Atomic Structure

Quantum Numbers and Electron Configuration

Every electron is described by four quantum numbers: $n$ (shell/energy), $l$ (subshell shape), $m_l$ (orbital orientation), and $m_s$ (spin, $\pm\tfrac{1}{2}$). Configurations follow the Aufbau principle, Hund's rule, and the Pauli exclusion principle. Know the exceptions Cr ($[Ar]4s^1 3d^5$) and Cu ($[Ar]4s^1 3d^{10}$), and remember that cations lose $4s$ electrons before $3d$.

Periodic Trends

Atomic radius increases down and to the left; ionization energy, electronegativity, and electron affinity increase up and to the right. Anomalies in successive ionization energies reveal when a core shell is being broken into, and half-filled or full subshells resist electron removal.

Bohr Model, Photons, and Nuclear Decay

For hydrogen-like atoms, energy levels are quantized: $E_n = -\frac{13.6\ \text{eV}}{n^2}$ Photon energy links spectra to transitions: $E = hf = hc/\lambda$. Photoelectron spectroscopy peaks map subshell energies and electron counts. Radioactive decay (alpha, beta-minus, positron emission, electron capture, gamma) conserves mass number and charge, and half-life follows $N = N_0 \left(\tfrac{1}{2}\right)^{t/t_{1/2}}$

Key Takeaways

• Aufbau/Hund/Pauli govern configurations; Cr and Cu are exceptions, and $4s$ leaves before $3d$.
• All periodic trends except radius increase toward fluorine.
• Emission lines correspond to $\Delta E$ between Bohr levels; PES counts electrons per subshell.
• Half-life problems reduce to counting halvings of the original sample.