Electronic Structure of the Atom

Quantum Numbers and Orbitals

• Orbitals: Regions around the nucleus where there is a $90\%$ probability of finding an electron. Energy increases as the distance from the nucleus increases.

• Principal quantum number ($n$): Describes the energy level and the size of the atom ($n = 1, 2, 3 \dots$).

• Angular momentum quantum number ($\ell$): Defines the energy sub-level and the shape of the orbital, where $s: \ell = 0$, $p: \ell = 1$, $d: \ell = 2$, and $f: \ell = 3$.

• Magnetic quantum number ($m_{\ell}$): Describes the three-dimensional orientation of the orbital in space ($-\ell \le m_{\ell} \le \ell$).

• Spin quantum number ($m_s$): Describes the magnetic field of an electron; values are $+\frac{1}{2}$ (spin up) and $-\frac{1}{2}$ (spin down).

Fundamental Principles of Electron Arrangement

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers; weight each orbital can hold a maximum of two electrons with opposite spins.

• Aufbau Principle: Also known as the "Lazy Tenant Rule," electrons occupy the lowest energy orbitals first.

• Hund’s Rule: Known as the "Empty Bus Seat Rule," electrons populate each orbital in a sub-level singly before pairing occurs.

Writing Electron Configurations and Patterns

• Longhand notation: Lists every orbital and electron count (e.g., $1s^2 2s^2 2p^6 \dots$).

• Condensed (Shorthand) notation: Uses the Noble Gas from the preceding period to represent core electrons (e.g., Magnesium is $[Ne] 3s^2$).

• Valence Electrons: Electrons in the outermost energy level used for bonding.

• Stability Exceptions: Atoms gain stability with full or half-full sub-levels.

  • Copper ($Cu$): Actual configuration is $[Ar] 4s^1 3d^{10}$ (full $d$ sub-level).

  • Chromium ($Cr$): Actual configuration is $[Ar] 4s^1 3d^5$ (half-full $d$ sub-level).

Ion Formation and Isoelectronic Series

• Anions: Formed when atoms gain electrons to achieve the configuration of the closest Noble Gas.

• Cations: Formed when atoms lose electrons. Electrons are first removed from the orbital with the largest principal quantum number ($n$).

  • Transition Metal Cations: Electrons are removed from the $4s$ orbital before the $3d$ orbital (e.g., $Fe^{2+}$ is $[Ar] 3d^6$).

• Isoelectronic Series: Different atoms and ions that possess the same electron configuration.

  • Example: $N^{3-}$, $Ne$, and $Mg^{2+}$ all share the configuration $1s^2 2s^2 2p^6$.