Hong Life CalculatorsUnderstanding the Compton wavelength calculator — concept and principle
The Compton wavelength of a particle is the wavelength of a photon whose energy equals the particle's rest energy. It sets the scale of Compton scattering and of the distance below which a particle cannot be localised without creating new particles. This calculator gives it for common particles or any rest mass.
How it is calculated
- λC = h ÷ (mc) = hc ÷ (mc²), with hc = 1,239.84 MeV·fm.
- Reduced Compton wavelength ƛ = λC ÷ 2π = ħ ÷ (mc).
- Frequency of a photon with that wavelength = c ÷ λC.
- Rest mass in kg = (mc² in MeV × 1.602176634 × 10⁻¹³ J/MeV) ÷ c².
The principle
Quantum mechanics links mass and length through Planck's constant and the speed of light. A photon with wavelength λC carries energy mc², enough to create a particle of mass m. Trying to confine a particle to a region smaller than its Compton wavelength requires so much energy that particle–antiparticle pairs can appear, so single-particle quantum mechanics breaks down. Heavier particles have shorter Compton wavelengths.
Worked example
Default input: electron (rest energy 0.510999 MeV).
- λC = 1,239.84 MeV·fm ÷ 0.510999 MeV ≈ 2,426.31 fm = 2.42631 pm.
- Reduced wavelength = 2,426.31 ÷ 2π ≈ 386.159 fm.
- Photon frequency = 299,792,458 ÷ 2.42631 × 10⁻¹² ≈ 1.236 × 10²⁰ Hz.
- Rest mass = 9.10938 × 10⁻³¹ kg.
How to read the result
The electron's Compton wavelength (2.43 pm) is much smaller than an atom (about 100 pm) but much larger than a proton (about 1 fm). The proton's Compton wavelength, about 1.32 fm, is close to its size. These scales tell you when relativistic quantum field theory is needed.
Common mistakes
- Confusing the Compton wavelength with the de Broglie wavelength, which depends on momentum.
- Mixing up λC and the reduced ƛ = λC ÷ 2π.
- Mixing fm, pm and m.
- Using mass in kg with hc in MeV·fm.
Frequently asked questions
What is the Compton wavelength of an electron?
About 2.426 pm (2.426 × 10⁻¹² m).
How is it different from the de Broglie wavelength?
The Compton wavelength depends only on rest mass; the de Broglie wavelength h ÷ p depends on the particle's momentum.
What is the reduced Compton wavelength?
λC ÷ 2π = ħ ÷ (mc), the form used in many quantum formulas.
Sources: CODATA 2018 recommended values of the fundamental physical constants, NIST (electron Compton wavelength) · Griffiths, D. J., Introduction to Elementary Particles, 2nd ed. Wiley-VCH