The general formula describing the wave number ($\bar{
u}$) of the spectral lines belonging strictl

Question

The general formula describing the wave number ($\bar{
u}$) of the spectral lines belonging strictly to the Paschen series of the hydrogen spectrum is

Professor PC Thomas Classes · Answer

(c) : The Rydberg formula for calculating the wave number of hydrogen spectral lines is $\bar{
u} = R_H \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$. For the Paschen series, the transitions invariably terminate at the third energy level, meaning $n_1 = 3$, and $n_2$ can be $4, 5, 6, \dots$ Given the Rydberg constant $R_H = 1.09677 	imes 10^5 \mathrm{~cm}^{-1}$, the formula perfectly matches $\bar{
u} = 1.09677 	imes 10^5 \left( \frac{1}{3^2} - \frac{1}{n^2} ight) \mathrm{cm}^{-1}$.