2.42631024e-12
m
2.42631
pm
2,426.310239
fm
3.86159268e-13
m
386.159268
fm
0.510999
MeV
1.235590e+20
Hz
2.42631024e-12
m
2.42631
pm
2,426.310239
fm
3.86159268e-13
m
386.159268
fm
0.510999
MeV
1.235590e+20
Hz
The Compton Wavelength Calculator computes the Compton wavelength and reduced Compton wavelength for any particle. The Compton wavelength is a fundamental quantum mechanical length scale associated with a particle of mass m, defined as: $$\lambda_C = \frac{h}{mc}$$ It represents the wavelength of a photon whose energy equals the particle's rest mass energy (mc²). The reduced Compton wavelength is ƛ = λ_C/(2π) = ħ/(mc), which appears more frequently in quantum field theory and relativistic quantum mechanics.
The Compton wavelength sets the length scale below which quantum field theory effects become important for a given particle. When a photon's wavelength approaches the Compton wavelength of an electron (~2.426 pm), photon-electron interactions enter the relativistic regime where pair production and vacuum polarization become significant. For protons and neutrons, the Compton wavelength (~1.32 fm) is on the scale of nuclear physics.
The Compton wavelength also provides a natural connection between a particle's mass and its quantum mechanical wave properties. It is inversely proportional to mass: heavier particles have shorter Compton wavelengths. For the electron, λ_C = 2.426 pm; for the proton, λ_C = 1.321 fm. This calculator includes presets for electron, proton, and neutron, and allows custom mass input for any particle. Results include both the standard and reduced Compton wavelengths in multiple units, plus the particle's rest energy in MeV.
The calculator computes the Compton wavelength using:
Standard Compton Wavelength:
$$\lambda_C = \frac{h}{mc}$$
where h = 6.626 × 10⁻³⁴ J·s, m is the particle mass, and c = 2.998 × 10⁸ m/s.
Reduced Compton Wavelength:
$$\lambdabar_C = \frac{\hbar}{mc} = \frac{\lambda_C}{2\pi}$$
Rest Energy:
$$E_0 = mc^2$$
converted to MeV by dividing by (1.602 × 10⁻¹³ J/MeV).
Particle presets use standard CODATA masses: electron (9.109 × 10⁻³¹ kg), proton (1.673 × 10⁻²⁷ kg), neutron (1.675 × 10⁻²⁷ kg).
The Compton wavelength is the distance scale at which relativistic quantum effects become dominant for a particle. If you try to localize a particle to within its Compton wavelength, the uncertainty in its momentum (via Heisenberg's principle) becomes large enough that particle-antiparticle pair creation becomes energetically possible. For the electron, λ_C = 2.426 pm is much smaller than an atom but much larger than a nucleus. For the proton, λ_C = 1.321 fm, on the scale of nuclear physics. The reduced Compton wavelength ƛ appears in the Dirac equation and is the natural length unit in relativistic quantum mechanics.
Inputs
Results
The electron Compton wavelength is 2.426 pm. Its rest energy is 0.511 MeV. Photons at this wavelength (hard gamma rays) have enough energy to create electron-positron pairs.
Inputs
Results
The proton Compton wavelength is 1.321 fm, comparable to the proton's own size (~0.88 fm charge radius). Its rest energy is 938.3 MeV.
The Compton wavelength λ_C = h/(mc) is the wavelength of a photon whose energy equals the rest mass energy of the particle (mc²). It represents the length scale below which quantum field effects (such as pair production) become significant for that particle. Attempting to probe distances shorter than λ_C requires photons energetic enough to create particle-antiparticle pairs.
The standard Compton wavelength is λ_C = h/(mc), while the reduced Compton wavelength is ƛ = ħ/(mc) = λ_C/(2π). The reduced form appears more naturally in relativistic quantum mechanics (e.g., the Dirac equation) and differs by a factor of 2π, just as ħ differs from h by the same factor.
The wavelength shift in Compton scattering is Δλ = λ_C(1−cosθ), where λ_C is the Compton wavelength of the electron. At 90° scattering, the shift exactly equals the electron's Compton wavelength (2.426 pm).
The Compton wavelength sets the resolution limit for probing a particle without creating new particles. At distances shorter than λ_C, the energy uncertainty exceeds 2mc², enabling pair creation from the vacuum. This marks the boundary where single-particle quantum mechanics breaks down and quantum field theory is needed.
The Compton wavelength is inversely proportional to mass: λ_C = h/(mc). Heavier particles have shorter Compton wavelengths. The electron (lightest charged particle) has the longest Compton wavelength at 2.426 pm. The proton, being ~1836 times heavier, has λ_C = 1.321 fm, about 1836 times shorter.
For a 1 kg object, λ_C = h/(mc) ≈ 2.2 × 10⁻⁴² m, far below the Planck length (1.6 × 10⁻³⁵ m). This is physically meaningless—the concept is relevant only for elementary and subatomic particles.
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