Atomic Structure | Quantum Theory & Electronic Config
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⚛️ Atomic Structure & Quantum Theory

Proton discovery • Planck’s Quantum • Photon • Orbitals • Quantum Numbers • H-Spectrum • Electronic Configuration (Aufbau, Pauli, Hund)

📡 2.1 & 2.2 Keynotes

🔬 Discovery of Proton: E. Goldstein (1886) observed positive rays (canal rays) in discharge tube with perforated cathode. Later Rutherford identified proton (p⁺) as H⁺ nucleus.
Properties: Charge = +1.602 × 10⁻¹⁹ C, mass = 1.6726 × 10⁻²⁷ kg, located in nucleus.

📐 Proton specific charge: e/m = 9.58 × 10⁷ C/kg

⚡ Planck’s Quantum Theory (1900): Energy is emitted/absorbed in discrete packets → Quanta. For light: Photon is a quantum of radiation energy.

📏 E = hν = h·c/λ
h = 6.626 × 10⁻³⁴ J·s (Planck’s constant)

Photon properties: zero rest mass, energy E = hν, momentum p = h/λ, speed = c.

🌀 2.3 & 2.4 Quantum Nos.

Orbital concept: Region in space where probability of finding electron is maximum (90-95%). Described by wave function ψ.

  • Principal (n) : energy level, n = 1,2,3…
  • Azimuthal (ℓ) : sub-level (s,p,d,f) ; ℓ = 0 to n-1
  • Magnetic (mₗ) : orientation, -ℓ … +ℓ
  • Spin (mₛ) : ±½
⚡ Energy sub-levels: s (ℓ=0), p (ℓ=1), d (ℓ=2), f (ℓ=3).
Each orbital max 2 electrons (Pauli).
Principal energy level n contains n sub-levels.

🎨 2.5 Shapes of Orbitals

⚫ s-orbital
Spherical symmetry
1s, 2s, 3s
🕊️ p-orbitals
Dumbbell (px, py, pz)
Nodal plane at nucleus

p-orbitals have two lobes; three orientations (mₗ = -1,0,+1). d-orbitals (cloverleaf) for n≥3.

🌈 2.6 Hydrogen Atom (Quantum Theory)

Bohr model + de Broglie + Schrödinger: Quantized energy levels.
Emission spectrum: Lyman (UV), Balmer (visible), Paschen (IR) series.

🔹 Energy of H-atom: Eₙ = -13.6 eV / n² (n=1,2,3…)
🔹 Rydberg formula: 1/λ = RH (1/n₁² – 1/n₂²)
RH = 1.097 × 10⁷ m⁻¹

Quantum picture: Orbitals are probability clouds, electron exists in stationary states. Spectral lines correspond to ΔE = hν.

📝 2.7 & 2.8 Electronic Configuration

Aufbau principle: Fill orbitals in order of increasing energy (1s,2s,2p,3s,3p,4s,3d…).
Pauli Exclusion: No two electrons have same set of four quantum numbers → max 2 e⁻/orbital, opposite spins.
Hund’s Rule: For degenerate orbitals, electrons fill singly with parallel spins before pairing.

Example: Carbon (Z=6): 1s² 2s² 2p² (Hund: 2p↑ ↑)
Oxygen (Z=8): 1s² 2s² 2p⁴
Iron (Z=26): [Ar] 4s² 3d⁶

📌 Essential Values & Constants

  • Planck constant (h) = 6.62607015 × 10⁻³⁴ J·s
  • Speed of light (c) = 2.998 × 10⁸ m/s
  • Rydberg constant (RH) = 1.097373 × 10⁷ m⁻¹
  • Electron rest mass = 9.109 × 10⁻³¹ kg
  • Proton mass = 1.6726 × 10⁻²⁷ kg
  • 1 eV = 1.602 × 10⁻¹⁹ J
  • Bohr radius (a₀) = 5.292 × 10⁻¹¹ m
📐 de Broglie wavelength: λ = h / p
🔆 Photon momentum: p = h/λ = E/c

🧬 Quantum Numbers Recap

n : 1,2,3… → size & energy
ℓ : 0 to n-1 → shape (s=0, p=1, d=2, f=3)
mₗ : -ℓ..+ℓ → orientation
mₛ : +½ or -½ (spin)

Max electrons in shell = 2n²
Sublevel capacity: s(2), p(6), d(10), f(14)