Problem 3: Calculate the longest wavelength of radiation for the Paschen series.
Paschen series radiations come from the transitions in the third orbit from the higher energy levels. The wavelengths of the radiations coming from the transition from farther energy levels is shorter (small) and the frequencies are higher whereas the wavelength of radiations produced from the transitions from the nearer energy levels are longer (and frequency lower). Therefore, the longest wavelength will come from the transition of closest energy level, i-e, energy level 4.
The equation for Paschen series is
Where λ is the wavelength of the corresponding radiation when transition takes place from the nth level. R is the Rydberg constant = 1.0973732 × 107. n = 4 in this case. Now put these values,