Introduction
Light and other forms of electromagnetic radiation exhibit a fascinating dual nature—behaving as both waves and particles. Understanding this duality is fundamental to atomic structure.
Wave Nature of Radiation
Electromagnetic radiation can be described as oscillating electric and magnetic fields traveling through space.
Key Wave Properties
| Property | Symbol | Unit | Description |
|---|---|---|---|
| Wavelength | $\lambda$ | meters (m) | Distance between two consecutive crests |
| Frequency | $\nu$ | Hertz (Hz) | Number of waves passing a point per second |
| Wave number | $\bar{\nu}$ | m⁻¹ | Number of wavelengths per unit length |
| Velocity | $c$ | m/s | Speed of light in vacuum |
Fundamental Wave Equation
All electromagnetic radiation travels at the speed of light in vacuum:
$$\boxed{c = \nu \lambda = 3 \times 10^8 \text{ m/s}}$$This means:
- Higher frequency → shorter wavelength
- Lower frequency → longer wavelength
Wave Number
Wave number is the reciprocal of wavelength:
$$\bar{\nu} = \frac{1}{\lambda}$$- 1 nm = 10⁻⁹ m
- 1 Å = 10⁻¹⁰ m
- 1 pm = 10⁻¹² m
For visible light: 400 nm (violet) to 700 nm (red)
Electromagnetic Spectrum
The electromagnetic spectrum arranges radiation by wavelength/frequency:
graph LR
A[Gamma rays] --> B[X-rays]
B --> C[UV]
C --> D[Visible]
D --> E[Infrared]
E --> F[Microwaves]
F --> G[Radio waves]
style A fill:#9b59b6
style D fill:#e74c3c| Region | Wavelength Range | Typical Use |
|---|---|---|
| Gamma rays | < 10⁻¹¹ m | Nuclear reactions |
| X-rays | 10⁻¹¹ to 10⁻⁸ m | Medical imaging |
| UV | 10⁻⁸ to 4×10⁻⁷ m | Sterilization |
| Visible | 4×10⁻⁷ to 7×10⁻⁷ m | Vision |
| Infrared | 7×10⁻⁷ to 10⁻³ m | Heat sensing |
| Microwaves | 10⁻³ to 10⁻¹ m | Communication |
| Radio | > 10⁻¹ m | Broadcasting |
Particle Nature of Radiation
Planck’s Quantum Theory
Max Planck (1900) proposed that energy is quantized—emitted or absorbed in discrete packets called quanta or photons.
Energy of a Photon
$$\boxed{E = h\nu = \frac{hc}{\lambda}}$$where:
- $E$ = energy of photon (Joules)
- $h$ = Planck’s constant = $6.626 \times 10^{-34}$ J·s
- $\nu$ = frequency (Hz)
- $\lambda$ = wavelength (m)
Interactive Demo: Visualize Wave-Particle Duality
See how light behaves as both waves and photons with different frequencies.
Momentum of a Photon
Even though photons are massless, they carry momentum:
$$p = \frac{h}{\lambda} = \frac{E}{c}$$Don’t confuse energy and intensity!
- Energy of a photon depends on frequency: $E = h\nu$
- Intensity depends on the number of photons per second
Calculations
Example 1: Energy from Wavelength
Problem: Calculate the energy of a photon of yellow light (λ = 580 nm).
Solution:
- Convert wavelength: $\lambda = 580 \times 10^{-9}$ m
- Apply formula: $$E = \frac{hc}{\lambda} = \frac{6.626 \times 10^{-34} \times 3 \times 10^8}{580 \times 10^{-9}}$$ $$E = 3.43 \times 10^{-19} \text{ J}$$
To convert to eV: $E = \frac{3.43 \times 10^{-19}}{1.6 \times 10^{-19}} = 2.14$ eV
Example 2: Frequency from Energy
Problem: A photon has energy 4.0 eV. Find its frequency.
Solution:
- Convert to Joules: $E = 4.0 \times 1.6 \times 10^{-19} = 6.4 \times 10^{-19}$ J
- Apply formula: $$\nu = \frac{E}{h} = \frac{6.4 \times 10^{-19}}{6.626 \times 10^{-34}} = 9.66 \times 10^{14} \text{ Hz}$$
Key Takeaways
- Wave properties: Wavelength, frequency, and velocity are related by $c = \nu\lambda$
- Particle properties: Energy is quantized as $E = h\nu$
- Inverse relationship: Higher frequency means higher energy
- Dual nature: Light exhibits both wave and particle behavior
Practice Problems
Calculate the wavelength of radiation with frequency $5 \times 10^{14}$ Hz.
Compare the energies of photons of UV (300 nm) and infrared (1000 nm) light.
How many photons of light with λ = 500 nm are needed to provide 1 J of energy?
Next: Photoelectric Effect →