Rydberg Constant - Alternative Expressions

Alternative Expressions

The Rydberg constant can also be expressed as the following equations.

and

where

is the electron rest mass

is the Planck constant

is the reduced Planck constant,

is the speed of light in a vacuum,

is the fine-structure constant,

is the Compton wavelength of the electron,

is the Compton frequency of the electron,

is the Compton angular frequency of the electron,

is the Bohr radius.

The last expression in the first equation shows that the wavelength of light needed to ionize a hydrogen atom is 4π/α times the Bohr radius of the atom.

The second equation is relevant because it is the coefficient for the energy of the atomic orbitals of a hydrogen atom: .