Formula and Method for Photon Energy
Light behaves as discrete packets of energy called photons. The energy carried by a single photon is given by the Planck-Einstein relation, E = hf, where h is Planck's constant (6.62607015 × 10⁻³⁴ J·s) and f is the light's frequency in hertz. Because frequency and wavelength are linked by the wave equation c = λf, the same relation is commonly rewritten as E = hc/λ, letting you compute photon energy directly from wavelength — the quantity most often quoted for light (color, laser specs, spectral lines).
Deriving E = hc/λ and the role of the medium
Starting from E = hf and c = λf, substitute f = c/λ to get E = hc/λ. This calculator converts your wavelength to meters, then applies that formula. If you supply a refractive index n greater than 1 (light traveling through glass, water, or another medium), the calculator accounts for the fact that the wavelength you measured is the wavelength inside that medium: the light's speed slows to c/n while its frequency — and therefore its photon energy — stays fixed at the vacuum value. The energy formula becomes E = hc / (n·λ), which correctly reduces to E = hc/λ when n = 1 (vacuum or, to a very close approximation, air).
Reading the results and avoiding common mistakes
- Joules vs. electronvolts: a single photon's energy in joules is an extremely small number (around 10⁻¹⁹ J for visible light), so physicists and chemists usually report it in electronvolts (eV) instead — divide joules by the elementary charge, 1.602176634 × 10⁻¹⁹ C, to convert.
- Wavelength scales with the medium, energy doesn't: don't assume a photon "loses energy" when light slows down in glass or water — frequency and photon energy are unchanged; only the wavelength and speed change.
- Molar photon energy: multiplying a single photon's energy by Avogadro's number (6.02214076 × 10²³ /mol) gives the energy of one mole of photons — a figure chemists use directly against bond dissociation energies (typically 150-500 kJ/mol) to see whether a given wavelength of light can drive a photochemical reaction.
- Shorter wavelength means more energy: because E is inversely proportional to λ, violet and ultraviolet photons carry more energy than red or infrared photons of the same intensity — this is why UV light can cause sunburn and ionize atoms while infrared mostly just warms them.