Rydberg constant — sets the wavelengths of hydrogen spectral lines; the most precisely measured constant in physics.The Rydberg constant is a fundamental physical constant that determines the wavelengths of light emitted or absorbed by hydrogen atoms. It appears in the Rydberg formula, which predicts the spectral lines of hydrogen with extraordinary precision. Because hydrogen is the simplest atom, this constant serves as a cornerstone for testing quantum electrodynamics and for defining the SI unit of length through atomic transitions.
The constant was empirically derived by Swedish physicist Johannes Rydberg in 1888, who noticed a pattern in the spectral lines of hydrogen and other elements. Later, Niels Bohr's 1913 model of the atom provided a theoretical derivation, linking the constant to more fundamental quantities.
The Rydberg constant emerges from the quantum mechanical description of the hydrogen atom. In the Bohr model, the energy levels of the electron are proportional to 1/n², and the constant sets the overall energy scale. More precisely, it combines fundamental constants: the electron mass, charge, Planck's constant, and the speed of light. When an electron jumps between energy levels, the emitted photon's wavelength is inversely proportional to the difference of the inverse squares of the principal quantum numbers, with the Rydberg constant as the proportionality factor.
It is used to calibrate atomic clocks and to define the meter in the International System of Units, as well as in spectroscopy for identifying elements in stars and laboratories.
The Rydberg constant is known to a relative uncertainty of about 1.9 × 10⁻¹², making it the most precisely measured fundamental constant in physics.
