Compton Wavelength
Calculate the Compton wavelength of any particle using λ = h/(mc) with preset particles (electron, proton, neutron) or custom mass. Free online quantum mechanics calculator with results in m, pm, fm, and eV.
About This Calculator
The Compton Wavelength Calculator computes the fundamental quantum mechanical wavelength of any particle using the formula λ = h / (m × c), where h is Planck's constant, m is the particle's rest mass, and c is the speed of light. Named after physicist Arthur Compton, this quantity is a cornerstone of quantum electrodynamics and sets the length scale at which relativistic quantum effects become dominant.
The Compton wavelength is derived by equating a photon's energy (E = hc/λ) with a particle's rest energy (E = mc²). Solving for λ gives λ = h/(mc). This wavelength is a fundamental property of each particle type — for example, an electron's Compton wavelength is approximately 2.426 picometers, while a proton's is about 1.321 femtometers. The shorter the Compton wavelength, the more massive the particle.
Key Applications
Quantum measurement limits: The Compton wavelength sets a fundamental bound on how precisely a particle's position can be measured. Shining light of wavelength shorter than the Compton wavelength provides photons with energy exceeding mc², which can create particle-antiparticle pairs from the vacuum, destroying the original particle.
Quantum field theory: At distances comparable to the Compton wavelength, quantum field theory must replace non-relativistic quantum mechanics. This scale determines where virtual particle-antiparticle pair creation becomes feasible, affecting phenomena from electron-positron annihilation to the Lamb shift in atomic spectra.
Compton scattering: Named after the same physicist, Compton scattering describes the increase in wavelength when a photon scatters off a charged particle. The Compton wavelength of the target particle determines the magnitude of the wavelength shift (Δλ = λc × (1 − cos θ)).
Supported Particles
The calculator includes presets for the electron, proton, neutron, muon, and tau particle, or you can enter a custom mass in kilograms. The corresponding photon energy is also displayed in electronvolts.
Frequently Asked Questions
What is the Compton wavelength?
The Compton wavelength is a quantum mechanical property of a particle, defined as the wavelength of a photon whose energy equals the rest energy (mc²) of that particle. It is calculated using the formula λ = h/(mc), where h is Planck's constant, m is the particle mass, and c is the speed of light.
What is the Compton wavelength of an electron?
The Compton wavelength of an electron is approximately 2.42631 × 10⁻¹² m (2.42631 pm). For a proton it is about 1.3214 × 10⁻¹⁵ m (1.3214 fm), and for a neutron it is about 1.3196 × 10⁻¹⁵ m (1.3196 fm).
How is the Compton wavelength used in physics?
The Compton wavelength sets the length scale at which quantum field theory becomes essential. It represents the distance at which particle-antiparticle pair creation from vacuum becomes energetically possible, imposing a fundamental limit on how precisely a particle can be localized.
What is the difference between Compton wavelength and de Broglie wavelength?
The Compton wavelength λc = h/(mc) depends only on the particle's rest mass and is constant for a given particle type. The de Broglie wavelength λ = h/p depends on the particle's momentum and varies with velocity. Both describe quantum mechanical wave-like properties but in different contexts.
What does the Compton wavelength tell us about measurement limits?
To localize a particle, you need light with wavelength comparable to its size. If the photon energy exceeds mc², the collision can create particle-antiparticle pairs, making the original position measurement meaningless. The Compton wavelength marks this fundamental quantum limit on position measurement.
Is this calculator free to use?
Yes, this Compton wavelength calculator is completely free to use with no registration or hidden charges. Results update instantly and can be shared via URL.