Compton Wavelength Calculator
Find the Compton wavelength λ = h/(mc), the quantum length scale that sets the resolution limit for a particle's position.
🌀 What is the Compton Wavelength Calculator?
This Compton wavelength calculator finds λ=h/(mc), the quantum length scale associated with a particle's rest mass. Choose an electron, proton, neutron, muon, or custom mass, and it returns the Compton wavelength in picometres and metres, plus the reduced Compton wavelength.
For the electron with its default settings, this calculator exactly reproduces the CODATA-listed Compton wavelength of 2.4263102389 picometres.
The Compton wavelength marks roughly the scale at which trying to localize a particle more precisely requires so much energy that pair production becomes likely, a boundary between single-particle quantum mechanics and quantum field theory.
This calculator is useful for particle physics and quantum mechanics students studying Compton scattering, natural length scales, and comparing this quantity across different particles.
📐 Formula
📖 How to Use This Calculator
Steps
💡 Example Calculations
Example 1 - Electron (CODATA match)
Example 2 - Proton
Example 3 - Muon
❓ Frequently Asked Questions
🔗 Related Calculators
What is the Compton wavelength?
The Compton wavelength, λ_C = h/(mc), is a quantum length scale associated with a particle's rest mass. It marks roughly the scale at which quantum field effects (like electron-positron pair production) become important when trying to localize the particle more precisely.
What is the formula for the Compton wavelength?
λ_C = h/(mc), where h is the Planck constant, m is the particle's rest mass, and c is the speed of light. This calculator generalizes the formula to any particle, not just the electron.
What is the Compton wavelength of the electron?
For the electron, λ_C ≈ 2.4263102389 picometres, a CODATA-listed fundamental physical constant. It appears directly in the Compton scattering formula that describes how X-rays scatter off electrons.
What is the difference between the Compton wavelength and the reduced Compton wavelength?
The Compton wavelength λ = h/(mc) appears directly in the Compton scattering wavelength-shift formula. The reduced Compton wavelength λ̄ = λ/(2π) = ħ/(mc) appears more naturally in quantum mechanics equations like the Klein-Gordon equation. This calculator reports both.
Why does the Compton wavelength get shorter for heavier particles?
Because λ_C is inversely proportional to mass (λ_C ∝ 1/m), a heavier particle's quantum length scale shrinks proportionally. This is why the proton's Compton wavelength is about 1836 times shorter than the electron's, matching the proton-to-electron mass ratio exactly.
How is the Compton wavelength used in physics?
It appears directly in Compton's 1923 X-ray scattering formula, Δλ = λ_C(1−cosθ), which describes the wavelength shift of a photon scattered off a free electron, historic evidence for the particle nature of light.
Is the Compton wavelength related to the classical electron radius?
Both are length scales built from the electron mass, but they represent different physics: the classical electron radius (~2.818 fm) comes from classical electrostatics, while the Compton wavelength (~2.426 pm) comes from quantum mechanics and is about 860 times larger.
Does the Compton wavelength represent the particle's physical size?
No, quantum field theory treats fundamental particles like the electron as point particles. The Compton wavelength is instead the length scale at which a purely single-particle (non-quantum-field) description of position starts to break down.
What units does this calculator use?
Results are given in picometres (pm, 10⁻¹² m) for the Compton wavelength, alongside the raw value in metres and the reduced Compton wavelength for reference.
What particles are included as presets?
Electron, proton, neutron, and muon are built in as presets, or you can enter any custom rest mass in kilograms to compute the Compton wavelength for other particles.