Final answer:
Atoms are most stable with completely filled or half-filled subshells, like in Cr or Cu, and elements follow the octet rule for stability by having eight electrons in their valence shell. Exceptions occur due to electron-electron repulsions and energy differences between subshells.
Step-by-step explanation:
The stability of atoms with respect to their electron configurations depends on the arrangement of electrons in shells and subshells. Atoms are most stable when they have completely filled or half-filled subshells; this reflects conditions of preferred stability. For instance, chromium (Cr) finds extra stability with a half-filled 3d subshell, while copper (Cu) gains stability from a completely filled 3d subshell.
The octet rule also plays a significant role in the stability of atoms. It states that atoms (with the exception of the innermost shell) are more stable energetically when they have eight electrons in their valence shell. Due to this, atoms will form chemical bonds to achieve a full outer shell which in turn stabilizes them. Valence electrons, being the outermost electrons, are crucial in determining an atom's chemical behavior and are the primary contributors in chemical bonding.
Exceptions to predicted filling patterns arise when electron-electron repulsions are greater than the small differences in energy between subshells, causing deviations from the expected order of orbital filling. Taking niobium (Nb) as an example, its experimental ground-state electron configuration is [Kr]5s¹4d⁴ rather than the predicted [Kr]5s²4d³, likely due to the lesser energy cost of moving an electron from the 5s to 4d subshell compared to pairing electrons within the 5s orbital.