I want to have a deep insigth to my problem i.e. I know that bonds between atoms(of different or same elements)to be formed are based on no. of electrons less in octet or duplet(say O2, each O atom has two electrons less in octet thus forms two bonds).But why bonds between e^- & e^- are formed to complete the octet even though they have same sign so must repel & not form a bond?

This is avery good question! This leads us directly into quantum mechanics, a branch of modern physics. It has been proven mathematically (very complex, so I will not bother you with the details!) that electrons can and must be assigned a number, either +1 or -1 denoting the so-called spin. Two electrons with a different spin can form such a bond as they do not repel each other respectively.

I might add that the electrons actually do repel each other since both have the same negative charge; however, the opposite spins give a magnetic moment that attract each other. The opposite spins are enough to overcome the repulsion forces.

To understand why bonds between electrons are formed to complete the octet, let's delve into the concept of chemical bonding, specifically covalent bonding.

In a covalent bond, atoms share electrons to achieve a more stable electron configuration. The octet rule is a general guideline stating that atoms tend to gain, lose, or share electrons in order to have a full outer electron shell, typically with eight electrons (except for some elements that require fewer or more). This stable configuration is similar to the noble gases, which have complete octets.

Now, when two atoms approach each other, their electron clouds overlap due to their negatively charged electrons. These negatively charged electrons do indeed repel each other, as like charges repel. However, the repulsion can be minimized by the formation of covalent bonds.

In a covalent bond, the sharing of electrons allows each atom to access additional electrons and complete its octet. By sharing, they both benefit in achieving a stable electron configuration. Consider the example of oxygen (O2) that you mentioned.

In an oxygen molecule (O2), each oxygen atom has six electrons in its valence shell, leaving it two electrons shy of an octet. When two oxygen atoms come close to each other, their partially filled valence orbitals overlap. This overlap allows the two oxygen atoms to share two pairs of electrons, forming a double covalent bond between them. By sharing these two pairs of electrons, both oxygen atoms can complete their octets, resulting in a more stable configuration for both.

So, while it is true that electrons carry a negative charge and repel each other, the formation of covalent bonds allows them to achieve a more stable electron configuration by sharing and completing their octets. This sharing creates a balance between the repulsion between electrons and the attractive forces between the positively charged atomic nuclei and the negatively charged electron cloud.