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Compton Wavelength Calculator

Use the Compton wavelength calculator to compute the Compton wavelength, a quantum characteristic of any particle.

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Compton wavelength2.4263 pmh/mc — a fixed property of the particle that does NOT depend on how fast it is moving, unlike the de Broglie wavelength above
de Broglie wavelength122.6366 pmh/p for a electron at 0.019781c — using the RELATIVISTIC momentum γmv
Non-relativistic estimate122.6606 pm0.0196% too long — h/mv ignores the γ, which matters once the kinetic energy approaches the rest energy
Speed5.9301e+6 m/s0.019781 times the speed of light
Lorentz factor γ1.0001957
Kinetic energy100 eV1.602e-17 J
Rest energy of the particle510999 eVmc² for the electron — the kinetic energy is 0.01957% of it, which is why the classical formulas are fine here
Momentum5.40301e-24 kg·m/s
Against an atom (0.1 nm)1.226×comparable to atomic spacing, so this particle diffracts off a crystal — which is how electron diffraction was discovered
Compton shift2.4263 pmat 90°: (h/mc)(1 − cos θ) — the wavelength a photon GAINS on scattering off this particle. It depends only on the angle, never on the incoming wavelength
Maximum Compton shift4.8526 pmat 180°, straight back — exactly twice the Compton wavelength
Minimum momentum uncertainty5.2729e-25 kg·m/sħ/2Δx — the Heisenberg limit for a position known to 100 pm
Minimum speed uncertainty5.7884e+5 m/s0.001931 times the speed of light
Minimum kinetic energy from confinement0.9525 eVconfining a particle COSTS energy — this is why atoms do not collapse, and why the zero-point energy cannot be removed
Uncertainty is not measurement errorit is intrinsicthe limit holds for a perfect apparatus. A particle does not HAVE a sharp position and momentum simultaneously for a measurement to reveal

The formula

λ = h/p; Δx Δp ≥ ħ/2; Δλ = (h/mc)(1 − cos θ)

Two different wavelengths

The de Broglie wavelength h/p depends on how fast a particle is moving and goes to infinity as it slows. The Compton wavelength h/mc is a fixed property of the particle and does not depend on its motion at all. They are easy to confuse because both are h over something with the units of momentum, but they answer different questions — the first is about interference, the second about the scale at which a particle can no longer be localised without creating more particles.

The Compton shift is stranger still: a photon scattering off an electron gains a wavelength that depends only on the scattering angle, never on the wavelength it arrived with. That angle-only dependence is what made the effect such decisive evidence that light carries momentum in discrete quanta.

Momentum should be relativistic

Textbooks often write the de Broglie wavelength as h/mv, which quietly assumes the particle is slow. An electron through only 100 volts is already at 2% of the speed of light, and by a few hundred kilovolts the error is several percent. This calculator uses γmv throughout and shows the non-relativistic figure alongside so the size of the difference is visible.

Uncertainty is not clumsiness

The Heisenberg limit is not a statement about disturbing what you measure. It holds for a perfect apparatus, because a particle does not possess a sharp position and a sharp momentum at the same time for any measurement to reveal. Confinement therefore costs energy — which is precisely why atoms do not collapse and why zero-point motion cannot be frozen out.