Atoms are most stable when they have full outer electron shells. This condition is typically achieved in noble gases, which naturally have complete valence shells, making them very unreactive. For other elements, stability is reached through bonding with other atoms to fill their outer shells, either by sharing electrons (covalent bonding) or transferring electrons (ionic bonding). When atoms achieve this optimal electron configuration, they are less likely to react with other atoms, as they have balanced attractive and repulsive forces acting on them.
To further understand this, consider the example of sodium and chlorine. Sodium has one electron in its outer shell, while chlorine has seven. Sodium tends to lose its electron to achieve a stable configuration similar to noble gases, while chlorine tends to gain an electron to complete its shell. When they react, sodium becomes positively charged and chlorine negatively charged, forming a stable ionic compound (NaCl).
In summary, atoms reach their highest stability by completing their outer electron shells, either through natural state (like in noble gases) or through chemical reactions with other elements.