Article — Energy to Wavelength Calculator
Energy to wavelength calculator
Energy to wavelength conversion uses the Planck–Einstein relation λ = hc/E. A 2.25 eV photon has a wavelength of 550 nm — green light. A 100 keV X-ray photon has a wavelength of 12.4 pm. A 1 MeV gamma ray has a wavelength of 1.24 pm. The convenient shortcut for photons is λ[nm] = 1240 / E[eV], accurate to better than 0.07%.
The relation links the wave description and particle description of light. Every photon carries energy proportional to its frequency, and frequency is inversely proportional to wavelength. That single equation underpins atomic spectroscopy, photochemistry, medical imaging, telecommunications, and the design of every camera sensor and solar cell.
What is energy to wavelength conversion?
Energy to wavelength conversion translates between two ways of describing a single photon. Energy (in joules, electron-volts, or any other energy unit) measures how much work the photon can do when absorbed. Wavelength (in nanometres, ångströms, metres) measures the spatial period of the photon's electromagnetic oscillation. The two are linked by Planck's constant h and the speed of light c.
The conversion is exact, not approximate, for photons in vacuum. In a medium with refractive index n, the wavelength shortens to λ_m = λ_vacuum / n while the energy and frequency stay the same. That is why a 550 nm green photon in air becomes a 413 nm wave inside water (n ≈ 1.33) without changing colour — energy, not wavelength, sets perceived colour.
The energy to wavelength formula
One equation, several useful rearrangements.
E = hν = hc/λ Planck–Einstein relationλ = hc/E solve for wavelengthλ[nm] = 1240 / E[eV] practical shortcuthc = 1.986 × 10⁻²⁵ J·m = 1240 eV·nm combined constantThe 1240 eV·nm shortcut is the most useful number to memorise in photon physics. Energy 1 eV → wavelength 1240 nm. Energy 4 eV → wavelength 310 nm. Energy 124 keV → wavelength 0.01 nm. It works because hc, expressed in electron-volts times nanometres, equals 1240 to four significant figures.
The electromagnetic spectrum by energy
Photon energy and wavelength sweep across more than 16 orders of magnitude in everyday physics, from kilometre-long radio waves at sub-microelectronvolt energies to picometre-scale gamma rays at megaelectronvolt energies.
- Radio (FM, 100 MHz): λ = 3 m, E = 0.4 μeV. Broadcasting, communications.
- Microwave (kitchen, 2.45 GHz): λ = 12.2 cm, E = 10 μeV. Heats water by rotational excitation.
- Infrared (body heat, 10 μm): λ = 10 μm, E = 0.124 eV. Thermal imaging band.
- Visible red (700 nm): λ = 700 nm, E = 1.77 eV. Long end of human vision.
- Visible green (550 nm): λ = 550 nm, E = 2.25 eV. Peak eye sensitivity.
- Visible violet (400 nm): λ = 400 nm, E = 3.10 eV. Short end of human vision.
- UV-C (254 nm): λ = 254 nm, E = 4.88 eV. Germicidal — breaks DNA bonds.
- Ionising UV (91 nm): λ = 91 nm, E = 13.6 eV. Hydrogen ionisation threshold.
- X-ray (medical, 30 keV): λ = 41 pm, E = 30 keV. Diagnostic radiography.
- Gamma (Co-60, 1.25 MeV): λ = 0.99 pm, E = 1.25 MeV. Radiotherapy and sterilisation.
A single photon of visible green light carries only 3.6 × 10⁻¹⁹ joules — about a million times less energy than a single grain of sand falling 1 cm. A 100-watt light bulb emits roughly 4 × 10²⁰ visible photons per second. The eye can detect, under perfect dark-adapted conditions, the arrival of just 5–9 photons within 100 ms — close to the absolute single-photon limit.
Energy to wavelength shortcuts
Beyond λ[nm] = 1240/E[eV], a few related shortcuts are worth remembering.
For X-rays, the same shortcut becomes λ[Å] = 12.4 / E[keV]. A copper Kα X-ray at 8.05 keV has wavelength 1.541 Å — the standard probe for X-ray crystallography. For frequency, ν[THz] = 300 / λ[μm] — a wavelength in micrometres converts to terahertz frequency with a divide.
For thermal radiation by molar bond energy, divide kilojoules per mole by 96.5 to get electron-volts per photon, then apply the 1240/E shortcut. A C–C single bond at 348 kJ/mol becomes 3.61 eV per photon → 344 nm. A 343 nm photon has just enough energy to break that bond, in principle.
Energy to wavelength for photochemistry
Photochemistry happens when a photon's energy matches a bond-dissociation or electronic-excitation energy. Photons below the threshold cannot drive the reaction regardless of intensity — Einstein's photoelectric insight, now textbook material. Photons above the threshold can drive it, with extra energy ending up as kinetic energy of the dissociation products or as fluorescence.
UV-C at 254 nm (4.88 eV) damages DNA because that energy exceeds the bond strength of typical covalent bonds in nucleotides. UV-A at 365 nm (3.40 eV) sits below most direct bond energies but generates damage through reactive-oxygen intermediates. Visible light at 1.8–3.1 eV is below most bond thresholds, which is why room light does not photolyse DNA the way UV does.
De Broglie and matter waves
The same λ = h/p relation that governs photons applies to matter through de Broglie's hypothesis. For a particle with momentum p, the wavelength is λ = h/p = h/√(2mE) for non-relativistic kinetic energy E. An electron accelerated through 100 V has 100 eV kinetic energy and a wavelength of 0.123 nm — the basis of electron microscopy, which sees structures far smaller than light microscopes can resolve.
The energy-to-wavelength formula uses vacuum wavelength. Inside a medium with refractive index n, wavelength shortens to λ/n while energy and frequency stay constant. For glass at n = 1.5, a 600 nm vacuum photon has wavelength 400 nm inside the glass. When specifying laser wavelength for visible-light experiments, the convention is vacuum (or air-equivalent) λ.
Common energy to wavelength mistakes
Check the unit of energy carefully — eV per photon is microscopic, kJ per mole is macroscopic. Mixing them produces answers off by a factor of 96,485 (Faraday's constant divided by 1000). For chemistry problems, divide kJ/mol by 96.485 to get eV per photon, then apply λ[nm] = 1240/E[eV].
The biggest pitfall is unit confusion in the energy input. A 100 kJ/mol bond energy is 1.04 eV per photon (around 1200 nm), not 100 eV per photon (around 12.4 nm). One is near-infrared, the other is extreme UV. The calculator above accepts both units explicitly to avoid the trap.
The second pitfall is forgetting that λ = hc/E applies to photons, not classical waves. A 60 Hz power line oscillates at 60 Hz, which corresponds to a vacuum photon wavelength of 5,000 km and energy 2.5 × 10⁻¹³ eV — vanishingly tiny per photon. Power transmission is described by classical electromagnetism, not by counting photons, but the formula still works mathematically.
The third pitfall is treating photon wavelength as if it described the size of the photon. Photons do not have a definite extent. Wavelength is the spatial period of the underlying electromagnetic field, not a physical width. A 550 nm photon is not 550 nm wide — it can interact with structures much smaller than λ if the geometry concentrates the field, which is how plasmonic nanoantennas work.