Wave Properties

Electromagnetic Radiation: Energy that travels through space as waves carrying electric and magnetic fields
  • Wavelength (λ): Distance between successive wave crests
  • Frequency (ν): Number of waves passing a point per second
  • Amplitude: Maximum height of wave
Fundamental Relationships:
$c = λν$ (speed of light)
$c = 2.998 × 10^8$ m/s
$E = hν$ (Planck's equation)
where $h = 6.626 × 10^{-34}$ J·s
Electromagnetic Spectrum (increasing energy):
  1. Radio waves
  2. Microwaves
  3. Infrared
  4. Visible light (400-700 nm)
  5. Ultraviolet
  6. X-rays
  7. Gamma rays

Quantum Theory Development

Key Concepts:
  • Blackbody Radiation: Led to Planck's quantum hypothesis
  • Photoelectric Effect: Einstein's photon theory
  • Atomic Spectra: Led to Bohr's atomic model
Energy Quantization:
$E_n = -\frac{R_H}{n^2}$ (Energy levels in hydrogen)
where $R_H = 2.178 × 10^{-18}$ J (Rydberg constant)
Bohr Model Rules:
  1. Electrons exist in specific energy levels
  2. Energy is absorbed/emitted when electrons transition between levels
  3. Angular momentum is quantized: $L = n\frac{h}{2π}$

Wave-Particle Nature

de Broglie Wavelength: Particles exhibit wave properties
Uncertainty Principle: Fundamental limit to precision of complementary measurements
Key Relationships:
$λ = \frac{h}{mv}$ (de Broglie wavelength)
$ΔxΔp ≥ \frac{h}{4π}$ (Heisenberg uncertainty)
where $Δx$ is position uncertainty and $Δp$ is momentum uncertainty
Applications:
  • Electron microscopes
  • Electron diffraction
  • Wave function interpretation

Quantum Mechanical Model

Quantum Numbers:
  • n (principal): Energy level (1, 2, 3, ...)
  • l (angular momentum): Orbital shape (0 to n-1)
  • mₗ (magnetic): Orbital orientation (-l to +l)
  • mₛ (spin): Electron spin (±½)
Orbital Characteristics:
Type l value Orbitals Shape
s 0 1 Spherical
p 1 3 Dumbbell
d 2 5 Complex
f 3 7 More complex

Electron Arrangement Rules

Three Key Principles:
  1. Aufbau Principle: Electrons fill lowest energy orbitals first
  2. Pauli Exclusion: Maximum two electrons per orbital with opposite spins
  3. Hund's Rule: Electrons in orbitals of same energy remain unpaired with parallel spins
Orbital Filling Order:
1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s → 5f → 6d → 7p
Example Configurations:
H: 1s¹
He: 1s²
Li: [He]2s¹
Be: [He]2s²
B: [He]2s²2p¹
C: [He]2s²2p²