# Why quantum mechanics follows octet rule?

#### Mr Virtual

Perhaps my thread title is a little confusing, but here is my actual question.
(It is a bit long though, sorry! )

A single atom of flourine has 9 protons and 9 electrons. The number of electrons is exactly balanced by the number of protons. But flourine has a huge tendency of gaining one electron.
A single atom of sodium has 11 protons and 11 electrons. Number of electrons is equal to number of protons here too. In this case, the atom has a huge tendency to lose an electron.
A single atom of argon has 10 electrons and 10 protons. The number of electrons here is also equal to number of protons. But argon has almost zero tendency to gain/lose electron.

Why is this so?
The most common answer is : Atoms follow the octet rule. To complete their octet, they do these things. We know that noble gases have eight electrons in their outermost shell, so we assume that all other elements try to attain this stability by gaining or losing electrons.

But helium is also a noble gas despite not having an octet. So octet rule cannot be the right answer.

So, we can modify the octet 'rule' to say that: whenever an atom has a single electron in its orbital, it has a tendency to get a fully filled orbital. Especially where the outermost orbital is half filled, the atom is highly reactive (or unstable). It tries to gain or lose one electron so that the orbital has two electrons, so as to achieve stability. Whether it will lose or gain the electron to attain stability depends on the distance of electron from the nucleus i.e. if it is far away, it will prefer losing it (metallic nature), otherwise it will prefer gaining it (non metals). It also depends on the number of electrons required. For example, nitrogen needs 3 electrons to fill-up all its three half-filled orbitals (1 electron in each orbital). But 7+3=10 electrons cannot be attracted by 7 protons, therefore it shares electrons with other atoms.

Why does a singly-filled outermost orbital make the atom so eager to gain/lose electrons?
Because the atom has an opportunity to have its energy still more lowered if its outermost orbital is fully filled (i.e. it contains two electrons).

But exactly how/why does the energy of an atom decrease if its orbital is fully filled?
Secondly, in case of non metals, where does the attraction to hold the extra electron(s) gained come from(since n number of protons are already holding n number of electrons)?

My own guess for first question: The energy possessed by an electron is equal to the work done on it by the nucleus. Suppose the nucleus did x joule work on an electron, then this energy of electron (-x joule) manifests itself in the form of angular momentum (both due to its 'revolution' around the nucleus <speaking in classical terms>, as well as its spin on its axis). When another electron with opposite spin is introduced in the orbital, it cancels the ang.moment. due to spin of the other electron, thus lowering the energy of the atom.
But I don't know how the nucleus attracts the electron it has gained to attain this stability, unless it is due to the fact that the size of atom decreases with increase in non-metallic character (as we move along a period), thus decreasing the distance between nucleus and the electron to be gained, resulting in stronger attraction on the electron by the nucleus. If this is true, then the opposite is true for the metals. That is, very weak attraction exists between valence electron(s) of a metal atom and its nucleus, resulting in easy loss of the valence electron, which leads to higher stability.
But one may ask a question here: if a metal/non metal is more stable in its ionic form, why does it exist as an atom in the first place. My answer here would be that a non metal rarely exists in its monoatomic form. It is always in search of an electron to become more stable. Even if a mono-atom is prepared artificially, it immediately reacts with an atom(s) of its own kind or of different kind to form diatomic molecules or ionic/covalent compounds. Similarly, suppose we have a metal atom. For this atom, losing its electron will make it stabler. But the problem is that if it loses its electron, it immediately develops a positive charge, which starts attracting nearby negative charges. Thus, the atom cannot leave its electron even if it wants to. It can only do so, if there is some external charge to keep the electron from coming back to the ion (for example non metals like chlorine, flourine etc.). So a metallic ion in a salt (like NaCl) is in its most stable form.

Am I right?

I will be grateful for your replies.
Thanks.

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#### mathman

Very simple short explanation. Quantum theory dictates that electrons in the atom occupy various energy levels, Due to Pauli principle (no more than one elctron per state), there are exactly 2 electrons per level (spin quantum number either + or -). The first level gives He. The next four levels are close in energy, giving 10 (2+8) for Ne. Another four levels gives A (2+8+8). After that things get some what more complicated - to get Kr, 5 more pairs are added to the third set before the fourth set is complete so Kr has 2+8+18+8. You will need to study atomic physics to get the details.

