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To become stable. In other words, they gain ( or sometimes lose) electron to acheive a stable octet. In most cases, this would mean that the atoms are trying to have 8 electrons in their valence (outermost) shell of electrons. In other cases, ( helium and hydrogen) they just need 2 electrons in their outer electron shell. Methane for example. (formula CH4) ... Carbon has four electrons in its outermost shell ( it has two in the inner shell ... 6 total). It has four electrons so hence it is in group 4 of the periodic table. So carbon wants 8 electrons in its valence shell, that means that it has four more to go. Hydrogen has 1 electron in its outer shell and only needs one more. So, the carbon and the 4 hydrogens bond covalently. The carbon shares one electron from each of the four hydrogens ( 4 [ from itself] and 4 [ one from each hydrogen] = 8). So the carbon is satisfied. On the other hand, each hydrogen would share one of carbon's electrons to attain 2 each in their outer shell. So hydrogen is stable with its two electrons and carbon is stable with its 8. They gain electrons to become more stable.

p.s. Google covalent and ionic bonding.

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