Photon
A photon is a massless elementary particle and the quantum of electromagnetic radiation, carrying energy proportional to its frequency. It is the force-carrier particle for the electromagnetic force and travels at the speed of light in a vacuum. Photons exhibit both wave and particle behaviour and are fundamental to understanding light-matter interactions, including the photoelectric effect, atomic emission spectra, and optical technologies.
Key Formula
E = h × ν = hc / λ
LaTeX: E = h\nu = \frac{hc}{\lambda}
| Symbol | Meaning | Unit |
|---|---|---|
| E | Energy of the photon | Joules (J) |
| h | Planck's constant (6.626 × 10⁻³⁴) | J·s |
| ν | Frequency of the electromagnetic radiation | Hertz (Hz) |
| c | Speed of light in vacuum (3 × 10⁸) | m/s |
| λ | Wavelength of the radiation | Metres (m) |
Worked Example
Problem
Calculate the energy of a photon of green light with a wavelength of 550 nm.
Solution
Step 1: Convert wavelength to metres. λ = 550 nm = 550 × 10⁻⁹ m = 5.50 × 10⁻⁷ m Step 2: Use the photon energy formula. E = hc / λ E = (6.626 × 10⁻³⁴ J·s × 3.00 × 10⁸ m/s) / (5.50 × 10⁻⁷ m) Step 3: Calculate numerator. hc = 6.626 × 10⁻³⁴ × 3.00 × 10⁸ = 1.988 × 10⁻²⁵ J·m Step 4: Divide by wavelength. E = 1.988 × 10⁻²⁵ / 5.50 × 10⁻⁷ = 3.61 × 10⁻¹⁹ J
Answer
E ≈ 3.61 × 10⁻¹⁹ J (approximately 2.26 eV)
Photon Properties Across the Electromagnetic Spectrum
| Radiation Type | Wavelength Range | Frequency Range (Hz) | Photon Energy (eV) |
|---|---|---|---|
| Radio waves | > 1 m | < 3 × 10⁸ | < 1.24 × 10⁻⁶ |
| Visible light | 400–700 nm | 4.3–7.5 × 10¹⁴ | 1.77–3.10 |
| Ultraviolet | 10–400 nm | 7.5 × 10¹⁴ – 3 × 10¹⁶ | 3.10–124 |
| X-rays | 0.01–10 nm | 3 × 10¹⁶ – 3 × 10¹⁹ | 124–1.24 × 10⁵ |
| Gamma rays | < 0.01 nm | > 3 × 10¹⁹ | > 1.24 × 10⁵ |
Interactive Tools
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Related Terms
Wave-Particle Duality
Wave-particle duality is the quantum mechanical principle stating that every quantum entity, such as an electron or photon, exhibits both wave-like and particle-like properties depending on how it is observed or measured. In experiments such as the double-slit experiment, particles produce interference patterns characteristic of waves when not observed, but behave as localized particles when detected at specific positions. This duality is central to quantum mechanics and demonstrates that classical concepts of "wave" and "particle" are complementary rather than contradictory descriptions of quantum objects.
Quantum Mechanics
Quantum mechanics is the fundamental theory of physics that describes the behaviour of matter and energy at the scale of atoms and subatomic particles, where classical Newtonian mechanics breaks down. It introduces concepts such as quantisation of energy, wave-particle duality, and the probabilistic nature of physical observables. Quantum mechanics underpins modern technologies including semiconductors, lasers, MRI machines, and quantum computing.
de Broglie Wavelength
The de Broglie wavelength is the wavelength associated with any moving particle, expressing the wave-like nature of matter as proposed by Louis de Broglie in 1924. It is inversely proportional to the momentum of the particle, meaning heavier or faster-moving objects have shorter wavelengths and thus exhibit negligible quantum wave behaviour. This concept was experimentally confirmed by electron diffraction experiments and forms the basis for electron microscopy and quantum confinement in nanomaterials.
From Greek "phōs" (light) + "-on" (subatomic particle suffix). The concept was introduced by Albert Einstein in 1905 to explain the photoelectric effect, though the term "photon" was coined by chemist Gilbert N. Lewis in 1926.