The Rydberg formula is a mathematical equation used to predict the wavelengths of spectral lines in hydrogen and other hydrogen-like atoms. It was developed by Johann Balmer and later generalized by Johannes Rydberg. The formula is expressed as \frac1\lambda = R \left( \frac1n_1^2 - \frac1n_2^2 \right) , where \lambda is the wavelength, R is the Rydberg constant, and n_1 and n_2 are integers representing energy levels. The formula highlights the transitions of electrons between energy levels in an atom. When an electron moves from a higher energy level to a lower one, it emits light at specific wavelengths, which can be observed as spectral lines. This principle is fundamental in quantum mechanics and helps scientists understand atomic structure and behavior.