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

Radio> 10 cm
Microwave1 mm - 10 cm
Infrared700 nm - 1 mm
Visible380-780 nm
Ultraviolet10-380 nm
X-rays0.01-10 nm
Gamma rays< 0.01 nm

Physical Constants

h

Planck's Constant

6.626×10⁻³⁴ J⋅Hz⁻¹

c

Speed of Light

2.998×10⁸ m/s

hc

Planck⋅Light

1.240 μeV⋅m

eV

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.