Electron Shells and Configurations

Atomic Representation and Energy Levels

Atoms are represented by their chemical symbol, atomic number ($Z$), and mass number ($A$). The atomic number ($Z$) defines the element and represents the number of protons, which equals the number of electrons in an uncharged atom. The mass number ($A$) is the sum of protons and neutrons. Electrons inhabit discrete energy levels, or shells, according to the Bohr Model. Electrons in the first shell ($n=1$) have the least energy and are held most tightly by the nucleus, while those in the outermost valence shell have the highest energy and are held most loosely.

Shell and Sub-shell Capacity

The maximum number of electrons in a shell is calculated using the formula $2n^2$. Specifically, the K shell ($n=1$) holds $2$ electrons, the L shell ($n=2$) holds $8$, the M shell ($n=3$) holds up to $18$, and the N shell ($n=4$) holds up to $32$. Shells are further divided into sub-shells ($s, p, d, f$), which contain atomic orbitals. Each individual orbital can accommodate a maximum of two electrons spinning in opposite directions.

Principles of Electron Filling

Electron configuration describes the arrangement of electrons following specific rules. The Aufbau Series (Madelung Rule) states that electrons fill the lowest energy levels first. Due to energy overlap, the $4s$ sub-shell is filled before the $3d$ sub-shell. Hund’s Law requires that every orbital in a sub-shell be singly occupied with one up-spin electron before any pairing occurs. Pauli’s Exclusion Principle dictates that an orbital can hold at most two electrons with opposite spins. Certain exceptions exist, such as Copper ($29Cu$), which has a measured configuration of $[Ar]3d^{10}4s^1$ to achieve a lower energy state.

Configurations and the Periodic Table

Electron configurations can be written in full (e.g., Sodium as $1s^2 2s^2 2p^6 3s^1$), simple (shell numbers only, e.g., $2, 8, 1$), or abbreviated using noble gas notation (e.g., $[Ne]3s^1$). The Periodic Table is organized into s, p, d, and f blocks based on the last orbital filled. The period number corresponds to the number of electron shells in use. These configurations allow for the prediction of ionic charges, such as $Na^+$, $Mg^{2+}$, $O^{2-}$, and $Cl^-$, by determining how many electrons must be gained or lost to achieve a stable outer shell.