Calculate Photon Energy
Conversion between frequency and photon energy with E = h·f
Photon Energy Calculator (JavaScript)
Planck relation
Photon energy follows E = h·f with Planck's constant h = 6.62607015·10⁻³⁴ J·s.
Example calculations
Example 1: Visible light
Given: f = 600 THz
Result: E ≈ 2.48 eV
Example 2: Frequency from 2.48 eV
Given: E = 2.48 eV
Result: f ≈ 600 THz
Example 3: UV range
Given: f = 1 PHz = 1000 THz
Interpretation: Higher frequency means higher photon energy.
Formulas and comprehensive description
Photon energy is a quantized energy value of electromagnetic radiation. The Planck relation links frequency directly to energy. It is fundamental in quantum physics, laser technology, spectroscopy, semiconductor physics, and photovoltaics. Increasing frequency increases the energy per photon linearly.
Photon energy
Frequency
Planck constant
eV conversion
Practical relevance
Comprehensive Description
What is Photon Energy?
A photon is the energy quantum of light and electromagnetic radiation. Each photon possesses a characteristic energy E that depends exclusively on its frequency f. Photon energy is quantized – it can only assume discrete values, not arbitrary intermediate values. This is a fundamental concept in quantum mechanics and explains many optical and electronic phenomena.
The Planck Relation: The Fundamental Formula
The energy of a photon is given by the famous Planck-Einstein relation:
- E – Photon energy (in Joules J)
- h – Planck constant = 6.62607015·10⁻³⁴ J·s (a fundamental constant of nature)
- f – Frequency of light (in Hertz Hz)
This formula shows: Higher frequency → higher photon energy
Alternative Formulas and Quantities
Since frequency and wavelength are related (c = λ·f), photon energy can also be expressed as:
- c – Speed of light = 3·10⁸ m/s
- λ – Wavelength of light
Or using the reduced Planck constant ℏ = h/(2π) ≈ 1.055·10⁻³⁴ J·s:
where ω = 2πf is the angular frequency.
Planck's Constants
| Quantity | Symbol | Value | Unit |
|---|---|---|---|
| Planck Constant | h | 6.62607015·10⁻³⁴ | J·s |
| Reduced Planck Constant | ℏ | 1.05457182·10⁻³⁴ | J·s |
| Elementary Charge | e | 1.602176634·10⁻¹⁹ | C |
| Speed of Light | c | 299,792,458 | m/s |
Unit: Electron Volts (eV)
In optics and atomic physics, photon energy is often expressed in electron volts (eV), rather than joules. This is the energy gained by an electron when accelerated through a potential difference of 1 volt:
- 1 eV ≈ 1.60·10⁻¹⁹ J
- Conversion: E_{eV} = E_{J} / (1.602·10⁻¹⁹)
- Advantage: eV values for photons are often simple decimals (e.g., 2.5 eV instead of 4.0·10⁻¹⁹ J)
Photon Energy in the Electromagnetic Spectrum
| Spectral Region | Wavelength λ | Frequency f | Photon Energy E |
|---|---|---|---|
| Radio Waves | mm to m | MHz to GHz | µeV to meV |
| Microwaves | µm to mm | GHz to THz | meV to µeV |
| Infrared (IR) | 700 nm to 1 mm | 300 GHz to 430 THz | 1.2 meV to 1.8 eV |
| Visible Light | 380–700 nm | 430–790 THz | 1.8–3.3 eV |
| Ultraviolet (UV) | 10–380 nm | 790 THz to 30 PHz | 3.3 eV to 120 eV |
| X-rays | 0.01–10 nm | 30 PHz to 30 EHz | 120 eV to 120 keV |
| Gamma Rays | < 0.01 nm | > 30 EHz | > 120 keV |
Visible Light – Colors and Energies
| Color | Wavelength | Frequency | Energy (eV) | Energy (Joules) |
|---|---|---|---|---|
| Red | 650 nm | 461 THz | 1.91 eV | 3.06·10⁻¹⁹ J |
| Orange | 600 nm | 500 THz | 2.07 eV | 3.31·10⁻¹⁹ J |
| Yellow | 570 nm | 526 THz | 2.18 eV | 3.49·10⁻¹⁹ J |
| Green | 530 nm | 566 THz | 2.34 eV | 3.75·10⁻¹⁹ J |
| Blue | 470 nm | 638 THz | 2.64 eV | 4.23·10⁻¹⁹ J |
| Violet | 400 nm | 750 THz | 3.10 eV | 4.97·10⁻¹⁹ J |
Practical Applications of Photon Energy
- Photosynthesis: Plants use photons of specific energies (visible light) to build organic compounds
- Photovoltaics: Solar cells harness photon energy to excite electrons and generate electricity (band gap energy)
- Semiconductors: LEDs and diode lasers emit photons with precisely defined energy (band gap)
- Spectroscopy: Atoms and molecules absorb/emit photons with specific energy (characteristic lines)
- Medicine: UV radiation has high photon energy → can damage DNA or be used for disinfection
- Quantum Electronics: The photoelectric effect shows: photon energy must exceed work function
The Photoelectric Effect – An Example
Albert Einstein's explanation of the photoelectric effect proved the photon concept:
- Φ – Work function of the material (energy to free an electron)
- Ekin – Kinetic energy of the emitted electron
Conclusion: The photon must have sufficient energy (f > Φ/h) to free an electron. One photon can free at most one electron – not "half-photons."
Quantization and Why It Matters
Classical Wave: Energy can assume all values (continuous) Quantized Photon: Energy can only assume discrete values (E = h·f for specific frequencies)
- This explains why atoms have discrete spectral lines (only certain transitions allowed)
- This explains why LEDs emit monochromatic light (only one frequency)
- This is the key to quantum mechanics
Frequently Asked Questions
Q: Can one photon free multiple electrons?
A: No. One photon can excite at most one electron. Multiple photons are required for multi-photon effects (only at very high intensities).
Q: Can intensity affect photon energy?
A: No. The energy of a single photon depends only on its frequency, not on intensity. Higher intensity means more photons, not more energetic photons.
Q: Why is photon energy often expressed in eV?
A: Because eV is the natural unit for light and electronics. An atom with a band gap of 2 eV absorbs photons with at least 2 eV energy – direct comparability.
Summary
Key Points:
- ✓ Planck Relation: E = h·f links frequency and energy
- ✓ Quantization: Photon energy is discrete, not arbitrarily divisible
- ✓ Color Dependence: Red light has less energy than blue light
- ✓ Practical Importance: Determines absorption, emission, LED colors, solar cells
- ✓ eV Unit: Natural for optics and electronics
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