The structure of the atom determines how matter interacts, forming the basis of all chemistry. Electrons, the negatively charged particles, occupy specific regions of space around the central nucleus. These regions are organized into different energy levels, which dictate an atom’s ability to bond with others and predict its properties.
Defining the Electron Home
The organization of electrons is hierarchical, starting with electron shells, also called principal energy levels (\(n=1, 2, 3\), etc.). These shells represent increasing distance and energy from the nucleus; electrons in higher-numbered shells possess greater energy.
Within each electron shell, electrons are grouped into subshells, identified by letters like \(s\), \(p\), \(d\), and \(f\). The number of available subshells increases as the shell number \(n\) increases. For example, the first shell (\(n=1\)) has only one subshell type, while the second shell contains two distinct types.
The most localized region is the orbital, a specific three-dimensional area where an electron is most likely to be found. Subshells are composed of one or more individual orbitals, and the orbital’s shape is associated with its subshell letter (e.g., the spherical \(s\) orbital).
The Fundamental Rule of Capacity
Every atomic orbital can accommodate a maximum of two electrons, regardless of its shape or energy level. This universal rule is the foundation for determining how electrons fill available spaces; no orbital can hold a third electron.
The explanation for this limitation is the Pauli Exclusion Principle, which states that no two electrons in an atom can possess the exact same set of four quantum numbers. These numbers describe the electron’s state, including its position, energy, and intrinsic angular momentum.
To share the same orbital, two electrons must differ in at least one property. Since the first three quantum numbers (shell, subshell, and specific orbital) are identical for electrons sharing the space, the fourth quantum number must be the differentiator.
This fourth property is electron spin, often simplified to an intrinsic magnetic moment pointing in one of two opposite directions. To coexist, the two electrons must have opposite spins—one “spin-up” and the other “spin-down”—satisfying the exclusion principle.
If a third electron attempted to enter, it would have the same spin as an existing electron. This identical set of four quantum numbers would violate the exclusion principle, making the arrangement physically impossible.
Grouping Orbitals into Subshells
The specific number of orbitals available changes depending on the type of subshell, which in turn determines the total electron capacity of that particular grouping.
s Subshell
The simplest subshell is the \(s\) subshell, which is spherical in shape and consists of only one orbital. Since one orbital can hold two electrons, the total capacity of any \(s\) subshell is limited to two electrons.
p Subshell
Moving to higher energy levels introduces the \(p\) subshell, which is composed of three distinct orbitals. These orbitals are shaped like dumbbells and are oriented along the three perpendicular axes (\(x\), \(y\), and \(z\)). Applying the two-electron rule, the three \(p\) orbitals together can accommodate a total of six electrons.
d Subshell
Further out from the nucleus, the \(d\) subshell becomes available, containing five individual orbitals. These orbitals exhibit more complex, multi-lobed shapes. The combined electron capacity of the \(d\) subshell is ten electrons, calculated by multiplying the five available orbitals by the standard two electrons per orbital.
f Subshell
The \(f\) subshell is found in the highest energy levels. This subshell is made up of seven unique orbitals, each possessing intricate and highly symmetrical shapes. Following the established rule, the \(f\) subshell has the largest capacity, totaling fourteen electrons.
This systematic progression demonstrates how the single rule of two electrons per orbital scales up to define the capacity of larger electron groupings. The electron capacity of any subshell is directly proportional to the number of orbitals it contains.
Total Capacity of Electron Shells
By summing the capacities of the subshells, we can determine the maximum number of electrons for an entire principal electron shell.
Shell 1 (n=1)
The first shell (\(n=1\)) contains only the \(s\) subshell, resulting in a total capacity of two electrons. This shell is the smallest and most tightly bound to the nucleus.
Shell 2 (n=2)
The second shell (\(n=2\)) contains both the \(s\) subshell (2 electrons) and the \(p\) subshell (6 electrons). Adding these capacities together gives the second shell a maximum capacity of eight electrons. This expansion is due solely to the introduction of the three \(p\) orbitals, which offer six additional spaces.
Shell 3 (n=3)
For the third shell (\(n=3\)), the \(d\) subshell (10 electrons) is added to the existing \(s\) (2 electrons) and \(p\) (6 electrons) subshells. Therefore, the third shell can hold a total of eighteen electrons. As the shell number increases, the number of available subshells and orbitals grows, leading to a geometrically increasing electron capacity.