For eV input: λ (nm) = 1240 / E (eV)
This works because hc ≈ 1240 eV·nm
Was this calculator helpful?
✓ Thanks for your feedback!
Sources & Methodology
⏱ Last reviewed: April 2026 — Physical constants verified against 2019 SI redefinition values
How to Convert Photon Energy to Wavelength
The relationship between a photon's energy and its wavelength is one of the most fundamental equations in all of physics. Known as the Planck-Einstein relation, it connects quantum mechanics (photon energy) to classical wave physics (wavelength) through two universal constants: Planck's constant (h) and the speed of light (c). Understanding this relationship is essential in quantum physics, spectroscopy, semiconductor engineering, and photonics.
Practical shortcut in convenient units: λ (nm) = 1240 / E (eV)
This comes from hc = 1240 eV·nm, which is an extremely useful value to memorize.
The Planck-Einstein Relation Explained
Max Planck introduced the concept of energy quanta in 1900, and Albert Einstein extended it in 1905 to explain the photoelectric effect (for which he received the Nobel Prize in 1921). Together their work established that light comes in discrete packets called photons, each carrying energy E = hf, where f is frequency. Since f = c/λ, this gives the wavelength-energy relation E = hc/λ → λ = hc/E.
The product hc = 1.98644568×10−²&sup5; J·m is a fundamental constant pairing. In practical units, hc ≈ 1240 eV·nm, which means a 1 eV photon has wavelength 1240 nm (near-infrared), and a 2.48 eV photon has wavelength 500 nm (green visible light). This convenient value eliminates the need to work with tiny exponents in everyday optics calculations.
Energy-Wavelength Relationship: Inversely Proportional
Energy and wavelength are inversely proportional: E = hc/λ. If you double the wavelength, the energy is halved. If you halve the wavelength (go from 600 nm red to 300 nm UV), the energy doubles. This is why ultraviolet radiation causes sunburn and DNA damage while visible red light does not — UV photons carry roughly twice the energy of red photons.
The entire electromagnetic spectrum can be understood through this relationship: gamma rays at 10−¹² m wavelength have energies of ~MeV; X-rays at 10−¹&sup0; m have keV energies; visible light at 380-700 nm corresponds to 1.77-3.26 eV; and FM radio waves at 3 meters carry only ~4×10−&sup7; eV per photon.
Converting Between eV, Joules, and Wavelength
The electronvolt (eV) is the natural unit of energy in atomic and optical physics. One eV is the kinetic energy gained by a single electron when accelerated through 1 volt potential difference: 1 eV = 1.602176634×10−¹&sup9; J (exact by the 2019 SI redefinition). For X-rays and nuclear physics, kiloelectronvolts (keV = 10³ eV) and megaelectronvolts (MeV = 10&sup6; eV) are used.
Applications in Science and Engineering
LED and Laser Design: LED emission wavelength is determined by the semiconductor bandgap energy. A bandgap of 1.85 eV gives a 670 nm red LED (λ = 1240/1.85). Blue LEDs use GaN with bandgap ~2.7 eV (λ = 1240/2.7 = 459 nm). Laser diodes require precise bandgap engineering to achieve specific wavelengths for optical communications, DVD players, and medical applications.
Spectroscopy and Chemical Analysis: Atomic emission spectra have characteristic lines at specific wavelengths corresponding to electron transitions between energy levels. The hydrogen Balmer series (visible lines) can be precisely calculated using the Rydberg formula combined with E = hc/λ. Mass spectrometers and optical spectrometers use energy-wavelength conversions constantly.
Solar Cell Engineering: Solar cells must absorb photons with energy above their bandgap. Silicon has bandgap 1.12 eV, corresponding to 1107 nm. Photons with wavelength longer than 1107 nm pass through unabsorbed. Multi-junction solar cells stack different bandgap materials to capture more of the solar spectrum, achieving efficiencies above 40%.
Medical Physics and X-rays: X-ray photon energies (60-120 keV for diagnostic radiology) determine tissue penetration depth. Higher energy X-rays penetrate more deeply. Mammography uses lower energy (25-30 keV, λ ≈ 0.04-0.05 nm) for better soft-tissue contrast. Radiation therapy uses MeV photons for deep tumor treatment.
Electromagnetic Spectrum Reference
The electromagnetic spectrum spans an extraordinary range of energies and wavelengths, all governed by the same E = hc/λ relationship:
| Spectrum Region | Wavelength Range | Energy Range (eV) | Applications |
|---|---|---|---|
| Gamma rays (γ) | <0.01 nm | >100 keV | Nuclear reactions, PET scans |
| Hard X-rays | 0.01–0.1 nm | 12–124 keV | Radiotherapy, CT scans |
| Soft X-rays | 0.1–10 nm | 0.12–12 keV | Mammography, crystallography |
| UV-C (deep UV) | 100–280 nm | 4.4–12.4 eV | Sterilization, lithography |
| UV-A / UV-B | 280–400 nm | 3.1–4.4 eV | Sunburn, vitamin D, forensics |
| Visible — Violet | 380–450 nm | 2.76–3.26 eV | Human vision, blue LEDs |
| Visible — Green | 495–570 nm | 2.18–2.50 eV | Peak human eye sensitivity |
| Visible — Red | 620–750 nm | 1.65–2.00 eV | Red LEDs, lasers |
| Near Infrared (NIR) | 750–2,500 nm | 0.50–1.65 eV | Fiber optics, remote controls |
| Mid/Far Infrared | 2.5 µm–1 mm | 0.001–0.50 eV | Thermal imaging, CO₂ sensing |
| Microwave | 1 mm–1 m | 1.24×10−³–1.24×10−&sup6; eV | WiFi, radar, 5G |
Worked Example: LED Wavelength from Bandgap
A semiconductor has a bandgap energy of 2.26 eV (corresponding to GaP, gallium phosphide). What color LED will it produce?
Step 1: λ = 1240 / 2.26 = 549 nm — this is green light!
Step 2: Verify it is in the visible spectrum: 380 nm < 549 nm < 700 nm — confirmed visible green.
Step 3: Convert to joules: E = 2.26 × 1.602×10−¹&sup9; = 3.62×10−¹&sup9; J per photon. This is the energy of a single photon emitted by this LED.
Frequency vs Wavelength vs Energy
Three equivalent ways to characterize a photon: wavelength (λ in meters or nm), frequency (f in Hz), and energy (E in joules or eV). They are related by: E = hf = hc/λ, and f = c/λ. Spectroscopists often use wavenumber (ν̄ = 1/λ in cm−¹) as well. All four quantities carry the same information; the choice depends on the application. Optical engineers prefer wavelength (nm); radio engineers prefer frequency (MHz, GHz); nuclear physicists prefer energy (MeV); infrared spectroscopists use wavenumber (cm−¹).