To understand how sharing a pair of electrons can hold atoms together, let's look at the simplest covalent bondthe bond that forms when two isolated hydrogen atoms come together to form an H₂ molecule.

H · + · H H-H

An isolated hydrogen atom contains one proton and one electron held together by the force of attraction between oppositely charged particles. The magnitude of this force is equal to the product of the charge on the electron (q_e) times the charge on the proton (q_p) divided by the square of the distance between these particles (r²).

When a pair of isolated hydrogen atoms are brought together, two new forces of attraction appear because of the attraction between the electron on one atom and the proton on the other.

But two forces of repulsion are also created because the two negatively charged electrons repel each other, as do the two positively charged protons.

It might seem that the two new repulsive forces would balance the two new attractive forces. If this happened, the H₂ molecule would be no more stable than a pair of isolated hydrogen atoms. But there are ways in which the forces of repulsion can be minimized. As we have seen, electrons behave as if they were tops spinning on an axis. Just as there are two ways in which a top can spin, there are two possible states for the spin of an electron: s = +¹/₂ and s = -¹/₂. When electrons are paired so that they have opposite spins, the force of repulsion between these electrons is minimized.

The force of repulsion between the protons can be minimized by placing the pair of electrons between the two nuclei. The distance between the electron on one atom and the nucleus of the other is now smaller than the distance between the two nuclei. As a result, the force of attraction between each electron and the nucleus of the other atom is larger than the force of repulsion between the two nuclei, as long as the nuclei are not brought too close together.

The net result of pairing the electrons and placing them between the two nuclei is a system that is more stable than a pair of isolated atoms if the nuclei are close enough together to share the pair of electrons, but not so close that repulsion between the nuclei becomes too large. The hydrogen atoms in an H₂ molecule are therefore held together (or bonded) by the sharing of a pair of electrons and this bond is the strongest when the distance between the two nuclei is about 0.074 nm.

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