Equation – Photons


Photon Energy

Photons are transverse waves of energy as a result of particle vibration. The equation to calculate photon energy uses the Energy Wave Equation and defines the volume (V) of the transverse wave packet. An explanation is provided in the section below.

Transverse Energy Equation

Transverse Energy Equation


Photon Wavelength

Photons can also be expressed in terms of wavelength size. The complete form of the Transverse Wavelength Equation is shown below, although most calculations on this site use the simpler version: Transverse Wavelength Equation – Hydrogen. Beyond hydrogen, many photon experiments present results as energy instead of wavelengths so the Transverse Energy Equations will be used.

Transverse Wavelength Equation - Complete

Transverse Wavelength Equation – Complete Form


  • δ: amplitude factor variable for constructive wave interference. A single proton and electron is one. All other configurations are found in the Amplitude Factors table.
  • r: distance variable for starting position (r0) and ending position (r) of electron in an atom (in meters).
  • Other Constants: The remaining constants in the equation are found here.



Explanation of Equation

The Transverse Energy Equation begins with the fundamental equation for calculating energy in a volume:

Fundamental Energy equation

Energy Wave Equation


A photon is generated by the vibration of a particle. It is a traveling wave originating from the particle, which is constantly reflecting longitudinal waves. Now, it also has a transverse component during its short-lived vibration before the particle comes to rest. Thus, it has a longitudinal component (l) and transverse component (t) that will become its electric and magnetic components.  The vibration creates two photons traveling in opposite directions. In the creation of a photon in an atom, one of the photons will be absorbed by the nucleus and cause recoil as explained here.


Photon Transverse Wave


The transverse component has a frequency that depends on the speed of the vibration of the particle, which may happen during orbital transitions in an atom until a particle like the electron settles into an orbital. The faster the vibration, the higher the frequency of the transverse component. Although the height of the photon is constant for electron interactions, the length will be based on the speed of vibration, affecting the volume (V).

Particle Vibration


The photon length, which affects the volume, is found in detail in the next illustration. The volume ratio of longitudinal energy (Vl) to transverse energy (Vt) is important because energy is always conserved in a given volume.

Complete Photon Transfer of Longitudinal to Transverse Energy


The volume is substituted into the Energy Wave Equation and solved to become the Transverse Energy Equation.  The complete list of steps for the derivation is found in the Particle Energy and Interaction paper. The paper also highlights the derivation for the Transverse Wavelength Equation.


Detailed Assumptions

The Transverse Wavelength Equations and Transverse Energy Equation are built and derived from these assumptions. The orbital distance calculations are found in the tables for orbital distances, with further detail in the Atomic Orbitals paper. An explanation of how photons are created and absorbed, including incident and scattered angles are presented in the Photons paper.

The following assumptions were made when understanding particle interaction, including atomic orbitals:

  • Particle vibration creates a transverse wave. A particle may vibrate upon annihilation, when transitioning between orbitals in an atom, or when an entire atom vibrates due to kinetic energy.
  • Longitudinal amplitude difference creates particle motion as particles seek to minimize amplitude.
  • The difference in longitudinal energy is transferred to transverse energy in a wave packet known as the photon.
  • Particles and their antimatter counterparts attract because of destructive waves between the particles; like particles (e.g. electron-electron) repel due to constructive waves, seeking to minimize amplitude.
  • Electrons in an atomic orbital are both attracted and repelled by the nucleus. A positron is assumed to be at its core to attract the orbital electron; opposing forces in the nucleus repel the orbital electron as explained in the Atoms section.


Calculations and Examples

A summary of calculations and some examples using the equations are provided here. The remainder of the calculations and examples are detailed in the Particle Energy and Interaction paper. A summary of photon interactions in atoms is detailed in the Photons paper.