#### olgranpappy

Homework Helper
also, the problem is quite complicated, so a simple explaination may not be possible, at least I can't give a simple explaination, but consider this:

Start with two atoms, one Na atom and one F atom, both very far seperated from each other and both sitting quietly in their ground states. As dictated by charge neutrality the Na atom possesses 11 electrons also it is in the configuration (Ne)(3s)^1. Similarly the F atom has nine electrons and is in the configuration (He)(2s)^2(2P)^5.

The isolated atoms can each be treated by atomic physics and the problem, although not simple, is somewhat tractable. That is how we arrive at the notion of "orbitals" and the ground state configurations I gave above.

Now, start to bring the atoms closer together. Soon they can no longer be thought of as isolated. In this intermediate region where the atoms are close enough to "see" each other we have a hard many-body problem consisting of 2 nuclei and 20 electrons. This is much more difficult than treating the 2 atoms seperately. in fact it is also much more difficult than the other limiting case when the distance between the nuclei is zero--that's just the case of atomic calcium!

The intermediate situation (the Na-F molecule) is a difficult problem. Obviously a correct physical treatement of the problem will result in the known fact that the Na "wants" to "loose" an electron and the F "wants" to "gain" one--we physicists can wave our hands just as hard as chemists.

I guess to treat the physics one would start out with a LCAO approach towards the molecule and attempt some kind of perturbation or variational treatment?

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#### Mr Virtual

The intermediate situation (the Na-F molecule) is a difficult problem. Obviously a correct physical treatement of the problem will result in the known fact that the Na "wants" to "loose" an electron and the F "wants" to "gain" one--we physicists can wave our hands just as hard as chemists.
Yeah, that's what my question is. Why does an element 'want' to lose or gain an electron. And if an element has this tendency, why does it ever exist in its atomic form, instead of its (stabler) ionic form?
I have attempted a guess in my original post. Can you have a look at it and tell me whether it is right or wrong?

thanks
Mr V

#### Mr Virtual

Very simple short explanation. Quantum theory dictates that electrons in the atom occupy various energy levels, Due to Pauli principle (no more than one elctron per state), there are exactly 2 electrons per level (spin quantum number either + or -). The first level gives He. The next four levels are close in energy, giving 10 (2+8) for Ne. Another four levels gives A (2+8+8). After that things get some what more complicated - to get Kr, 5 more pairs are added to the third set before the fourth set is complete so Kr has 2+8+18+8. You will need to study atomic physics to get the details.
Thanks for the details, but my question is somewhat different (I think your answer is based on my thread title, not what I have actually asked). I am asking, why does a stable atom have a tendency to fill up its half-filled orbitals (if it has any)? An atom of chlorine is quite stable, but why does it have a tendency to gain one electron? Simply because its energy is decreased further. Then why does chlorine not remain in its ionic form all the time? Here I am guessing that though Cl(1-) is a stabler ion than Cl, but it has a negative charge on it, which attracts positive ions. So either it shares electrons to form diatomic gases or compounds, or it forms ionic bonds.

Thanks
Mr V

#### Mr Virtual

I have noted that fewer people are interested in this forum as compared to forums devoted to quantum, classical and general physics. There, you have more chances of getting replies in a short time. I hope someone visits this place too.

#### meopemuk

An atom of chlorine is quite stable, but why does it have a tendency to gain one electron? Simply because its energy is decreased further.
Yes. More precisely, the energy of Cl(-1) is lower than the energy of separated Cl(0) and electron. People also say that Cl(0) has "electron affinity". Actually almost all neutral atoms have some electron affinity. In the case of halogen atoms, like Cl(0) the affinity is especially high.

Then why does chlorine not remain in its ionic form all the time? Here I am guessing that though Cl(1-) is a stabler ion than Cl, but it has a negative charge on it, which attracts positive ions. So either it shares electrons to form diatomic gases or compounds, or it forms ionic bonds.
Yes, you are basically right. First, nature doesn't like free charged ions. They quickly find their positive counterparts to make bonds. Second, nature doesn't like free atoms, unless they are noble gases. All free atoms rush to make bonds wherever they can. They are highly reactive. The basic rule is that any system tries to minimize its chemical energy, releasing excess energy into heat.

