The electron shells of an atom represent specific regions of space around the nucleus where electrons are likely to be found. Each shell corresponds to a principal quantum number, \(n\), starting with \(n=1\) for the shell closest to the nucleus. The third shell, designated by \(n=3\), is often a source of confusion regarding its capacity. The maximum capacity of the third shell is 18 electrons, a number derived from the fundamental rules of quantum mechanics that govern electron behavior.
Calculating Maximum Shell Capacity
The maximum number of electrons a shell can hold is determined by the formula \(2n^2\), where \(n\) is the principal quantum number. This formula reflects the fixed number of quantum states available within that energy level. According to the Pauli Exclusion Principle, electrons must each occupy a unique quantum state.
Applying this rule to the third shell (\(n=3\)), substituting the value into the formula gives \(2 \times (3)^2\). This simplifies to \(2 \times 9\), confirming the maximum capacity of 18 electrons for the third shell.
The Structure of the Third Shell Sublevels
The 18-electron capacity of the third shell (\(n=3\)) is realized by its internal structure, which is divided into three distinct subshells: s, p, and d. Each subshell contains a specific number of orbitals, which are the three-dimensional regions where electrons exist.
The s, p, and d subshells contain one, three, and five orbitals, respectively. Since each orbital holds a maximum of two electrons, the capacities are: 3s (2 electrons), 3p (6 electrons), and 3d (10 electrons). Summing these capacities (\(2 + 6 + 10\)) confirms the overall maximum of 18 electrons for the third shell.
Why the Third Shell Often Appears to Hold Eight
Confusion about the third shell’s capacity stems from the octet rule, where many elements achieve stability with only eight electrons in their outermost shell. This observation conflicts with the theoretical maximum of 18. This difference is explained by the Aufbau Principle, which dictates that electrons fill subshells based on the rule of lowest energy.
Electrons occupy the subshells with the lowest available energy first. As atomic number increases, the 4s subshell (in the fourth shell) has a lower energy level than the 3d subshell. Therefore, after the 3s (2 electrons) and 3p (6 electrons) subshells are filled, the next electrons skip the 3d subshell and enter the 4s subshell. This leaves the third shell with a temporary outer configuration of eight electrons (\(3s^23p^6\)) before the fourth shell begins to fill.
Once the 4s subshell is full, electrons return to fill the higher-energy 3d subshell with its remaining 10 electrons. The elements that fill these 3d orbitals are the transition metals found in the fourth row of the periodic table. This filling order means that for elements like potassium and calcium, the outermost shell is the fourth shell, even though the third shell is not yet completely full. The maximum capacity of 18 remains true, but the third shell is filled in two separate stages.