Considering the valence shell again, why can atoms in the third (or greater) period accommodate more than eight electrons (sum of the bonding and nonbonding electrons)?

The concept of valence shell electron pairs is essential for understanding how atoms form bonds. The valence shell refers to the outermost electron shell of an atom and is where the bonding occurs. Electrons occupying this shell are either involved in forming bonds (bonding pairs) or exist as lone pairs (nonbonding pairs).

According to the octet rule, atoms are generally most stable when they have eight electrons in their valence shell, reminiscent of noble gas electron configurations. This tendency can be seen in the formation of electron pairs, where each bond involves two electrons, one from each bonding atom. However, this rule modifies when we observe elements in the third period and beyond, which can exceed the octet due to their capacity to utilize additional orbitals for bonding.

Third period elements, like Sodium (Na), Magnesium (Mg), and Phosphorus (P), have distinguishing properties that allow them to exceed the octet rule. These elements are situated on the periodic table starting with Sodium (atomic number 11) and ending with Argon (atomic number 18).

Unlike their counterparts in the first and second periods, these elements possess a third shell that can be populated with electrons. The additional space is due to the inclusion of d orbitals, starting with the 3d orbital. The availability of these orbitals permits third period elements to have more than eight electrons in their valence shells, which is a crucial factor for compounds with expanded octets.

The presence of d orbitals begins in the third period of the periodic table, adding a new dimension to the electron configuration and bonding capabilities of the elements found in this period and beyond. When we refer to d orbitals, we're discussing a set of five orbitals, each capable of holding up to two electrons, therefore increasing the maximum number of electrons in a valence shell from eight to eighteen.

Due to their energy level, d orbitals come into play when the s and p orbitals have already been filled. This extra capacity enables elements, especially transition metals, to form various oxidation states and coordination complexes by allowing them to bond with additional elements.

Electron configuration refers to the distribution of electrons in an atom or molecule across different orbitals. The arrangement follows a specific order, filling from the lowest energy levels to the higher ones, following the Aufbau principle. S orbitals are filled first, followed by p, then d, and finally f orbitals.

In the context of the valence shell and expanded octets, understanding electron configuration is crucial. For third period elements, after the 3s and 3p orbitals are filled, the 3d orbitals are the next in line to accept electrons. Elements in higher periods have even more orbitals at their disposal, which explains the ability of some atoms to hold more than eight valence electrons and form stable molecules despite breaking the traditional octet rule.