Table of Contents
Photon Energy
Every photon carries a discrete quantum of energy determined by its wavelength (or equivalently, its frequency). This fundamental relationship, discovered by Max Planck and Albert Einstein, is the cornerstone of quantum mechanics and explains phenomena like the photoelectric effect, atomic spectra, and blackbody radiation.
Shorter wavelength photons carry more energy. Gamma rays (picometer wavelengths) have millions of electron volts, while radio waves (meter wavelengths) have only micro-electron volts. The energy of visible light photons ranges from about 1.8 eV (red) to 3.1 eV (violet).
Planck-Einstein Relation
Where h = 6.626 × 10&supmin;³&sup4; J·s (Planck's constant), c = 2.998 × 10&sup8; m/s (speed of light), λ is wavelength, and f is frequency. In practical units: E(eV) = 1239.84 / λ(nm).
Energy of Common Wavelengths
| Wavelength | Type | Energy (eV) | Frequency (THz) |
|---|---|---|---|
| 0.01 nm | Gamma ray | 124,000 | 3.0 × 10&sup7; |
| 10 nm | Extreme UV | 124 | 30,000 |
| 400 nm | Violet light | 3.10 | 749 |
| 550 nm | Green light | 2.25 | 545 |
| 700 nm | Red light | 1.77 | 428 |
| 10,000 nm | Thermal IR | 0.124 | 30.0 |
Applications
- Spectroscopy: Identifying elements by their emission/absorption wavelengths and corresponding energy transitions.
- Solar cells: Photons must exceed the semiconductor bandgap energy to generate electron-hole pairs.
- Laser selection: Choosing wavelengths with appropriate photon energies for material processing.
- Medical imaging: X-ray energies must penetrate tissue but be absorbed by bone/contrast agents.
Frequently Asked Questions
What is an electron volt (eV)?
An electron volt is the energy gained by an electron accelerated through a 1-volt potential difference. It equals 1.602 × 10&supmin;¹&sup9; joules. It is convenient for atomic-scale energies because photon and atomic transition energies are typically 0.1-10,000 eV.
Why do shorter wavelengths have more energy?
Energy is inversely proportional to wavelength (E = hc/λ). Shorter wavelengths mean higher frequencies, and each oscillation cycle carries a fixed quantum of energy (E = hf). More cycles per second means more energy per photon.
Can I use this for sound waves?
No. The Planck-Einstein relation applies only to photons (electromagnetic radiation). Sound waves are mechanical vibrations of matter and do not have quantized photon energies. Sound energy depends on amplitude, not frequency, unlike light.