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Frequency, Wavelength & Photon Energy Converter

Convert bidirectionally between electromagnetic frequency (Hz, GHz, THz), wavelength (m, μm, nm, Å), photon quantum energy (eV, Joules), and spectroscopic wavenumber (cm⁻¹) with an interactive rainbow spectrum SVG.

Electrodynamics & Nuclear Physics Engine

Quantum Wave-Particle Conversion Matrix

Sci Notation

Decimals:

INPUT PROPERTY:NM

TARGET CONVERSION:

545.0772

Reference Presets:

Electromagnetic Spectrum Continuum VisualizerBand: Visible Light (550.0 nm)

Wavelength: 550.00 nmPhoton Energy: 2.254 eV (3.61e-19 J)Frequency: 545.08 THz

Physical Derivation & Planck Equation:

1. Wave relation: c = ν · λ = 299,792,458 m/s

2. Quantum relation: E = h·ν = (4.135667 × 10⁻¹⁵ eV·s) × (5.4508e+14 s⁻¹)

3. Calculated Photon Energy: 2.2543 eV = 3.6117e-19 Joules

Complete Conversion MatrixClick copy on any row

Quantity / Unit	Symbol	Converted Value
Wavelength (Nanometers)	nm	550
Wavelength (Micrometers)	μm	0.55
Wavelength (Angstroms)	Å	5,500
Wavelength (Meters)	m	5.5000e-7
Frequency (Terahertz)	THz	545.0772
Frequency (Gigahertz)	GHz	545,077.1964
Frequency (Hertz)	Hz	5.4508e+14
Photon Energy (Electron-volts)	eV	2.2543
Photon Energy (Joules)	J	3.6117e-19
Wavenumber (Spectroscopy)	cm⁻¹	18,181.8182

What is the Frequency-Wavelength-Photon Energy Relation?

In electrodynamics, light travels at speed $c = 299,792,458\,\text{m/s}$, tying frequency ($\nu$) and wavelength ($\lambda$) inversely together via $c = \nu \cdot \lambda$.

Through quantum mechanics and the Planck-Einstein relation, every photon carries discrete quantized energy: $E = h\nu = hc / \lambda$, where $h = 6.62607015 \times 10^{-34}\,\text{J}\cdot\text{s}$ ($4.135667 \times 10^{-15}\,\text{eV}\cdot\text{s}$). Infrared spectroscopy indexes this via wavenumber $\tilde{\nu} = 1/\lambda$ in $\text{cm}^{-1}$.

Formula & Step-by-Step Calculation

c = \nu \lambda, \quad E = h\nu = \frac{hc}{\lambda}, \quad \tilde{\nu} = \frac{1}{\lambda} \; [\text{cm}^{-1}]

Fundamental wave-particle duality equations linking classical optics and quantum electrodynamics.

Worked Step-by-Step Examples

Example 1

Find the frequency and photon energy of a 632.8 nm helium-neon laser beam.

Solution: 632.8 nm ≈ 4.738 × 10¹⁴ Hz ≈ 1.959 eV

• Compute frequency: ν = c / λ = (2.9979 × 10⁸ m/s) / (6.328 × 10⁻⁷ m) ≈ 4.738 × 10¹⁴ Hz (473.8 THz).

• Compute energy in eV: E = (4.135667 × 10⁻¹⁵ eV·s) × (4.738 × 10¹⁴ s⁻¹) ≈ 1.959 eV.

Common Real-World & Academic Use Cases

✓ Spectroscopy (FTIR, Raman, UV-Vis) wavenumber and photon energy calculations
✓ Optoelectronic LED and laser diode semiconductor band gap engineering
✓ Wireless RF communications and 5G microwave frequency-to-wavelength sizing
✓ Astrophysical redshift spectroscopy and cosmic microwave background analysis

How to Use the Frequency, Wavelength & Photon Energy Converter

Enter Known Variable

Input either frequency, wavelength, photon energy, or wavenumber.

Select Unit

Pick nm, Hz, GHz, eV, Joules, or cm⁻¹.

View Spectrum Visualizer

See the interactive position marker move along the radio, visible rainbow, and gamma ray spectrum.

Frequently Asked Questions

Q: What is the visible light wavelength range?

The human eye perceives electromagnetic radiation between approximately 380 nm (violet) and 750 nm (deep red).

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