Nanometre to Electron Volt Converter
Convert wavelength (nm) to photon energy (eV) with precision
Wavelength to Energy Converter
Popular Wavelength to Energy Conversions
| Wavelength (nm) | Energy (eV) | Spectrum Region | Application |
|---|---|---|---|
| 121.6 | 10.20 | Extreme UV | Hydrogen Lyman-alpha line |
| 193 | 6.42 | Deep UV | Photolithography |
| 248 | 5.00 | UV-C | Excimer lasers |
| 365 | 3.40 | UV-A | Black light, curing |
| 400 | 3.10 | Violet | Visible light threshold |
| 532 | 2.33 | Green | Laser pointers |
| 632.8 | 1.96 | Red | Helium-neon laser |
| 700 | 1.77 | Deep red | Visible light boundary |
| 850 | 1.46 | Near infrared | Optical communications |
| 1064 | 1.17 | Near infrared | Nd:YAG laser |
| 1550 | 0.80 | Near infrared | Fibre optic communications |
Conversion Formula and Method
Primary Conversion Formula:
Inverse Formula:
Derivation from First Principles
The relationship between wavelength and photon energy stems from Planck’s equation and the wave nature of light:
Step 1: Planck’s energy equation
Where:
- h = Planck’s constant = 6.62607015 × 10⁻³⁴ J·s
- c = Speed of light = 2.99792458 × 10⁸ m/s
- λ = Wavelength in metres
Step 2: Convert to practical units
Step 3: Convert joules to electronvolts
Step 4: Final formula in nm and eV
Step-by-Step Conversion Example
Example: Convert 589 nm (sodium D-line) to eV
- Identify the wavelength: λ = 589 nm
- Apply the formula: E = 1239.84193 / 589
- Perform the division: E = 2.105 eV
- Result: A photon at 589 nm has an energy of 2.105 eV
Electromagnetic Spectrum Guide
Gamma Rays
X-Rays
Extreme UV
Ultraviolet
Visible Light
Near Infrared
Mid Infrared
Far Infrared
Key Observation: As wavelength increases, photon energy decreases inversely. This inverse relationship is fundamental to spectroscopy, photonics, and quantum mechanics. Shorter wavelengths (UV, X-rays) carry more energy per photon, whilst longer wavelengths (infrared, radio) carry less energy.
Physical Constants Reference
| Constant | Symbol | Value | Units |
|---|---|---|---|
| Planck constant | h | 6.62607015 × 10⁻³⁴ | J·s |
| Planck constant in eV | h | 4.135667696 × 10⁻¹⁵ | eV·s |
| Speed of light | c | 2.99792458 × 10⁸ | m/s |
| Electron charge | e | 1.602176634 × 10⁻¹⁹ | C |
| Energy conversion constant | hc | 1239.84193 | eV·nm |
| Alternative constant | hc | 1.98644568 × 10⁻²⁵ | J·m |
Frequently Asked Questions
What is the relationship between nanometres and electronvolts?
Nanometres (nm) measure wavelength, whilst electronvolts (eV) measure photon energy. They are inversely related through the equation E = 1239.84193 / λ. As wavelength increases, energy decreases proportionally. This relationship is fundamental in spectroscopy, photonics, and quantum physics.
Why is the constant 1239.84193 used in the formula?
This constant combines Planck’s constant (h), the speed of light (c), and the electron charge conversion factor. When h (6.626 × 10⁻³⁴ J·s) is multiplied by c (2.998 × 10⁸ m/s) and converted from joules to electronvolts whilst accounting for nanometre units, the result is approximately 1239.84193 eV·nm.
How do I convert 550 nm green light to eV?
Apply the formula: E = 1239.84193 / 550 = 2.254 eV. Green light at 550 nm wavelength corresponds to photons with an energy of approximately 2.25 electronvolts. This wavelength sits in the middle of the visible spectrum where human eyes are most sensitive.
What wavelength corresponds to 1 eV?
Rearranging the formula: λ = 1239.84193 / 1 = 1239.84 nm. A photon with 1 eV energy has a wavelength of approximately 1240 nm, which falls in the near-infrared region just beyond the visible spectrum’s red edge.
Why do shorter wavelengths have higher energy?
According to quantum mechanics, photon energy is directly proportional to frequency (E = h × f) and inversely proportional to wavelength (E = h × c / λ). Shorter wavelengths mean higher frequencies, resulting in more energetic photons. This explains why ultraviolet and X-rays are more energetic and potentially harmful than visible or infrared light.
What are typical photon energies in visible light?
Visible light spans 400-700 nm, corresponding to energies of approximately 1.77-3.10 eV. Violet light (400 nm) has the highest energy at about 3.1 eV, whilst deep red light (700 nm) has the lowest at about 1.77 eV. This energy range is sufficient to trigger photochemical reactions in the human retina, enabling vision.
How does this conversion apply to laser technology?
Lasers are often specified by wavelength (e.g., 532 nm green laser) or photon energy. Converting between these units helps determine appropriate applications, safety requirements, and interaction with materials. For instance, a 532 nm laser produces 2.33 eV photons, suitable for presentations but insufficient to ionise most atoms.
What is the significance of 1240 eV·nm?
The value 1240 eV·nm (or more precisely 1239.84193 eV·nm) is a fundamental constant in photonics and semiconductor physics. It’s commonly used as a convenient approximation for quick mental calculations. Many researchers memorise this value for rapid wavelength-energy conversions in laboratory settings.
Can this formula be used for all electromagnetic radiation?
Yes, the formula E = 1239.84193 / λ applies to all electromagnetic radiation, from radio waves to gamma rays. However, for very short wavelengths (X-rays and gamma rays), it’s more common to express wavelength in picometres or energy in keV. The inverse relationship holds throughout the entire electromagnetic spectrum.