[Indranil (OP)]

As I know 'O' is neutral as O has the same number of protons(8 protons) and electrons(8 electrons). But O fulfills its octet getting 2 extra electrons. So the sign of O is O²⁻. So in this condition, why should I call oxygen stable? but why not should I call a neutral oxygen a stable element? Could you explain it, please?

[Kryptid]

All oxygen atoms are stable unless they are of a radioactive isotope. Perhaps what you meant was "reactive" versus "unreactive"? Atoms prefer to have their outer electron shells filled, which is why O^2- is less reactive than O.

[Indranil (OP)]

All oxygen atoms are stable unless they are of a radioactive isotope. Perhaps what you meant was "reactive" versus "unreactive"? Atoms prefer to have their outer electron shells filled, which is why O^2- is less reactive than O.

Why is O^2- less reactive?

[Kryptid]

Why is O^2- less reactive?

I told you, it's because it has a full valence electron shell. Since neutral oxygen atoms only have 6 valence electrons, that gives it room to accept 2 more electrons in order to fill up its shell. Reacting with other atoms is how it can gain those extra electrons. Since O^2- already has all 8 valence electrons, it doesn't have room to accept any more electrons from other atoms.

[Indranil (OP)]

Why is O^2- less reactive?

I told you, it's because it has a full valence electron shell. Since neutral oxygen atoms only have 6 valence electrons, that gives it room to accept 2 more electrons in order to fill up its shell. Reacting with other atoms is how it can gain those extra electrons. Since O^2- already has all 8 valence electrons, it doesn't have room to accept any more electrons from other atoms.

My question is 'why does an element become stable'? what is the necessity?

[evan_au]

My question is 'why does an element become stable'? what is the necessity?

In the end, necessity comes down to thermodynamics.

In nature (and technology), systems tend to move towards their maximum disorder, which often means their lowest energy state.
- That is, unless you inject some energy, which might temporarily move it away from that lowest energy state.
- The act of increasing order in one part of a system merely increases disorder in a different part of the system.

Atoms tend to be in their lowest energy state when they have a full outer shell of electrons.
You could imagine an isolated, neutral oxygen atom - it has 2 unpaired electrons in its outer shell.
Electrons have a spin, and they are in a lower energy state when they are paired with another electron of opposite spin.

So a lower energy state for an oxygen atom is to gain two extra electrons in its outer shell - but only if there is something in the environment that is also in a lower energy state by giving up 2 electrons
- like the Hydrogen atoms in H₂SO₄, and a suitable environment, like a water solution.
- or like another isolated oxygen atom, in which case they share their outer 2 electrons, giving each of them a full outer shell and forming O₂
See: https://en.wikipedia.org/wiki/Chemical_thermodynamics

Thermodynamics also governs many systems around us - physics, biology, geology, weather, cosmology, etc.
See:  https://en.wikipedia.org/wiki/Thermodynamics