532.121023
nm
563.391493
THz
18,792.72
cm^-1
3.733072e-19
J
0.532121
um
532.121023
nm
563.391493
THz
18,792.72
cm^-1
3.733072e-19
J
0.532121
um
The Energy to Wavelength Calculator converts photon energy to the corresponding electromagnetic wavelength using the Planck-Einstein relation. This conversion is fundamental in quantum mechanics, photochemistry, materials science, and spectroscopy. When studying electronic transitions, band gaps in semiconductors, or photon absorption processes, energy is often the primary quantity of interest, but experimental measurements are frequently reported in wavelength. This calculator bridges that gap by accepting energy in electron volts (eV), joules (J), or kilojoules per mole (kJ/mol) and returning the corresponding wavelength in nm, μm, and m, along with frequency and wavenumber. It is especially useful for determining what wavelength of light is needed to excite a particular energy transition or to characterize the emission from quantum dots, LEDs, and laser systems.
The Planck-Einstein relation connects photon energy to wavelength:
$$E = hf = \frac{hc}{\lambda}$$
Solving for wavelength:
$$\lambda = \frac{hc}{E}$$
where h = 6.626 × 10⁻³⁴ J·s is Planck's constant and c = 2.998 × 10⁸ m/s is the speed of light. The product hc = 1.989 × 10⁻²⁵ J·m. For energy in electron volts, the conversion factor is:
$$\lambda (\text{nm}) = \frac{1239.84}{E (\text{eV})}$$
For energy in kJ/mol, we first convert to energy per photon by dividing by Avogadro's number (6.022 × 10²³ mol⁻¹):
$$E_{\text{photon}} = \frac{E_{\text{kJ/mol}} \times 1000}{N_A}$$
The calculator also outputs the corresponding frequency (f = E/h) and wavenumber (ν̃ = 1/λ) for comprehensive spectroscopic referencing.
The wavelength result indicates what color or region of the electromagnetic spectrum corresponds to the given energy. Energies of 1.65–3.26 eV map to visible light (380–750 nm). Energies above ~3.3 eV correspond to ultraviolet radiation, while energies below ~1.65 eV correspond to infrared. In semiconductor physics, the band gap energy directly determines the absorption edge wavelength — for example, silicon's 1.12 eV band gap corresponds to ~1107 nm (near-IR), which is why silicon solar cells absorb visible light efficiently. The frequency and wavenumber outputs provide alternative ways to reference the same photon energy in different spectroscopic contexts.
Inputs
Results
A photon with 2.33 eV energy has a wavelength of approximately 532 nm, which is green light — the same wavelength emitted by frequency-doubled Nd:YAG lasers.
Inputs
Results
Many chemical bonds have dissociation energies around 300–500 kJ/mol. At 400 kJ/mol, the corresponding wavelength is ~299 nm (UV-B region), explaining why UV radiation can break chemical bonds and cause photodegradation.
The Planck-Einstein relation (E = hf = hc/λ) states that the energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This equation, combining Planck's quantization hypothesis with Einstein's photon theory, is one of the foundational equations of quantum mechanics.
Multiply eV by 96.485 to get kJ/mol. This conversion factor comes from multiplying the elementary charge (1.602 × 10⁻¹⁹ C) by Avogadro's number (6.022 × 10²³ mol⁻¹) and dividing by 1000 to convert J to kJ. For example, 2.33 eV = 224.8 kJ/mol.
Visible light ranges from approximately 1.65 eV (red, 750 nm) to 3.26 eV (violet, 380 nm). In kJ/mol, this corresponds to approximately 159–315 kJ/mol. The most sensitive wavelength for human vision (555 nm, green-yellow) has an energy of about 2.24 eV.
The shortcut λ(nm) = 1239.84/E(eV) ≈ 1240/E(eV) eliminates the need to use Planck's constant and the speed of light explicitly. It is widely memorized by physicists and chemists for quick mental conversions between energy and wavelength.
A semiconductor's band gap energy determines its absorption edge wavelength: λ_edge = hc/E_gap. Photons with wavelengths shorter than λ_edge (higher energy) are absorbed, while longer wavelengths are transmitted. This determines the material's color and its suitability for photovoltaic and LED applications.
Medical X-rays typically have energies of 20–150 keV (0.008–0.062 nm). Dental X-rays use ~70 keV photons. By comparison, visible light photons have energies around 2–3 eV — roughly 10,000 to 50,000 times less energetic than diagnostic X-rays.
Yes. Enter the energy in eV (gamma rays typically range from 100 keV to several MeV). For example, the 662 keV gamma ray from Cs-137 corresponds to a wavelength of about 0.00187 nm or 1.87 pm. The calculator handles any energy range.
The boundary between ultraviolet and visible light at approximately 380–400 nm (3.1–3.3 eV) corresponds to the short-wavelength limit of human vision. UV photons above this energy threshold can cause photochemical reactions including DNA damage, sunburn, and degradation of polymers and dyes.
Solar cell designers use energy-wavelength conversion to match the solar spectrum to semiconductor band gaps. The ideal single-junction solar cell band gap is about 1.34 eV (925 nm), as predicted by the Shockley-Queisser limit. Silicon (1.12 eV, 1107 nm) and GaAs (1.42 eV, 873 nm) are close to this optimum.
The ionization energy of hydrogen is 13.6 eV, corresponding to a wavelength of 91.2 nm (far UV). This is the Lyman limit — photons with shorter wavelengths can ionize hydrogen atoms from the ground state. This has important implications in astrophysics and plasma physics.
Roboculator Team
The Roboculator Team explains calculations, planning tools, and practical formulas in clear language for real-life situations.
How helpful was this calculator?
Be the first to rate!
