Formula & Calculator
Photon Energy
Calculates the energy of a single photon from its wavelength, using Planck's constant and the speed of light.
Interpretation
E = h·c/λ. Energy of a photon from its wavelength. Used in quantum optics, photovoltaics, and spectroscopy.
Variables
| Symbol | Quantity | Unit |
|---|---|---|
| E | Photon energy | J or eV |
| h | Planck's constant | J*s |
| c | Speed of light | m/s |
| λ | Wavelength | m |
What it means
The energy of a photon is inversely proportional to its wavelength. This is fundamental in quantum mechanics and photonics. It is used to determine whether a photon has enough energy to excite an electron (as in solar cells or photodetectors), to calculate the energy levels in atoms, and to interpret spectra. Understanding this is essential for anyone working with light‑matter interactions and quantum optics.
Worked example
Photon Energy – Two Detailed Examples
Real‑World| Parameter | Value |
|---|---|
| λ (nm) | 400 |
| Parameter | Value |
|---|---|
| λ | 1550 |
Common mistakes
- Photon energy: E = h·c / λ – where h is Planck’s constant, c is speed of light.
- Units: h in J·s, c in m/s, λ in m → E in J. Or use h = 4.136×10⁻¹⁵ eV·s and c = 3.00×10⁸ m/s to get energy in eV.
- Alternative: E = h·f – where f is frequency (Hz).
- Quantum nature: Light energy is quantised in photons.
- Photoelectric effect: The photon energy must exceed the work function to eject electrons.
Applications
Photon energy, E = h·c/λ, relates the energy of a photon to its wavelength. This is fundamental in photonics, quantum optics, and spectroscopy. Engineers use it to design photodetectors, solar cells, and optical communication systems. By calculating photon energy, they can determine whether a photon has enough energy to be absorbed by a semiconductor, to excite an electron, or to cause a photochemical reaction. This formula is also used in medical imaging (PET, X‑ray) and in astronomy to interpret spectra. Understanding photon energy is essential for any work involving light‑matter interactions.
- Design of photodetectors and solar cells (bandgap matching)
- Spectroscopic interpretation of atomic and molecular lines
- Optical communication – energy per bit calculations
- Medical imaging (X‑ray, gamma) – energy and dose
- Education on quantum nature of light
Frequently Asked Questions
It calculates the energy of a single photon from its wavelength: E = h c / λ.
E = photon energy (Joules).
h = Planck's constant (6.626×10⁻³⁴ J·s).
c = speed of light (3.0×10⁸ m/s).
λ = wavelength (m).
E (eV) = 1240 / λ (nm), because hc ≈ 1240 eV·nm.
From quantum mechanics: E = hν, and ν = c/λ, so E = hc/λ.
Photon energy is the energy per photon; total power is the product of photon energy and the photon flux (number of photons per second).
λ = 500 nm (green light). E = (6.626×10⁻³⁴ × 3.0×10⁸) / (500×10⁻⁹) = 3.975×10⁻¹⁹ J = 2.48 eV.
- Confusing photon energy with total energy of a light beam.
- Forgetting to convert wavelength to metres when using SI units.
- Using the wrong value of h or c.
If photon energy exceeds the work function of a material, electrons are emitted; the excess energy becomes kinetic energy.
It determines the transitions between energy levels in atoms and molecules, giving characteristic spectra.
Photon energy is inversely proportional to wavelength; shorter wavelengths (e.g., UV) have higher energy.