Hong Life CalculatorsUnderstanding the photon energy and wavelength calculator — concept and principle
Light comes in packets called photons, and each photon's energy is fixed by its wavelength. This calculator converts a wavelength in nanometres into photon energy in electronvolts and joules, frequency in terahertz and wavenumber in cm⁻¹. Spectroscopists, laser users, photochemists and physics students use it to switch between the units their instruments and textbooks use.
How it is calculated
- E = h × c / λ, with h = 6.62607015 × 10⁻³⁴ J·s and c = 2.99792458 × 10⁸ m/s (both exact SI values)
- E (eV) = 1239.84198 / λ (nm), a shortcut that combines h, c and the electron charge
- ν = c / λ, shown in THz (10¹² Hz)
- wavenumber ν̃ = 1 / λ = 10⁷ / λ (nm), in cm⁻¹
The wavelength is entered in nm and converted to metres by × 10⁻⁹. All four results are proportional to 1/λ, so they all move together.
The principle
Planck proposed in 1900 that energy is exchanged in quanta E = hν, and Einstein used light quanta in 1905 to explain the photoelectric effect. Because a wave's frequency and wavelength satisfy c = νλ, the energy can be written hc/λ: shorter wavelength means more energy per photon. The number 1239.84 eV·nm is hc expressed in convenient units. Wavenumber is popular in infrared and Raman spectroscopy because it is directly proportional to energy, unlike wavelength.
Worked example
- Input: λ = 532 nm (a common green laser line).
- E = 1239.84198 ÷ 532 = 2.3305 eV.
- E = 6.62607015 × 10⁻³⁴ × 2.99792458 × 10⁸ ÷ (532 × 10⁻⁹) = 3.7339 × 10⁻¹⁹ J.
- ν = 2.99792458 × 10⁸ ÷ 532 × 10⁻⁹ = 5.6352 × 10¹⁴ Hz = 563.52 THz.
- ν̃ = 10⁷ ÷ 532 = 18,796.99 cm⁻¹.
| Wavelength (nm) | Energy (eV) |
|---|---|
| 133 | 9.32212015 |
| 266 | 4.661060075 |
| 399 | 3.107373383 |
| 532 | 2.330530038 |
| 665 | 1.86442403 |
| 798 | 1.553686692 |
| 1,064 | 1.165265019 |
How to read the result
Visible light spans roughly 400–700 nm, or about 3.1–1.8 eV. Photons above a few eV (ultraviolet) can break chemical bonds and damage DNA; infrared photons below about 1.6 eV mostly cause heating and molecular vibrations. To compare a photon with a material's band gap, use eV: a semiconductor absorbs photons whose energy exceeds its gap. Multiply by Avogadro's number to get energy per mole of photons (about 225 kJ/mol at 532 nm).
Common mistakes
- Entering the wavelength in metres or micrometres instead of nanometres.
- Confusing frequency with angular frequency (ω = 2πν).
- Using an air wavelength where a vacuum wavelength is meant; they differ by about 0.03% in visible light.
- Mixing up eV per photon with kJ per mole.
Frequently asked questions
How do I convert eV back to wavelength?
λ (nm) = 1239.84 ÷ E (eV). For example, 1 eV corresponds to about 1240 nm.
How many photons per second does a 1 mW, 532 nm beam carry?
Divide power by photon energy: 0.001 ÷ 3.734 × 10⁻¹⁹ ≈ 2.7 × 10¹⁵ photons per second.
Why do chemists use wavenumber?
It is proportional to energy and gives convenient numbers for vibrational spectra, typically hundreds to a few thousand cm⁻¹.
Sources: BIPM, The International System of Units (SI Brochure), 9th edition (exact values of h and c) · CODATA 2018 recommended values of the fundamental physical constants (NIST)