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
$c = λν$ (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):
- Radio waves
- Microwaves
- Infrared
- Visible light (400-700 nm)
- Ultraviolet
- X-rays
- 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)
$E_n = -\frac{R_H}{n^2}$ (Energy levels in hydrogen)
where $R_H = 2.178 × 10^{-18}$ J (Rydberg constant)
Bohr Model Rules:
- Electrons exist in specific energy levels
- Energy is absorbed/emitted when electrons transition between levels
- 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
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
$λ = \frac{h}{mv}$ (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:
- Aufbau Principle: Electrons fill lowest energy orbitals first
- Pauli Exclusion: Maximum two electrons per orbital with opposite spins
- 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
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
H: 1s¹
He: 1s²
Li: [He]2s¹
Be: [He]2s²
B: [He]2s²2p¹
C: [He]2s²2p²