Atoms are built around a dense nucleus containing protons and neutrons, surrounded by electrons. These electrons are confined to specific regions called electron shells or energy levels, which can be visualized like the layers of an onion. Each successive shell is farther from the nucleus and represents a higher, discrete amount of energy. The capacity of these shells to hold electrons is governed by the laws of quantum mechanics.
Understanding Atomic Shells and Energy Levels
The position and energy of an electron shell are described by the principal quantum number, \(n\). This number is a positive integer, starting with \(n=1\) for the shell closest to the nucleus. The third shell corresponds to \(n=3\) and is historically known as the M shell.
As the value of \(n\) increases, the shell is located at a greater average distance from the nucleus. This increased distance means the electrons are less tightly bound to the nucleus. Consequently, a higher principal quantum number also indicates a higher energy level and a larger capacity to accommodate electrons.
Calculating the Maximum Electron Capacity
The maximum number of electrons a shell can hold is determined by the formula \(2n^2\). Here, \(n\) is the principal quantum number, designating the shell number. This formula accounts for the fact that each orbital can hold a maximum of two electrons.
Applying this formula to the third electron shell (\(n=3\)), the calculation is straightforward. Squaring the shell number gives \(3^2\), which equals 9. Multiplying this result by two yields a total of 18. Therefore, the maximum capacity of the third electron shell is 18 electrons.
The Subshell Structure of the Third Shell
The 18-electron capacity of the third shell is justified by the presence of smaller, distinct energy subdivisions called subshells. The third shell (\(n=3\)) contains three types of subshells: \(s\), \(p\), and \(d\). These subshells represent different shapes and spatial orientations for the electrons.
The \(s\) subshell holds a maximum of 2 electrons. The \(p\) subshell has a capacity for up to 6 electrons. The \(d\) subshell, which the third shell is the first to contain, accommodates a maximum of 10 electrons. Adding these capacities (\(2 + 6 + 10\)) confirms the total capacity of 18 electrons for the \(n=3\) shell.
Explaining the Octet Rule and Electron Stability
While the third shell can hold up to 18 electrons, many atoms achieve stability with only 8 electrons in their outermost shell. This behavior is described by the Octet Rule, which states that atoms tend to react to achieve a full set of eight valence electrons (\(s^2p^6\)). The reason for this discrepancy between the 18-electron maximum and the chemical rule of 8 lies in the relative energies of the subshells.
In multi-electron atoms, the energy levels of the subshells can overlap between shells. Specifically, the \(4s\) subshell (from \(n=4\)) is lower in energy than the \(3d\) subshell (from \(n=3\)). Since electrons fill the lowest available energy levels first, the \(4s\) subshell fills immediately after the \(3p\) subshell is full. This causes the third shell to behave like a valence shell with only 8 electrons (\(3s^23p^6\)) for lighter elements.
The remaining 10 electrons that complete the third shell’s capacity reside in the \(3d\) subshell. These are only filled later in the periodic table, specifically in the transition metals. Elements in the third period and beyond can use the empty \(3d\) subshell to accommodate more than eight valence electrons in certain chemical compounds, known as an expanded octet. This confirms that 18 electrons is the true capacity limit.