Table of Contents
Energy-Wavelength Relationship
The energy of a photon is inversely proportional to its wavelength through the Planck-Einstein relation. Higher energy photons have shorter wavelengths (gamma rays, X-rays), while lower energy photons have longer wavelengths (infrared, radio). This fundamental relationship connects quantum mechanics with classical electromagnetic wave theory.
Understanding this relationship is essential for spectroscopy, photonics, solar cell design, and medical imaging. Each photon carries a discrete packet of energy determined entirely by its frequency, which is the foundation of quantum theory first proposed by Max Planck in 1900.
Planck-Einstein Relation
Where h = 6.626 × 10⁻³&sup4; J·s is Planck's constant, c = 3 × 10⁸ m/s is the speed of light, f is frequency, and λ is wavelength. The convenient conversion factor 1240 eV·nm makes quick calculations easy.
EM Spectrum
| Type | Wavelength | Energy |
|---|---|---|
| Gamma | < 0.01 nm | > 124 keV |
| X-Ray | 0.01-10 nm | 124 eV - 124 keV |
| UV | 10-400 nm | 3.1-124 eV |
| Visible | 400-700 nm | 1.77-3.1 eV |
| Infrared | 700 nm - 1 mm | 1.24 meV - 1.77 eV |
Frequently Asked Questions
What is the energy of visible light?
Visible light ranges from about 1.77 eV (red, 700 nm) to 3.1 eV (violet, 400 nm). Green light at 550 nm has about 2.25 eV per photon. These energies correspond to electronic transitions in atoms and molecules that our eyes evolved to detect from sunlight.
Why do higher energy photons have shorter wavelengths?
Since E = hc/λ, energy and wavelength are inversely proportional. Higher energy means higher frequency oscillations, which pack more cycles into a given distance, producing shorter wavelengths. This is why ultraviolet light is more energetic than visible light.
What is the 1240 eV·nm conversion factor?
The product hc = 1240 eV·nm provides a convenient shortcut: λ(nm) = 1240/E(eV). For example, a 2 eV photon has wavelength 1240/2 = 620 nm (orange light). This is widely used in photonics and semiconductor physics.