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There are several rules related to stability of an atom, like octet rule, half filled or fully filled d orbital etc. But none of them (at my best knowledge) does not explain why an atom is stable when it obeys those rules. So, is there any reason at all or are they just based on experimental results?

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    $\begingroup$ It is an experimental fact that isolated atoms are stable. These rules are used to try to explain in simple terms, sort of 'rules of thumb' , how electrons are arranged. The proper understanding of these rules flows naturally from Quantum Mechanics. $\endgroup$ – porphyrin May 18 at 8:03
  • $\begingroup$ The term "stability" is a big problem here. stability under what conditions? stability to what possible reaction? Defining the term would resolve many of the possible questions. $\endgroup$ – matt_black Oct 19 at 11:49
  • $\begingroup$ @porphyrin I don't think that is a strongly established empirical fact. I doubt that isolated fluorine atoms are stable to many reactions, for example. Fluorine molecules aren't exactly "stable" by most definitions either. $\endgroup$ – matt_black Oct 19 at 11:52
  • $\begingroup$ @matt_black I don't follow your argument: I'm sure an isolated fluorine atom remains as a fluorine atom for as long as you wish to observe it, or remain as a fluorine atom when it reacts, say to form HF. $\endgroup$ – porphyrin Oct 19 at 16:49
  • $\begingroup$ @porphyrin If the question is related to isolated atoms, then fine: everything is stable, charged or neutral as absolutely no change can happen (mostly). If it reacts with something else, it isn't an isolated fluorine, is it? So I strongly doubt the question is about the esoteric stability of isolated atoms, rather it is about the general rules relating to chemical bonding. $\endgroup$ – matt_black Oct 19 at 17:23
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First you need to understand what stability is. Normally, octet rule is based on noble gas configuration. Since, noble gases hardly react with other atoms, and they have 8 electrons as their shell configuration, thus we consider them "stable".

So, taking noble gas 8 electrons shell configuration, we tend to generalise all other atoms/elements to have 8 electron filled orbit to gain stability.

You must understand that scientist create models to explain natural phenomena. Rules are designed to explain already existing phenomena. Stability truly means "less energy" or inert behaviour where the atom neither gains nor lose electrons to other atoms/molecules. The lesser the energy of the atom/system, more the stability.

Thus your doubt on "does not explain why an atom is stable when it obeys those rules" is very vague. Think of inert gases, their configuration, their inert nature and you will understand.

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