# Rydberg Unit of Energy

## Explanation

The Rydberg unit of energy is used to calculate the energy levels in the hydrogen spectrum – energy which is absorbed or emitted in the form of photons as electrons move between shells in the hydrogen atom.  It is related to the Rydberg constant, which is more typically used, to calculate wavelengths.

The Rydberg unit of energy and the Rydberg constant were derived in detail in the Particle Energy and Interaction paper.  For a single electron and proton (ground state of hydrogen), the Rydberg unit of energy is the binding energy between the electron and proton.  At this energy, the Bohr radius is calculated as the position where two forces are equal.  Energy is a force exerted at distance.  The Rydberg unit of energy is this force exerted over a distance of the Bohr radius. ## Derivation – Rydberg Unit of Energy

The Rydberg unit of energy can be derived classically from the Planck mass, Planck length, fine structure constant, electron radius and Planck time.  It is derived in wave constant format from the Transverse Energy Equation.  Since it is based on the electron, it is K=10 (ten wave centers).

### Classical Constant Form ### Wave Constant Form Using classical constants Using energy wave constants

Calculated Value: 2.1799E-18
Difference from CODATA: 0.000%
Calculated Units: Joules (kg m2/s2)

### Alternative Derivation

An alternative derivation in classical form is shown with the magnetic constant, elementary charge, speed of light and Bohr radius.  This version shows the consistency of energy and mass equations in classical format, as explained on the page for Coulomb’s constant. Its value was calculated and shown to match the known value in the Summary of Calculations table. The derivation of this constant is available in the Fundamental Physical Constants paper.