The exact frequency of the limiting line (series limit) in the Paschen series of the hydrogen emissi

Question

The exact frequency of the limiting line (series limit) in the Paschen series of the hydrogen emission spectrum is approximately ($c = 3 	imes 10^8 \mathrm{~m/s}$, $R_H \approx 1.097 	imes 10^7 \mathrm{~m}^{-1}$)

Professor PC Thomas Classes · Answer

(b) : The limiting line of any series corresponds to a transition from infinity. For the Paschen series, the transition is from $n_2 = \infty$ down to $n_1 = 3$. The wave number is $\bar{
u} = R_H \left(\frac{1}{3^2} - \frac{1}{\infty^2}ight) = \frac{R_H}{9}$. The frequency is $
u = c \cdot \bar{
u} = \frac{c \cdot R_H}{9}$. Substituting values: $
u = \frac{3 	imes 10^8 	imes 1.097 	imes 10^7}{9} = \frac{3.291 	imes 10^{15}}{9} \approx 3.656 	imes 10^{14} \mathrm{~Hz}$.