The Lyman and Paschen series are part of the hydrogen atom's emission spectra. The Lyman series corresponds to transitions where the final state is , while the Paschen series corresponds to transitions where the final state is . The wavelength of light emitted during these transitions can be found using the Rydberg formula for hydrogen: where: - is the wavelength of the emitted radiation, - is the Rydberg constant, - and are the principal quantum numbers of the initial and final states, respectively. For the Lyman series limit, the transition is from , and the wavelength corresponds to the transition where . Thus, for Lyman: For the Paschen series limit, the transition is from , and the wavelength corresponds to the transition where . Thus, for Paschen: Now, the ratio of the wavelengths is the inverse of the ratio of the terms: Thus, the ratio of the wavelength of Lyman to Paschen is , meaning the wavelength of the Lyman series limit is 9 times greater than that of the Paschen series limit.