Compton Wavelength Calculator
Calculate the characteristic quantum wavelength for particles and fundamental quantum limitations
Calculate Compton Wavelength
Compton Wavelength Results
Formula: λc = h/(mc) where h = Planck's constant, m = particle mass, c = speed of light
Physical meaning: Wavelength of photon with energy equal to particle's rest mass energy
Quantum field theory: Sets scale for particle creation from vacuum
Quantum Scale Analysis
Example: Fundamental Particles
Electron
Mass: 9.109 × 10⁻³¹ kg = 0.511 MeV/c²
Compton wavelength: 2.426 pm
Significance: Sets scale for electron-photon interactions
Applications: X-ray scattering, quantum electrodynamics
Proton
Mass: 1.673 × 10⁻²⁷ kg = 938.3 MeV/c²
Compton wavelength: 1.321 fm
Significance: Nuclear scale physics, much smaller than atomic scales
Applications: High-energy particle physics, accelerator design
Comparison
λc(electron)/λc(proton) ≈ 1836 (proton-to-electron mass ratio)
Lighter particles have longer Compton wavelengths
Quantum field effects more significant for lighter particles
Physical Significance
Quantum Threshold
Distance scale where quantum field theory becomes necessary
Measurement Limit
Fundamental limit on precise position measurement
Particle Creation
Scale for particle-antiparticle pair production
Energy Equivalence
Photon wavelength with energy = mc²
Fundamental Constants
Length Scale References
fm scale: Nuclear physics, proton size (~1 fm)
pm scale: Atomic physics, electron wavelength
nm scale: Molecular physics, chemical bonds
Planck length: 1.616 × 10⁻³⁵ m (quantum gravity)
Understanding the Compton Wavelength
What is the Compton Wavelength?
The Compton wavelength is a fundamental quantum mechanical property of particles that represents the wavelength of a photon whose energy equals the rest mass energy of the particle. It sets important scales in quantum field theory and particle physics.
Physical Interpretation
- •Characteristic length scale for quantum field effects
- •Minimum uncertainty in position measurement
- •Scale where particle creation becomes significant
- •Important for high-energy scattering processes
Compton Wavelength Formula
λc = h/(mc)
- λc: Compton wavelength (meters)
- h: Planck constant (6.626 × 10⁻³⁴ J⋅s)
- m: Rest mass of particle (kg)
- c: Speed of light (2.998 × 10⁸ m/s)
Related formula: The reduced Compton wavelength is λ̄c = λc/(2π) = ℏ/(mc), where ℏ is the reduced Planck constant.
Quantum Field Theory Significance
Measurement Limits
To measure a particle's position precisely, we need photons with wavelength comparable to the desired resolution. But photons with λ ≤ λc have enough energy to create particle pairs, fundamentally limiting measurement precision.
Vacuum Fluctuations
At distances comparable to the Compton wavelength, quantum vacuum fluctuations become significant. Virtual particle pairs can be created and annihilated, leading to observable quantum field effects.
Relativistic Quantum Mechanics
The Compton wavelength marks the transition from non-relativistic quantum mechanics to relativistic quantum field theory. Below this scale, particle creation and annihilation processes become important.