Atoms, ions, and molecules are rather complex complex systems of interacting nuclei and electrons obeying rules of quantum mechanics. In order to calculate relative energies of different configurations one needs to solve a multiparticle Schroedinger equation. This is a difficult task, and over the years dozens of approximations were developed. These approximations range from very precise and sophisticated computer algorithms all the way down to hadwavings and "rules of thumb", like the "octet rule".

#### arivero

Gold Member
Quantisation of angular momentum implies the "spherical armonics", and the classification of these special kind of funtions implies, in turn, notion of "orbitals", explained above, and then the periodic table.

PLEASE do not call it "octet rule". This name is used mostly in subnuclear physics for a completely different thing, related to the SU(3) group, not to the O(3) group.

#### Mr Virtual

Thanks so much for your replies!

Another question I had asked was: OK, an atom of chlorine will have less energy if it gains one more electron. But where does the attraction needed to trap an electron come from, since 17 protons are already engaged with 17 electrons?

regards
Mr V

#### meopemuk

Thanks so much for your replies!

Another question I had asked was: OK, an atom of chlorine will have less energy if it gains one more electron. But where does the attraction needed to trap an electron come from, since 17 protons are already engaged with 17 electrons?

regards
Mr V
One simple explanation could be this: The nuclear charge 17+ is concentrated in one point, so it creates an attractive field that follows Coulomb law everywhere in space. The electron charge 17- is diffusely spread over electron shells. So, its field is not as strong in the vicinity of the atom. So, in spite of perfect charge balance, there is some residual attraction between the extra electron and the chlorine atom.

#### Mr Virtual

A chlorine atom has a tendency to gain one electron to achieve more stability. But does this have to do with the fact that chlorine posseses electron affinity, which means if an electron enters the influence of the nucleus, then the nucleus will work on this electron, bringing it into its shell and thus, eventually possessing lower energy. If chlorine did not have electron affinity, then this tendency would not be there, would it?

#### Mr Virtual

The nuclear charge 17+ is concentrated in one point, so it creates an attractive field that follows Coulomb law everywhere in space. The electron charge 17- is diffusely spread over electron shells. So, its field is not as strong in the vicinity of the atom. So, in spite of perfect charge balance, there is some residual attraction between the extra electron and the chlorine atom.
Can you please explain in a little more detail as to how, even after having a perfect balance in charges, there is no balance between fields due to them.

thanks
Mr V

#### meopemuk

Can you please explain in a little more detail as to how, even after having a perfect balance in charges, there is no balance between fields due to them.

thanks
Mr V
Suppose that electron density in the atom has a diffuse spherically symmetric distribution. If you place an extra electron at a very large distance from the atom, then the attractive force from the nucleus is exactly compensated by the repulsive force from the electron density. You are right about this.

Now place the electron at some small distance r from the nucleus, then the attractive force is Z/r^2, but the repulsive force is weaker. This is because laws of electrostatics tell us that this extra electron will only feel the repulsive force from that part of atom's electron density, which is closer to the nucleus than r. This means that in the vicinity of the nucleus the extra electron feels some net attraction. The reason for this force imbalance is that nucleus is point-like, but electrons in the atom are spread out in space.

#### Mr Virtual

Thanks meopemuk

This is my previous post...
A chlorine atom has a tendency to gain one electron to achieve more stability. But does this have to do with the fact that chlorine posseses electron affinity, which means if an electron enters the influence of the nucleus, then the nucleus will work on this electron, bringing it into its shell and thus, eventually possessing lower energy. If chlorine did not have electron affinity, then this tendency would not be there, would it?

Thanks again!
Mr V

#### meopemuk

A chlorine atom has a tendency to gain one electron to achieve more stability. But does this have to do with the fact that chlorine posseses electron affinity, which means if an electron enters the influence of the nucleus, then the nucleus will work on this electron, bringing it into its shell and thus, eventually possessing lower energy. If chlorine did not have electron affinity, then this tendency would not be there, would it?
Yes, this is true. If the energy of Cl- was higher that "Cl_0 plus distant electron" then the negative ion would not be able to exist as a stable species. It would be a short-lived metastable state without much importance for chemistry.

#### Mr Virtual

Thanks a lot to all (especially meopemuk) for clearing my doubts.

Mr V

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