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 because of their wavelengths. Further detail was provided in the Photon section. In this section, the relationship of photon energy and how photons are created with various wavelengths are discussed.

As explained in the Atoms section, electrons reside in orbitals surrounding the nucleus of an atom. If an electron changes orbitals then a photon may be emitted or absorbed.

  • When an electron moves to a higher energy level in the atom (further from the nucleus) it requires energy. It must absorb a photon.
  • When an electron moves to a lower energy level in the atom (closer to the nucleus), it emits a photon.

 

Photon absorption and emission

 

Since energy is always conserved, an electron that has a greater energy level change within the atom’s orbitals will result in a photon with greater energy (shorter wavelength).

 


 

Photon Wavelengths

In energy wave theory, a transverse wave is created from a vibrating particle, perpendicular to the direction of 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. This is seen when an electron transitions between orbitals such as the following diagram.

 

Electron Path - Transverse Wave

This is also seen in particle annihilation. For example, two gamma rays (high energy photons) are generated when an electron and positron collide (annihilate). This can be described as a vibration of two particles until these particles come to rest. In the diagram below, an electron (red) and positron (blue) are attracted to each other. Their momentum carries them past each other, then once attracted again, they reverse position and continue this pattern until finally coming to rest where wave amplitude is minimal (purple). During this process, each particle vibrates at very high frequency, each producing a gamma ray.

 

Electron Positron Annihilation

Credit: Bernard Burchell

 

In addition to the particle’s longitudinal wave, the vibration creates a secondary, transverse wave that includes a new transverse amplitude and wavelength component. During vibration, longitudinal energy is transferred to a transverse wave in a volume (shape) that resembles a cylinder. The characteristic of this transition has an impact on the volume in which energy is stored. The figure below shows this volume transition from a spherical particle (Vl) to a cylindrical photon (Vt).

 

Vibrating Particle

 

As the wave transitions from spherical to the cylindrical shape of the photon, the new, transverse wavelength is related to the original longitudinal amplitude (Al) and volume transformation (Vlt) for a single shell.

The wavelengths and energies will be calculated over a difference between wavelength counts with a starting position (n0) and ending position (n). An illustration is provided to understand the initial and final starting positions of the electron in an orbital. It starts at initial position n0 wavelengths from the nucleus core and ends at position n. Also pictured in the figure is a difference in amplitude as a result of constructive or destructive wave interference – amplitude factor δ.

 

Energy transition of electron in an atom

 

This model was used to derive the Transverse Wavelength Equation, which is used to calculate hydrogen wavelengths. The complete derivation is found in Particle Energy and Interactionbut the final result is shown below. Also, examples are provided for both hydrogen ionization and shell transitions to reproduce the calculations.

 

Transverse Wavelength Equation

 

Note: The Transverse Wavelength Equation is also used to model transverse wavelengths for ionization and particle annihilation. For ionization, n is set to infinity as the electron leaves the atom; for an electron-positron annihilation, n is set to 5 electron wavelengths (half of the electron’s classical radius).  The latter results in the calculation of the Electron Compton Wavelength.