broadly speaking, the calculated energy jumps considerably with each increase in the value of n. An electron added to a neon atom would have to go into the third shell; it will have lower energy if it goes anywhere else, so that's exactly what it does, leaving neon neutral and inert. Bump one of neon's inner electrons up to the third shell with a high voltage jolt, and it will drop back down immediately, releasing energy in the form of light (and you've just made yourself a neon lamp.)

The lone electron present in sodium's third shell is in a very similar situation, but is weakly held in place by the higher charge on the nucleus. If you give it a lower-energy option (say, by throwing the sodium into water), it will happily depart to leave behind a sodium ion, Na+. And so it goes: atoms give and take electrons until energy is minimized, and that usually happens when a shell is full.