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Compton Wavelength Calculator

Calculate Compton wavelength, reduced Compton wavelength, frequency, and rest energy for any particle mass. Supports electrons, protons, neutrons, and custom masses.

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About

The Compton wavelength λC defines the quantum-mechanical scale at which a particle's wave-like nature dominates over its localized mass. It sets the fundamental length below which pair-production becomes energetically favorable: confining a particle to a region smaller than its Compton wavelength requires energy exceeding mc2, violating single-particle descriptions. For the electron, λC ≈ 2.426 pm. Getting this wrong in QED calculations or scattering cross-section estimates propagates into incorrect Compton scattering predictions and Thomson limit breakdowns.

This calculator computes λC = h ÷ (mc) and the reduced form λ = ℏ ÷ (mc) from CODATA 2018 constants. It handles mass input in kg, MeV/c2, or unified atomic mass units u. The tool approximates assuming free particles at rest. It does not account for binding energy corrections or relativistic momentum. Note: for composite particles (atoms, molecules), the Compton wavelength loses direct physical meaning beyond order-of-magnitude estimates.

compton wavelength quantum mechanics particle physics de broglie rest mass planck constant reduced compton wavelength

Formulas

The Compton wavelength is derived from equating a photon's energy to the rest-mass energy of a particle. For a particle of rest mass m, the standard Compton wavelength is:

λC = hm ⋅ c

The reduced (or rationalized) Compton wavelength divides by 2π:

ƛC = ℏm ⋅ c = λC2π

The associated Compton frequency and rest energy are:

fC = m ⋅ c2h    E0 = m ⋅ c2

Where: h = 6.62607015 × 10−34 J⋅s (Planck constant), ℏ = h ÷ 2π ≈ 1.05457 × 10−34 J⋅s (reduced Planck constant), c = 299792458 m/s (speed of light in vacuum), m = rest mass of the particle in kg.

Mass unit conversions used internally: 1 u = 1.66053906660 × 10−27 kg, 1 MeV/c2 = 1.78266192 × 10−30 kg.

Reference Data

ParticleSymbolRest Mass (kg)Rest Mass (MeV/c2)λC (m)λC (pm)Reduced ƛC (fm)
Electrone−9.1094 × 10−310.511002.4263 × 10−122.4263386.16
Muonμ−1.8835 × 10−28105.661.1734 × 10−140.0117341.8676
Tauτ−3.1675 × 10−271776.866.978 × 10−166.978 × 10−40.11105
Protonp1.6726 × 10−27938.271.3214 × 10−151.3214 × 10−30.21031
Neutronn1.6749 × 10−27939.571.3196 × 10−151.3196 × 10−30.21002
Pion (charged)π±2.4880 × 10−28139.578.880 × 10−158.880 × 10−31.4133
Pion (neutral)π02.4060 × 10−28134.989.182 × 10−159.182 × 10−31.4614
Kaon (charged)K±8.8006 × 10−28493.682.510 × 10−152.510 × 10−30.39946
W bosonW±1.4332 × 10−25803791.543 × 10−171.543 × 10−50.002455
Z bosonZ01.6255 × 10−25911881.360 × 10−171.360 × 10−50.002164
Higgs bosonH02.2322 × 10−251251009.902 × 10−189.902 × 10−60.001576
Deuterond3.3436 × 10−271875.616.612 × 10−166.612 × 10−40.10524
Alpha particleα6.6447 × 10−273727.383.325 × 10−163.325 × 10−40.05293
Planck massmP2.1764 × 10−81.221 × 10191.016 × 10−341.016 × 10−221.616 × 10−20

Frequently Asked Questions

The Compton wavelength λC sets the length scale where quantum field effects become dominant. When a photon's wavelength approaches λC of a particle, the photon carries enough energy to produce particle-antiparticle pairs. Below this scale, single-particle quantum mechanics breaks down and quantum field theory is required. For the electron, λC ≈ 2.426 pm, which is roughly 20 times smaller than the Bohr radius.
The reduced Compton wavelength ƛC = ħ ÷ (mc) appears naturally in equations using angular frequency or natural units. It defines the Compton scattering minimum impact parameter and sets the scale of Yukawa potentials. In natural units where ħ = c = 1, the reduced form equals the inverse mass 1÷m, making it the standard choice in high-energy physics.
The de Broglie wavelength λdB = h ÷ p depends on momentum and varies with velocity. The Compton wavelength is a fixed property of the particle determined solely by its rest mass. They become equal when the particle's momentum equals mc, corresponding to a Lorentz factor γ = √2 (velocity ≈ 0.707c). At higher momenta, λdB drops below λC and pair production becomes possible.
Formally, you can compute λC for any mass, but the physical interpretation weakens for composite systems. An atom's Compton wavelength is extremely small (for hydrogen: ≈ 1.32 fm), far below its size. At that scale, internal structure (nuclear and electronic) dominates. The result becomes an order-of-magnitude estimate of the energy needed to probe sub-nuclear scales rather than a meaningful scattering parameter.
It does not. The Compton wavelength depends exclusively on the rest mass m, which is Lorentz invariant. Thermal energy or kinetic energy changes the de Broglie wavelength, not the Compton wavelength. However, in thermal field theory, the thermal de Broglie wavelength λth = h ÷ √2πmkBT is used instead. When λth approaches interparticle spacing, quantum degeneracy effects emerge.
The calculator rejects non-positive mass values. Physically, massless particles (photons, gluons) have no defined Compton wavelength since λC → ∞ as m → 0. Negative mass has no established physical meaning in the Standard Model. Tachyonic fields use imaginary mass parameters, but Compton wavelength is not conventionally defined for them.