Overview Summary: 10-Sentence Condensed

Electromagnetic radiation follows E = hν = hc/λ with c = $3 \times 10^{8}$ m/s and h = $6.626 \times 10^{-34}$ J·s.
In the photoelectric effect, electrons are ejected only when ν ≥ ν_{0}; kinetic energy KE = h(ν − ν_{0}) depends on frequency alone, not intensity.
The hydrogen spectrum is described by the Rydberg formula: 1/λ = R_H(1/n_{1}^{2} − 1/n_{2}^{2}), with only the Balmer series (n_{1}=2) visible to the naked eye.
Bohr's model gives E_n = −13.6 $Z^{2}$ / $n^{2}$ eV, r_n = 0.529 $n^{2}$ /Z Å, and v_n = $2.18 \times 10^{6}$ Z/n m/s for hydrogen-like atoms.
Total spectral lines when electrons de-excite from level n = n(n−1)/2 (not $n^{2}$ which counts orbitals).
de Broglie wavelength λ = h/mv applies to all matter; the standing wave condition nλ = 2πr justifies Bohr's angular momentum quantization.
The Heisenberg uncertainty principle ( $\Delta x$ · $\Delta p$ ≥ h/4π) makes simultaneous exact knowledge of position and momentum impossible, invalidating Bohr's definite orbits.
Four quantum numbers describe each electron: n (shell), l (shape, 0 to n−1), mₗ (orientation, −l to +l), mₛ (spin, ±½); nodes: total=n−1, angular=l, radial=n−l−1.
Aufbau (n+l rule), Pauli (max 2 per orbital), and Hund's (maximum unpaired) govern electron filling; Cr=[Ar]3 $d^{5}$ 4 $s^{1}$ and Cu=[Ar]3 $d^{10}$ 4 $s^{1}$ are anomalous due to half/full d stability.
For transition metal cations, 4s electrons are removed before 3d electrons (e.g., $Fe^{3+}$ = [Ar]3 $d^{5}$ after removing 4 $s^{2}$ and one 3d from Fe).