In the late 1800s, Max Planck studied the effects of radiation (electromagnetic waves). In the following years, Albert Einstein extended the work to “quantize” radiation, eventually becoming the quantum energy equation for light and for all frequencies in the electromagnetic spectrum (e.g. radio waves, microwaves, x-rays, etc).  The equation, E=hf, is referred to as the Planck relation or the Planck-Einstein relation. The letter h is named after Planck, as Planck’s constant.  Energy (E) is related to this constant h, and to the frequency (f) of the electromagnetic wave.

Planck relation E=hf and the electromagnetic wave

In energy wave theory, Planck’s relation describes the energy of a transverse wave, emitted or absorbed as an electron transitions energy levels in an atom. When an electron is contained within an atom, destructive wave interference between protons in the nucleus and the electron causes destructive waves, resulting in binding energy. This binding energy becomes the energy of a photon that is released when an electron is captured or moves states in an atom. The electron’s vibration causes a transverse wave and the photon’s energy is based on the frequency of this vibration.




This energy and its derivation is very similar to Coulomb’s law, with the exception that one is measured as energy and one is measured as a force.  In an atom, the electron’s position is stable in an orbit and it is therefore stored energy. When electrons interact and cause motion, it is measured as a force, as seen in the next page on F=kqq/r2.



Derivation – Classical Constants

The Planck relation can be derived using only Planck constants (classical constants), and the electron’s energy at distance (r).  The derivation is very similar to the Coulomb’s law as they are both related to the electron’s energy at distance.  Energy is conserved, yet wave formation (geometry) changes, as explained in the geometry of spacetime page. The geometries (α1 and α2) are described in Eq. 1.3.2. When all of the variables in the α2 ratio are the electron’s classical radius (re), with the exception of slant length (l), which is πre, it resolves to be the fine structure constant (described in Eq. 1.3.5).  Further details can be found in the Geometry of Spacetime paper.

Planck relation derivation from classical constants


Planck Constant: Solving for the classical constants in Eq. 1.3.11 for Planck constant yields the accurate numerical value and units.


Hydrogen Frequency (Ground State): Solving for Eq. 1.3.12 at the Bohr radius (a0) for a hydrogen atom (no constructive wave interference- Δ=1) yields the correct frequency.




Derivation – Wave Constants

The derivation starts with a difference in longitudinal wave energy from the Energy Wave Equation from the wave constant form, as the particle’s vibration creates a secondary, transverse wave. However, it also requires explanation about the derivation of a transverse wave that can be found in the Photons section. Further details can be found, including the reference to Eq. 1.16, in the Key Physics Equations and Experiments paper.

E=hf derived


Planck Constant: Solving for the wave constants in Eq. 2.3.9 for Planck constant yields the accurate numerical value and units.

Planck Constant Derived


Hydrogen Frequency (Ground State): Solving for Eq. 2.3.4 at the Bohr radius (a0) for a hydrogen atom (amplitude factor is one – δ=1) yields the correct frequency.

Hydrogen Ground State Frequency Derived


Rydberg Unit of Energy: Solving for the energy of a hydrogen atom at the Bohr radius (a0) in Eq. 2.3.6 yields the Rydberg unit of energy.

Rydberg Energy Derived


The equations use wave constants explained here.