Atomic Structure - Electron configuration

Main energy levels are defined by the principal quantum number $n$. Each level can hold a maximum of $2n^2$ electrons.

Energy levels are split into sub-levels ($s, p, d, f$), which consist of orbitals. An orbital is a region of space where there is a high probability of finding an electron.

The Aufbau Principle states that electrons occupy the orbitals of lowest energy first (e.g., $1s < 2s < 2p < 3s < 3p < 4s < 3d$).

The Pauli Exclusion Principle dictates that an orbital can hold a maximum of two electrons, and they must have opposite spins.

Hund's Rule states that for degenerate orbitals (orbitals of the same energy, like the three $p$ orbitals), electrons fill them singly with parallel spins before pairing up to minimize inter-electron repulsion.

Exceptions to the Aufbau Principle: Chromium ($Cr$) has the configuration $[Ar] 3d^5 4s^1$ and Copper ($Cu$) has $[Ar] 3d^{10} 4s^1$. This is due to the increased stability of half-filled and fully-filled $d$-subshells.

When transition metals form positive ions (cations), electrons are removed from the $4s$ subshell before the $3d$ subshell because the $4s$ electrons are in a higher principal energy level ($n=4$ vs $n=3$).

Continuous spectra are produced when all wavelengths of light are present, whereas line emission spectra are produced by excited electrons falling to lower energy levels, emitting specific frequencies of photons defined by $\Delta E = h\nu$.