Electromagnetic Radiation:

• c = νλ; E = hν = hc/λ; h = $6.626 \times 10^{-34}$ J·s
• High frequency = short wavelength = high energy
• Increasing order of wavelength: γ < X < UV < Vis < IR < Micro < Radio

Photoelectric Effect:

• Below ν_{0}: NO emission (regardless of intensity)
• Above ν_{0}: KE = h(ν − ν_{0}); KE depends only on frequency
• Intensity → number of electrons (not KE)
• Einstein: light = photons; each photon interacts with one electron

Hydrogen Spectrum:

• Rydberg: 1/λ = R_H(1/n_{1}^{2} − 1/n_{2}^{2}); R_H = $1.097 \times 10^{7}$ $m^{-1}$
• Only Balmer series is visible (n_{1}=2)
• Lines from level n = n(n−1)/2
• Series limit (min λ): n_{2} → ∞

Bohr Model:

• E_n = −13.6$Z^{2}$/$n^{2}$ eV; r_n = 0.529$n^{2}$/Z Å; v_n = $2.18 \times 10^{6}$Z/n m/s
• Energy: most negative at n=1; increases toward 0 as n→∞
• Ground state H: $E_{1}$ = −13.6 eV; r_{1} = 0.529 Å; v_{1} = $2.18 \times 10^{6}$ m/s
• $He^{+}$ at n=2 has same energy as H at n=1 (both = −13.6 eV)

de Broglie and Heisenberg:

• λ = h/mv; applies to all particles
• de Broglie-Bohr link: nλ = 2πr → mvr = nh/2π
• Heisenberg: $\Delta x$·$\Delta p$ ≥ h/4π; no exact orbits possible

Quantum Numbers:

• n: 1,2,3,...; l: 0 to n−1 (l < n always!); mₗ: −l to +l; mₛ: ±½
• s=0, p=1, d=2, f=3 (l values)
• Total nodes = n−1; angular = l; radial = n−l−1

Filling Rules:

• Aufbau: n+l rule (lower n first for ties)
• Pauli: max 2 electrons per orbital (opposite spins)
• Hund's: maximum unpaired spins in degenerate orbitals
• Anomalous: Cr=[Ar]3$d^{5}$4$s^{1}$; Cu=[Ar]3$d^{10}$4$s^{1}$
• Cations: remove 4s before 3d in transition metals

NEET Exam Traps:

• Lines ≠ $n^{2}$ (that's orbitals); Lines = n(n−1)/2
• l < n (not l ≤ n); for n=2, max l=1
• Intensity does NOT affect KE in photoelectric effect
• Cr and Cu are anomalous (memorize!)