Rydberg constant - Illuminating Science

The Rydberg constant is a number for calculating the ground state energy of an electron. The constant is part of the Rydberg energy formula which multiplies the Rydberg constant by the energy constant $hc$ to produce the correct ground state energy.

The elementary form of the Rydberg constant contains four operators but no maximum potentials

The Planck length is normally a maximum potential in historical constants, but in this case the Planck length is only used to remove another unnecessary quantity of Planck length in the energy constant $hc$ .

The Rydberg constant includes all four operators in the expanded form of the energy formula. The spin operator is present in the ratio one-half; the rest mass operator appears in the ratio of the electron’s rest mass to the Planck mass; and for the ground state of an electron, the momentum and velocity operators are equal to $\alpha$ , the fine-structure constant. This is evident in the wavelength and velocity of the ground state electron.

Given the electron’s rest mass, its wavelength in the ground state is

$\lambdabar = \displaystyle\frac{\lambdabar_C}{\alpha}$

and its velocity is

$v = \alpha c$ .

The following equivalent form of the Rydberg constant replaces the fine-structure constant with dimensionless ratios of wavelength and velocity in the ground state electron