Explanation
Named after Arthur Compton, the electron Compton wavelength is the wavelength of the electromagnetic wave when the photon energy matches the rest energy of the electron. Each particle will have a different Compton wavelength. This page highlights the calculation of the Compton wavelength for the electron.
The electron Compton wavelength occurs when the electron and its antiparticle, the positron, annihilate. These particles are equal in energy but are placed on opposite nodes of a standing wave, such that their wave phase is opposite and create destructive wave interference when combined. After annihilation, the particles (i.e. their wave centers) still remain but they are not detectable with electromagnetic apparatus as their standing waves have collapsed. The Compton wavelength is calculated when the particles reach a distance of half the electron radius, a convenient position for the two particles to have complete destructive wave interference. The energy of the standing waves is transferred to transverse waves as the particles vibrate before coming to rest, creating two photons traveling in opposite directions.
See also: What is Annihilation (for animation of the process)
Derivation – Electron Compton Wavelength
The electron Compton wavelength is derived from the Transverse Wavelength Equation, also illustrated in detail in the Particle Energy and Interaction paper. The positron is the anti-particle to the electron, where it sits at a halfway point (anti-phase) within the electron’s standing waves and is perfectly destructive with the electron. A distance of one-half of the electron’s classical radius is used in the Transverse Wavelength Equation for the derivation in wave constant form.
Classical Constant Form
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Wave Constant Form
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| Using classical constants | Using energy wave constants |
Calculated Value: 2.4263E-12
Difference from CODATA: 0.000%
Calculated Units: meters (m)
G-Factor: gλ
Its value was calculated and shown to match the known value in the Summary of Calculations table. The derivation of this constant is available in the Fundamental Physical Constants paper.
