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Wavelength, frequency and photon energy calculator

Convert wavelength to frequency and photon energy, or back, with c = fλ and E = hf, and see where the wave sits in the electromagnetic spectrum.

Mis à jour Exemples vérifiés : 6

Essayer
Fréquence
Hz
Fréquence: 5.45077 × 10¹⁴ Hz
Chiffres significatifs : 6 ; Au plus proche, égalités en s’éloignant de zéro
Part of the spectrum
Visible light
Colour
Green
Wavelength
5.5 × 10⁻⁷m / 550nm
Photon energy
2.25426eV / 3.612 × 10⁻¹⁹J
Energy per mole of photons
217.503kJ/mol
Wavenumber
18,181.8cm⁻¹
Band edges are conventions and differ slightly between sources; the wavelength is the vacuum value (divide by the refractive index for a medium).

550 nm is visible light (green): it oscillates at 545.08 THz and each photon carries 2.25426 eV.

Where it sits in the electromagnetic spectrum (wavelength, log scale)

GammaX-rayUVVisibleInfraredMicrowaveRadio1 pm1 nm1 µm1 mm1 m1 km550 nm

Approximate colour

Green
550 nm
Comment le calcul est effectué S

  1. Wavelength

    λ=5.5×10−7 m\lambda = 5.5 \times 10^{-7}\ \mathrm{m}

  2. Fréquence

    f=cλ=545,077,000,000,000 Hzf = \frac{c}{\lambda} = 545{,}077{,}000{,}000{,}000\ \mathrm{Hz}

  3. Photon energy

    E=hcλ=3.61172×10−19 J=3.61172×10−191.602176634×10−19=2.25426 eVE = \frac{hc}{\lambda} = 3.61172 \times 10^{-19}\ \mathrm{J} = \frac{3.61172 \times 10^{-19}}{1.602176634\times10^{-19}} = 2.25426\ \mathrm{eV}

    c, h and e are exact in the 2019 SI (CODATA 2022).

  4. Wavenumber

    ν~=1λ=18,181.8 cm−1\tilde\nu = \frac{1}{\lambda} = 18{,}181.8\ \mathrm{cm^{-1}}

À propos de Wavelength, frequency and photon energy calculator

Light and every other electromagnetic wave travel at c = 299,792,458 m/s in a vacuum, so wavelength and frequency fix each other through c = fλ. Each photon carries energy E = hf = hc/λ, where h is Planck's constant. Enter any one of the three and the calculator returns the other two, plus the wavenumber, the energy per mole of photons and the band of the spectrum.

Students use it for photon-energy problems, and radio and optics work uses it to move between frequency and wavelength. Green light at 550 nm has a frequency of 5.45 × 10¹⁴ Hz and 2.25 eV per photon; the 2.45 GHz wave in a microwave oven is 12.2 cm long.

Wavelengths are vacuum values: inside glass or water, divide by the refractive index, while the frequency stays the same. Band edges are conventions that differ slightly between sources.

Exemples détaillés

Green light, 550 nm

Start from
Wavelength
Wavelength (in vacuum)
550 nm
Fréquence
5.45077 × 10¹⁴ Hz
Photon energy
2.25426 eV
Wavenumber
18,181.8 cm⁻¹
Energy per mole of photons
217.503 kJ/mol
Part of the spectrum
Visible light
Colour
Green

Source de vérification : Python 3.8 decimal with exact SI c, h, e: f = c/λ, E = hc/λ/e = 2.2542582 eV

Microwave oven, 2.45 GHz

Start from
Fréquence
Fréquence
2.45 GHz
Wavelength
0.122364 m
Photon energy
0.00001 eV
Part of the spectrum
Microwaves

Source de vérification : Python 3.8 decimal: λ = 299792458/2.45e9 = 0.1223643 m

Hydrogen ionisation energy, 13.6 eV

Start from
Photon energy
Photon energy
13.6 eV
Wavelength
91.1649 nm
Part of the spectrum
Ultraviolet

Source de vérification : Python 3.8 decimal: λ = hc/(13.6 e) = 91.16485 nm (the Lyman limit is 91.2 nm)

FM radio, 100 MHz

Start from
Fréquence
Fréquence
100 MHz
Wavelength
2.99792 m
Part of the spectrum
Radio waves

Source de vérification : c/f = 2.99792458 m exactly (c is defined)

Questions

How do you convert wavelength to frequency?

