## Background

The Rydberg constant is used to calculate the wavelengths in the hydrogen spectrum – energy which is absorbed or emitted in the form of photons as electrons move between shells in the hydrogen atom. This constant can also be expressed in terms of the fundamental constants of the wave equation.

See also: Rydberg Unit of Energy

## Energy Wave Constants – Equivalent

The following is the representation of this fundamental physical constant expressed in energy wave theory. Using energy wave constants, its value was calculated and shown to match the known value in the Summary of Calculations table.

### Rydberg Constant

The Rydberg constant is derived from the Transverse Wavelength Equation. It is based on the electron at K=10 (ten wave centers).

The Rydberg constant is used with hydrogen calculations and the amplitude factor for a single electron-proton interaction is one (refer to the amplitude factor explanation in the Atoms section). A nucleus with two or more protons will have a different amplitude factor, which is why the Rydberg constant only works for hydrogen.

**Calculated Value**: 1.0974E+07

**Difference from CODATA:** 0.000%

**Calculated Units**: m^{-1}

The complete derivation of this constant is available in the Fundamental Physical Constants paper.

## Alternative Derivation

An alternative version after substituting for O_{e}.

## Relationship to the Fine Structure Constant

Some of the derivations of the wave energy equations appear to be complex, yet their calculations match the known CODATA value. This is one of the energy wave constants that has a connection to the fine structure constant that simplifies the equation and provides some meaning to the constant itself.

The ratio of the fine structure constant squared, and the Rydberg constant, simplifies to 4/3rds wave amplitude (A) over the square of the number of wave centers. This is the volume transformation from spherical waves to cylindrical waves as described in the *Fundamental Physical Constants *paper.