Photon Wavelengths

Background

The photon is the carrier of the electromagnetic wave, which is responsible for light, radio waves, microwaves, X-rays, etc. All of these types of waves are based on the same electromagnetic wave but are differentiated by their wavelengths. Photon wavelength has an inverse relationship to photon energy. For example:

  • A gamma ray is a photon with very high energy, but a very short wavelength
  • A radio wave is a photon with low energy, but a long wavelength

Photon Wavelength

 


 

Explanation

In energy wave theory, a transverse wave is created from a particle that is vibrating perpendicular to the direction of wave motion. A faster vibrating particle results in a transverse wave with a shorter wavelength than a particle that vibrates slower. The greater the longitudinal amplitude differences in a particle’s interaction with surrounding particles, the faster the particle’s vibration.  In an atom, one photon will escape and the other photon will be absorbed by the nucleus and cause it to recoil.

Photon Creation

 

The creation of photons from electrons are not only seen within the atom, but also in the annihilation of an electron and its antimatter counterpart, the positron.  In this case, two photons with short wavelengths (gammay rays) are created during the annihilation.

 

Transverse Wavelength

In addition to the particle’s longitudinal wave, the vibration creates a secondary, transverse wave that includes a new transverse amplitude and wavelength component. There is now a longitudinal component and a transverse component in the photon. The differences in the types of waves in the electromagnetic spectrum, however, are dependent only on the wavelength of the transverse component. An example of a spherical electron with wave centers (K=10), vibrating to create the transverse wave is shown below.

 

Photon 2D view

 

The transverse wavelength is based on the speed of the vibration of the particle, which itself is based on the longitudinal energy difference from the electron’s starting position and ending position relative to the atomic nucleus. It is calculated using the transverse wavelength equations. These equations can be used for any atom, but since photon wavelengths are typically reported for hydrogen, the Transverse Wavelength Equation – Hydrogen was created as a simpler version. Photons beyond hydrogen are often reported in terms of energy, not wavelength.

The wavelength for the hydrogen version of the equation is calculated as difference between wavelength counts with a starting position (n0) and ending position (n). It is described this way to be able to do a conversion of longitudinal wave energy, also counted as wavelengths (n) from the nucleus.  Also pictured in the figure is a difference in amplitude as a result of constructive or destructive wave interference – amplitude factor δ – which is one for hydrogen. Note that the complete form of the wavelength equation uses distance (r) instead of wavelength count (n).

Energy transition of electron in an atom

 

The complete derivation is found in Particle Energy and Interactionbut the final result was described on the photon equation page. The photon wavelengths for hydrogen are accurately calculated using this equation.

 


 

Proof

Proof of the energy wave explanation for photon wavelengths: