Bohr S Model Of Hydrogen Atom

The wavelength of a photon can be related to its frequency using the equation: where: - is the wavelength of the photon, - is the speed of light in a vacuum ( ), - is the frequency of the photon. This is the general relation for the wavelength of any electromagnetic radiation, including photons.

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.