Photon Energy
Convert between wavelength, frequency and photon energy — plus the de Broglie wavelength of matter.
3.9729e-19 J · Green
λ = 7.2739e-10 m = 0.72739 nm
Light carries energy in fixed packets: E = hf, or equivalently hc ÷ λ. Green light at 500 nm has a frequency of about 600 THz and each photon carries 2.48 eV, which is 3.97×10⁻¹⁹ J. Shorter wavelength always means a more energetic photon.
Energy comes in packets
Classical physics treats light as a wave whose energy depends on brightness. That picture fails for the photoelectric effect: dim blue light ejects electrons from a metal while intensely bright red light does not. Einstein’s resolution was that light arrives as discrete quanta, each carrying E = hf, and a single photon either has enough energy to free an electron or it does not. Turning up the brightness sends more photons, not more energetic ones.
Because frequency and wavelength are tied together by c = fλ, the two forms E = hf and E = hc ÷ λ are the same equation. Frequency is directly proportional to energy, wavelength inversely so — which is why gamma rays at picometre wavelengths are dangerous and radio waves at metre wavelengths are not.
Matter has a wavelength too
De Broglie inverted the idea: if a wave can behave as a particle, a particle should behave as a wave, with λ = h ÷ mv. For everyday objects the result is unmeasurably small, because h is about 6.6×10⁻³⁴ and a thrown ball has a large momentum. For an electron it is around a nanometre — comparable to atomic spacing, which is why electrons diffract through crystals and why electron microscopes can resolve far finer detail than optical ones.
h = 6.626×10⁻³⁴ J·s, c = 2.998×10⁸ m/s; 1 eV = 1.602×10⁻¹⁹ J
- 1 Put the wavelength in metres. 500 nm is 500×10⁻⁹ = 5.00×10⁻⁷ m.
- 2 Find the frequency. f = c ÷ λ = 2.998×10⁸ ÷ 5.00×10⁻⁷ = 5.996×10¹⁴ Hz, or about 600 THz.
- 3 Multiply by Planck’s constant. E = 6.626×10⁻³⁴ × 5.996×10¹⁴ = 3.973×10⁻¹⁹ J.
- 4 Convert to electronvolts if you need them. 3.973×10⁻¹⁹ ÷ 1.602×10⁻¹⁹ = 2.48 eV.
- 5 Sanity-check against the shortcut. hc ≈ 1240 eV·nm, so 1240 ÷ 500 = 2.48 eV — the same answer in one step.
The spectrum by photon energy
Approximate boundaries; the bands blend into one another rather than switching sharply.
| Band | Wavelength | Photon energy |
|---|---|---|
| Radio | > 1 mm | < 0.001 eV |
| Infrared | 700 nm – 1 mm | 0.001 – 1.8 eV |
| Red light | ≈ 700 nm | ≈ 1.77 eV |
| Green light | ≈ 500 nm | ≈ 2.48 eV |
| Violet light | ≈ 400 nm | ≈ 3.10 eV |
| Ultraviolet | 10 – 400 nm | 3.1 – 124 eV |
| X-ray | 0.01 – 10 nm | 124 eV – 124 keV |
The 1240 shortcut, and what to watch
Because hc works out to about 1240 eV·nm, a photon’s energy in electronvolts is roughly 1240 divided by its wavelength in nanometres. That one relationship covers most spectroscopy questions without touching a calculator, and it is worth memorising — 1240 ÷ 400 = 3.1 eV for violet, 1240 ÷ 700 = 1.77 eV for red.
Two cautions. Prefixes are where answers go wrong: nanometres are 10⁻⁹ m, terahertz is 10¹² Hz, and mixing them up moves the answer by orders of magnitude. And the energies here are per photon — a laser pointer emits something like 10¹⁵ of them per second, so the total power is a very different quantity from the single-photon energy that decides whether a chemical bond breaks.