Divide the speed of light by the wavelength: f = c/λ, with c = 299,792,458 m/s and λ in metres. For 550 nm green light, f = 299,792,458 ÷ 0.000000550 = 5.45 × 10¹⁴ Hz, or 545 THz. The reverse is λ = c/f: an FM station at 100 MHz has a wavelength of 3.00 m.

How do you calculate the energy of a photon?

Multiply Planck's constant by the frequency, E = hf, or divide hc by the wavelength, E = hc/λ, with h = 6.62607015 × 10⁻³⁴ J·s. In electronvolts, E = 1239.84 ÷ λ in nanometres, so a 700 nm red photon carries 1.77 eV and a 400 nm violet one 3.10 eV. h and the electron charge have been exact in the SI since 2019, and c since 1983.

What wavelength range is visible light?

About 380 to 750 nanometres, from violet to red; this calculator uses those edges for the visible band. Sources put the red end anywhere from 700 to 780 nm because eye sensitivity fades gradually; ISO 21348 uses 380–760 nm. Photon energies across the range run from 3.26 eV at 380 nm down to 1.65 eV at 750 nm.

What is the wavelength of Wi-Fi and microwave ovens?

About 12 cm. Microwave ovens run at 2.45 GHz, a wavelength of 12.24 cm, and 2.4 GHz Wi-Fi is 12.49 cm; 5 GHz Wi-Fi is 6.00 cm. Each 2.45 GHz photon carries 0.0000101 eV, over 200,000 times less than a green-light photon and far below the 13.6 eV needed to ionise a hydrogen atom, so microwaves heat food without ionising it.

What is a wavenumber?

The number of waves per centimetre, 1/λ, quoted in cm⁻¹ in infrared and Raman spectroscopy. From nanometres, the wavenumber is 10,000,000 ÷ λ: 550 nm is 18,182 cm⁻¹. An infrared band at 3,000 cm⁻¹, where C–H bonds stretch, lies at 3.33 µm. Wavenumber is proportional to photon energy, which is why spectroscopists use it as an energy scale.

Quelle est la précision de « Wavelength, frequency and photon energy calculator » ?

La précision dépend de vos données et des hypothèses de la méthode. Le calcul décimal utilise 50 chiffres significatifs, mais les estimations, méthodes numériques et données sources peuvent être moins précises ; l’arrondi affiché ne supprime pas ces limites. Exemples résolus vérifiés à partir de sources indépendantes : 6. Par exemple, « Green light, 550 nm » est vérifié à l’aide de Python 3.8 decimal with exact SI c, h, e: f = c/λ, E = hc/λ/e = 2.2542582 eV.

D’où vient cette méthode ?

CODATA 2022 — c, h and e are exact in the SI; NASA Science — Tour of the electromagnetic spectrum (band names and ranges); ISO 21348:2007 — Definitions of solar irradiance spectral categories.

À propos de ce calculateur

c=fλ,E=hf=hcλ,ν~=1λc = f\lambda,\qquad E = hf = \frac{hc}{\lambda},\qquad \tilde\nu = \frac{1}{\lambda}

Sources

  1. CODATA 2022 — c, h and e are exact in the SI
  2. NASA Science — Tour of the electromagnetic spectrum (band names and ranges)
  3. ISO 21348:2007 — Definitions of solar irradiance spectral categories

Vérifié avec les références

Ce calculateur comprend 6 exemples résolus dont les réponses proviennent de sources indépendantes. Ils font partie de la suite de tests et peuvent aussi être exécutés ici.

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