Energy To Wavelength
Convert photon energy in eV to wavelength in nanometers using Planck's equation λ = hc/E. Free online calculator with frequency, wavenumber, and interactive charts for quantum mechanics and spectroscopy.
About This Calculator
The Energy to Wavelength Calculator converts photon energy in electronvolts (eV) to its corresponding wavelength using the inverse of Planck's equation: λ = hc/E. This is a fundamental conversion in quantum mechanics and spectroscopy — every photon has an energy determined by its wavelength, and knowing one lets you compute the other. Physicists, chemists, engineers, and students use this conversion for problems involving atomic transitions, laser design, solar energy analysis, and optical spectroscopy.
The calculation uses Planck's constant (h = 6.62607015 × 10⁻³⁴ J·s) and the speed of light (c = 299,792,458 m/s), both CODATA-recommended fundamental constants. Enter the photon energy in eV and the calculator instantly returns the wavelength in nanometers (nm) and meters (m), the frequency in hertz (Hz), and the wavenumber in reciprocal meters (m⁻¹). A breakdown table and interactive charts give you a complete view of the photon's physical properties.
Understanding the energy-wavelength relationship is essential across many fields: spectroscopy identifies materials by their absorption and emission lines at specific wavelengths; quantum mechanics describes atomic energy levels where photon energy determines electron transitions; solar energy analysis requires knowing the spectral distribution of sunlight; medical imaging uses photons at specific energy levels for X-rays and PET scans; and telecommunications engineers select infrared wavelengths with optimal photon energies for fiber-optic transmission.
Convenient rule of thumb: For quick mental calculations, use λ (nm) = 1240 / E (eV). This approximation is within 0.2% of the exact value. For example, green light at 2.38 eV has a wavelength of about 1240 / 2.38 ≈ 520 nm. The calculator uses the exact formula for accurate results.
Frequently Asked Questions
How do you convert energy to wavelength?
Use Planck's equation rearranged as λ = hc/E, where h is Planck's constant (6.626 × 10⁻³⁴ J·s), c is the speed of light (299,792,458 m/s), and E is the photon energy in joules. If the energy is given in eV, first multiply by 1.602 × 10⁻¹⁹ to convert to joules. The result is the wavelength in meters; divide by 10⁻⁹ to get nanometers.
What is the formula for energy to wavelength conversion?
The energy to wavelength formula is λ = hc/E derived from Planck's equation E = hf and the wave equation c = fλ. Combining them: E = hc/λ, so rearranging gives λ = hc/E. Planck's constant h = 6.62607015 × 10⁻³⁴ J·s and the speed of light c = 299,792,458 m/s are both CODATA-recommended values.
How do you calculate wavelength from energy in eV?
To calculate wavelength from energy in eV, first convert the energy to joules by multiplying by 1.602 × 10⁻¹⁹ (the electronvolt to joule conversion factor). Then apply λ = hc/E, where h is Planck's constant and c is the speed of light. The calculator does this automatically — just enter the energy in eV and get the wavelength in nanometers instantly.
What is the relationship between photon energy and wavelength?
Photon energy and wavelength are inversely proportional: higher energy photons have shorter wavelengths. For example, gamma rays have energies above 100 keV and wavelengths below 0.01 nm, while radio waves have energies below 10⁻⁴ eV and wavelengths over a meter. Visible light sits in the middle with energies from 1.65 eV (red) to 3.10 eV (violet) and wavelengths from 400 to 750 nm.
What is the wavelength of a 1 eV photon?
A 1 eV photon has a wavelength of approximately 1240 nm, which lies in the infrared region of the electromagnetic spectrum. This is derived from the handy rule of thumb λ(nm) = 1240 / E(eV), which comes from the constants hc = 1.986 × 10⁻²⁵ J·m divided by the eV-to-J conversion factor.
How accurate is this energy to wavelength calculator?
This calculator uses CODATA-recommended values for Planck's constant (6.62607015 × 10⁻³⁴ J·s), the speed of light (299,792,458 m/s), and the electronvolt conversion (1.602176634 × 10⁻¹⁹ J/eV). Results are accurate to 4 significant figures, suitable for physics, chemistry, and engineering applications.
What is an electronvolt and why is it used for photon energy?
An electronvolt (eV) is the energy gained by a single electron when accelerated through a potential difference of one volt, equal to 1.602 × 10⁻¹⁹ joules. It is the standard unit for photon energies because atomic and quantum energy levels are conveniently sized in eV — for example, visible photons range from 1.65 to 3.10 eV, and hydrogen's ground state energy is −13.6 eV.
How is energy to wavelength conversion used in spectroscopy?
In spectroscopy, energy to wavelength conversion is essential because instruments measure wavelengths while energy levels are naturally expressed in eV. When a material absorbs or emits photons, the transition energy ΔE between quantum states determines the observed spectral line wavelength via λ = hc/ΔE. This conversion lets scientists identify elements by their spectral fingerprints and study molecular structure.