How this instrument works
This instrument inverts the photon relation E = hc ⁄ λ to solve for λ directly: λ = hc ⁄ E. The physics is identical either way — h and c are the same two SI-defined constants — but the starting point differs, and that difference is the whole reason a separate page earns its keep. Spectral-line tables, semiconductor bandgap datasheets, and particle-detector readouts routinely state a transition or threshold as an energy in electronvolts, never as a wavelength, because energy is what a diode's forward voltage, a calorimeter's pulse height, or a photon-counting sensor's output actually measures.
Colloidal quantum dots make the point concretely. Confining an electron inside a few nanometres of cadmium selenide raises its energy above the bulk semiconductor's bandgap by an amount a materials scientist calculates from a particle-in-a-box model and states in electronvolts, not nanometres — shrink the crystal and that confinement energy climbs. A dot engineered to 2.00 eV emits at 619.9 nm once run through λ = hc ⁄ E, a warm orange the eye reads directly, which is how a display maker picks crystal size for a wanted pixel colour long before a spectrometer confirms it.
Two boundaries matter. The wavelength returned here is a vacuum figure; inside glass, water, or a semiconductor the same photon slows to c ⁄ n and its wavelength shrinks by that factor even though its energy, and therefore its colour in the everyday sense, does not change. And the input must be one photon's energy, never the total energy of a pulse or a beam: a 1 mJ laser pulse and a single 2 eV photon differ by roughly fifteen orders of magnitude, and feeding the former into a field meant for the latter returns a wavelength for a gamma ray that was never actually emitted.
- Enter the single photon's energy into Photon energy, eV — read off a spectral-line table, a bandgap datasheet, or a detector's pulse-height output.
- Convert first if your source uses other units: multiply keV by 1000, or divide a joule figure by 1.602176634 × 10⁻¹⁹, before typing it in.
- Read Wavelength in nanometres by default, or switch its unit menu to micrometres for infrared results or metres for radio-scale photons.
- Check the direction of the answer: raising Photon energy always shortens Wavelength, and the two move in exact inverse proportion.
Worked example — a photon at 2.00 eV
Set Photon energy, eV to 2.00 — perhaps read straight off a quantum-dot datasheet, or any spectroscopy table quoting a transition at that energy. Convert to joules first: E = 2.00 × 1.602176634 × 10⁻¹⁹ = 3.204353268 × 10⁻¹⁹ J. Planck's constant times the speed of light is a fixed 1.986445857 × 10⁻²⁵ J·m, so λ = 1.986445857 × 10⁻²⁵ ⁄ 3.204353268 × 10⁻¹⁹ = 6.19920992166 × 10⁻⁷ m.
Switch Wavelength to nanometres and that reads 619.9 nm — a warm orange sitting between the sodium D lines and deep red, squarely inside what a healthy eye can see. The eV·nm shortcut confirms it without the unit juggling: 1239.84 ⁄ 2.00 lands on the same 619.9 nm directly, which is the whole appeal of carrying that constant around.
Questions
When would I know a photon's energy before I know its wavelength?
Whenever the source quotes energy natively. Spectral-line tables such as the NIST Atomic Spectra Database list transitions in electronvolts, semiconductor datasheets state a bandgap in eV, and particle detectors report deposited energy straight from a pulse height — none of them mention a wavelength until you ask this calculator for one.
Why does doubling the input energy exactly halve the wavelength?
Because λ = hc ⁄ E is a plain inverse proportion once h and c are held fixed. A 1 eV photon sits at 1239.8 nm, deep infrared; a 2 eV photon at the same hc lands at 619.9 nm, orange visible light — exactly half. Multiply energy by ten and wavelength shrinks by that same factor of ten, with no offset or exponent involved.
How far does this stretch toward X-rays and gamma rays?
A long way, and linearly the whole distance. A 1240 eV photon, a soft X-ray, lands at essentially 1.00 nm — the eV·nm shortcut's namesake case. Push to 1.022 MeV, twice an electron's rest-mass energy, and wavelength shrinks to about 1.21 picometres; past that threshold a photon can convert into an electron-positron pair near a nucleus, though its wavelength stays perfectly well defined right up to the moment it does.
Does the wavelength change inside glass, water, or a semiconductor?
The figure this instrument returns is always the vacuum value. Inside a medium of refractive index n, the same photon travels at c ⁄ n and its physical wavelength shrinks by that factor even though its energy, and its colour, stay fixed; a 2 eV photon reads 619.9 nm in vacuum but roughly 408 nm inside crown glass, n ≈ 1.52.
What's the most common mistake when using this calculator?
Typing in a beam's total energy instead of one photon's. A 5 mW laser pointer delivers about 5 millijoules of energy each second, while a single visible photon carries only a few times 10⁻¹⁹ joules of it — a gap of roughly sixteen orders of magnitude. Only the single-photon figure, in electronvolts, belongs in Photon energy, eV.