The octet rule

The octet rule is an observation that main group elements (periods 1–2 and 13–18) tend to be most stable when they have eight electrons in their valence shell. It is a subset of the rule that all atoms tend toward noble gas configurations. Each orbital can hold 2 $e^{-}$ so a filled shell will contain twice as many electrons as orbitals. $H$ follows the duet rule because its valence shell is just the 1s orbital; larger elements often follow the 18-electron rule because their valence shells have 9 total orbitals (one s, five d, and three p orbitals).

More examples

• Oxygen has 6 $e^{-}$ in its valence shell, so it is often found either as $O^{2-}$ or with two covalent bonds to achieve the electron configuration of $Ne$: $[He]2s^{2}2p^6$
• Phosphorus has 5 $e^{-}$ in its valence shell, so it tends to gain 3 $e^{-}$ through three covalent bonds to achieve the electron configuration of $Ar$: $[Ne]3s^{2}3p^6$
• Bromine is often described to have 7 $e^{-}$ in its valence shell like F and Cl above it, but it is more accurate to say it has 17 $e^{-}$ from having the configuration $[Ar]4s^{2}3d^{10}4p^5$. Either way you think about it, it only needs one more $e^{-}$ to have the electron configuration of $Kr$: $[Ar]4s^{2}3d^{10}4p^6$.

Physical explanation

Energy levels go down with increasing effective nuclear charge, but up with increasing quantum number. A figure will be key to making this point.

Exceptions

The octet rule is more of an octet suggestion. We regularly encounter atoms that do not conform to the octet rule. Atoms that do not have a complete octet are called electron deficient atoms and those that have more than a complete octet are called hypervalent atoms.