Atomic Structure
Atomic Structure is tested through quantum numbers, orbital shapes, electronic configurations, and quantitative photon/particle calculations. The exam expects you to connect models rather than recite them.
Core rules
- Bohr energy for hydrogen-like species: E_n = −13.6 Z^2/n^2 eV. It explains line spectra but fails for multi-electron atoms.
- de Broglie: λ = h/mv; Heisenberg: Δx·Δp ≥ h/4π.
- Allowed quantum numbers: n ≥ 1; l = 0 to n−1; m_l = −l to +l; m_s = ±1/2.
- Fill by the Aufbau/(n+l) rule, then Pauli and Hund. Cr is [Ar]3d5 4s1 and Cu is [Ar]3d10 4s1.
- For many-electron atoms use effective nuclear charge and shielding; 4s fills before 3d in neutral atoms because lower (n+l), then lower n, wins.
- Spin-pairing lowers energy, while exchange energy stabilizes half-filled sets.
Worked example
Find the wavelength emitted when H falls from n=3 to n=2. E3 = −13.6/9 = −1.51 eV; E2 = −13.6/4 = −3.40 eV. ΔE = 1.89 eV. Using λ(nm) = 1240/ΔE(eV), λ = 1240/1.89 = 656 nm. This is the red H-alpha line. The photon carries the energy difference; the electron loses it.
Traps
Do not treat orbitals as fixed paths. Do not allow l=n. For ions, remove electrons from the highest n shell first, but remember that 4s is filled before 3d in K and Ca while 3d electrons are lost first when transition metals ionize. Use Kelvin and consistent units in photon calculations.