Wavelength, Frequency & Photon Energy

A wave's speed, wavelength and frequency are tied by v = λ·f; the period is T = 1 ÷ f and the spectroscopist's wavenumber is 1 ÷ λ in cm⁻¹. For light the speed in vacuum is c = 299 792 458 m/s (exact); in a medium it is c ÷ n, so the wavelength shortens by the refractive index while the frequency — and therefore the colour and the photon energy — stays the same. For sound, water waves or a string you enter the speed (343 m/s in air at 20 °C, about 1 480 m/s in water) and the same λ = v ÷ f applies.

Electromagnetic energy comes in photons of E = h·f = h·c ÷ λ, with Planck's constant h = 6.626 070 15 × 10⁻³⁴ J·s — exact since the 2019 SI. The energy is given in joules, in electron-volts (1 eV = 1.602 176 634 × 10⁻¹⁹ J, also exact) and per mole of photons in kJ/mol (× Avogadro's number 6.022 140 76 × 10²³). Sound has no photons, so the energy line is left out for a custom speed.

The spectrum band is named from the vacuum wavelength: radio above 1 m, microwave 1 mm–1 m, infrared 700 nm–1 mm, visible 380–700 nm with the colour by wavelength (red 625+, orange, yellow, green 500–565, cyan, blue 450–485, violet), ultraviolet 10–380 nm, X-ray 0.01–10 nm, gamma below. The boundaries are conventional and blurry. Each quantity is shown in the unit that keeps its number between 1 and 1 000, and in SI. Nothing leaves the browser; the same four anonymous usage counts as the rest of the site apply.