What Is the Rydberg Equation?

The Rydberg Equation, or Rydberg Formula, predicts the light wavelength that results from the motion of an electron between an atom's different energy levels. Electron movement from one atomic orbital to another changes the energy of that electron.

When electrons shift from high energy orbitals to lower states of energy, the process creates a photon of light; conversely, movement from low-energy to high-energy orbitals absorbs a photon of light. Every element has its own fingerprint on the spectrum, which means that observing the photons of light through a diffraction grating or prism reveals the specific element involved in the reaction, through a series of colored lines.

Johannes Rydberg, a Swedish scientist, attempted to discover the mathematical relationship between successive lines on the spectrum of different elements. He discovered that the wavenumbers of consecutive lines had an integral relationship. Combining this with the Bohr model of the atom, he derived the formula (1/lambda) = RZ^2(1/n1^2 - 1/n2^2), in which lambda is the wavelength (the inverse of the wavenumber), Z is the atom's atomic number, R is Rydberg's constant (1.9073731568539 * 10^7 m^(-1), and n1 and n2 are integers, with n2 larger than n1. While this formula works well with small numbers of electrons, as with hydrogen (which only features one electron), atoms that have multiple electrons cause the formula to produce errors.