What is the Compton wavelength?
The Compton wavelength is a quantum characteristic length associated with a particle. It equals the wavelength of a photon whose energy is the same as the particle's rest mass energy (E = mc²). It sets a fundamental quantum scale for a particle, below which quantum field effects dominate classical descriptions. See also our Energy to Wavelength Calculator.
What is the Compton wavelength equation?
The Compton wavelength is given by λ = h / (mc), where h is Planck's constant (6.62607 × 10⁻³⁴ J·s), m is the particle's mass in kilograms, and c is the speed of light (299,792,458 m/s). The reduced Compton wavelength ƛ = ħ / (mc) uses the reduced Planck constant ħ = h / (2π).
What is the Compton wavelength of an electron?
The Compton wavelength of an electron is approximately 2.42631 × 10⁻¹² m (about 2.43 pm or 2426.31 fm). The reduced Compton wavelength of the electron is approximately 3.86159 × 10⁻¹³ m. These values arise from the electron's mass of about 9.109 × 10⁻³¹ kg.
What is the Compton wavelength of a proton?
The Compton wavelength of a proton is approximately 1.32141 × 10⁻¹⁵ m (about 1.321 fm), which is roughly 1836 times smaller than that of an electron. This reflects the proton's much larger mass of about 1.6726 × 10⁻²⁷ kg.
What is the difference between the Compton wavelength and the reduced Compton wavelength?
The standard Compton wavelength is λ = h/(mc), while the reduced Compton wavelength is ƛ = ħ/(mc) = λ/(2π), where ħ is the reduced Planck constant. The reduced form appears more naturally in quantum mechanics equations and is often called the 'Compton radius' of a particle.
What limitation on measurement does the Compton wavelength imply?
The Compton wavelength represents a fundamental limit on how precisely you can localize a particle. If you try to measure a particle's position to within its Compton wavelength, the photon used must have enough energy to create a particle-antiparticle pair, making the original particle indistinguishable. This connects quantum mechanics with special relativity.
How does the Compton wavelength relate to the de Broglie wavelength?
The de Broglie wavelength (λ = h/p) depends on a particle's momentum and changes with its velocity, while the Compton wavelength (λ = h/mc) is a fixed property depending only on rest mass. At relativistic speeds, a moving particle's de Broglie wavelength approaches its Compton wavelength when its kinetic energy equals its rest energy.
Does the Compton wavelength change with velocity?
No — the Compton wavelength is computed from the particle's invariant rest mass, so it does not change with velocity. It is a fixed quantum property of a particle, unlike the de Broglie wavelength which varies with momentum. However, if you use the relativistic mass in the formula, the effective Compton wavelength would decrease at higher speeds.