Atomic Spectra

Step 1: Identifying the Longest Wavelength Transition The longest wavelength in any spectral series corresponds to the transition from to . - For the Paschen series, this occurs at .
- For the Lyman series, it happens at . Using the Rydberg formula: where: - is the Rydberg constant.
- is the atomic number.
- and represent the lower and upper energy levels, respectively.
Step 2: Wavelength Ratio for Different Series For a hydrogen-like ion, the wavelength of a given transition is inversely proportional to , meaning: Given that Lithium ( ) has and Hydrogen ( ) has , the ratio of their wavelengths is:
Step 3: Compute the Required Wavelength For Paschen series (longest wavelength): For Lyman series (longest wavelength): Thus, the correct answer is .