Energy to Wavelength Calculator
Calculate photon wavelength, energy, and frequency using Planck's equation E = hc/λ
Quantum Mechanics Calculator
Example Calculations
Green Light Wavelength
Given: Energy = 2.48 eV (green light)
Step 1: Convert to Joules: E = 2.48 × 1.602×10⁻¹⁹ = 3.973×10⁻¹⁹ J
Step 2: Apply formula: λ = hc/E
Step 3: Calculate: λ = (6.626×10⁻³⁴ × 2.998×10⁸) / 3.973×10⁻¹⁹ = 500 nm
X-ray Energy
Given: Wavelength = 0.1 nm (hard X-ray)
Calculation: E = hc/λ = (6.626×10⁻³⁴ × 2.998×10⁸) / 1×10⁻¹⁰ = 1.988×10⁻¹⁵ J
In eV: E = 1.988×10⁻¹⁵ / 1.602×10⁻¹⁹ = 12.4 keV
Electromagnetic Spectrum
Physical Constants
Planck's Constant
6.626×10⁻³⁴ J⋅Hz⁻¹
Speed of Light
2.998×10⁸ m/s
Planck⋅Light
1.240 μeV⋅m
Electron Volt
1.602×10⁻¹⁹ J
Understanding Photon Energy and Wavelength
Planck-Einstein Relation
The energy of a photon is directly proportional to its frequency and inversely proportional to its wavelength. This fundamental relationship was discovered by Max Planck and Albert Einstein and forms the basis of quantum mechanics.
Applications
- •Spectroscopy: Identify materials by their emission/absorption spectra
- •Quantum Physics: Energy level transitions in atoms and molecules
- •Photonics: Design of lasers, LEDs, and optical devices
- •Medical Physics: X-ray and gamma ray therapy calculations
Key Equations
E = hf = hc/λ
λ = hc/E
f = c/λ = E/h
- E: Photon energy (J, eV, etc.)
- λ (lambda): Wavelength (m, nm, etc.)
- f: Frequency (Hz, THz, etc.)
- h: Planck's constant (6.626×10⁻³⁴ J⋅Hz⁻¹)
- c: Speed of light (2.998×10⁸ m/s)
Note: Higher energy photons have shorter wavelengths. This inverse relationship explains why gamma rays are so energetic and radio waves are low energy.
Energy-Wavelength Relationship
Low Energy
Long wavelengths (radio, microwave). Low frequency photons with minimal energy per photon.
Moderate Energy
Visible light and near infrared/UV. Moderate energy suitable for chemical processes.
High Energy
Short wavelengths (X-rays, gamma rays). High energy photons capable of ionization.