Planck’s relation (E=hf) is a result of a transverse wave, from the vibration of a particle due to a difference in wave amplitude. Particles move to minimize their displacement (minimize amplitude) on a wave. This happens during motion, including annihilation of a particle or when a particle transitions between orbitals in an atom. Its vibration causes a secondary, transverse wave and the energy is based on the frequency of this vibration.








The derivation starts with the Energy Wave Equation, 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 – specifically the explanation of transverse and longitudinal wave components, and the volume to amplitude ratios (not described or derived here in this section).

This section also derives the Planck constant (h). It’s value is validated in the Planck’s Constant page as proof of the derivation. References to Eqs. 1.1, 1.2 and 1.11 and 1.74 come from the Key Physics Equations and Experiments paper.






Solving for the wave constants in Eq. 2.2.8 for Planck constant yields the accurate numerical value and units: 6.6261E-34 kg m2 / s.

Planck Constant