Accurate Compton & reduced Compton wavelength using exact SI constants. Verified against NIST reference values.
Definition: Compton wavelength λC = h/(m c) is the quantum-mechanical length scale associated with a particle of mass m. The reduced Compton wavelength ƛ = ħ/(m c) = λC/(2π) appears more naturally in quantum field equations.
Arthur Compton observed that X‑ray photons scattered by electrons increase in wavelength. The shift depends only on the scattering angle θ:
The constant h/(m_e c) ≈ 2.426 pm is the Compton wavelength of the electron. This experiment provided direct evidence for the particle nature of light and confirmed that electrons have a quantum length scale.
When a particle is confined to a region smaller than its reduced Compton wavelength, the uncertainty in energy exceeds mc², allowing virtual particle‑antiparticle pairs to appear. Thus the Compton wavelength marks the boundary where single‑particle quantum mechanics must be replaced by quantum field theory.
For an electron, ƛ ≈ 386 fm. Probing below this scale (e.g., in high‑energy collisions) reveals pair creation and vacuum polarisation.
The Planck mass MP is defined by equating a particle's reduced Compton wavelength to its Schwarzschild radius:
At this mass, quantum mechanics and general relativity meet — the Compton wavelength (~10−35 m) equals the Planck length. This is why the Planck mass is often called the "quantum of mass".
Heavier particles have shorter Compton wavelengths because λ ∝ 1/m. The electron, being the lightest common particle, has the largest Compton wavelength (~2.4 pm). Protons and neutrons are ~2000 times heavier, so their Compton wavelengths are in the femtometer range — comparable to the size of a nucleus.
| Particle | Mass (kg) | Compton λ (m) | Reduced λ (m) |
|---|---|---|---|
| Electron | 9.109×10-31 | 2.4263×10-12 | 3.8616×10-13 |
| Proton | 1.6726×10-27 | 1.3214×10-15 | 2.1031×10-16 |
| Neutron | 1.6749×10-27 | 1.3196×10-15 | 2.1002×10-16 |
| Muon | 1.8835×10-28 | 1.1734×10-14 | 1.8673×10-15 |
Values from CODATA 2018; calculator uses exactly these masses and the 2019 defined constants.
✅ Calculator verification: Using h = 6.62607015×10−34 J·s, c = 299792458 m/s (exact since 2019) and the CODATA 2018 masses listed above, the computed Compton wavelengths match the NIST reference values to 8 significant figures. For the electron, λ = 2.42631023867×10−12 m (NIST) – our result agrees within the displayed precision.
The Compton wavelength emerged from Compton's 1923 experiment, which earned him the Nobel Prize in 1927. It was one of the first demonstrations that quantum mechanics applies not only to light but also to matter, paving the way for de Broglie's wave‑particle duality and the development of quantum electrodynamics.
Calculator features:
h6.62607015e-34 J·sħ1.054571817e-34 J·sc299792458 m/sme9.1093837015e-31 kgmp1.67262192369e-27 kg1 u1.66053906660e-27 kg