Question

Ratio of wavelength of series limit of Balmer and Paschen series for an atom is

Answer 1

Ratio of wavelength of series limit of Balmer and Paschen series for an atom is

series limit means shortest wavelength

for wavelength of series limit of Balmer , $\frac{1}{\lambda_1}=R_H\left(\frac{1}{2^2}-\frac{1}{\infty^2}\right)$

where $R_H$ is Rydberg's constant.

⇒$\lambda_1=\frac{4}{R_H}$.....(1)

for wavelength of series limit of Paschen, $\frac{1}{\lambda_2}=R_H\left(\frac{1}{3^2}-\frac{1}{\infty^2}\right)$

⇒$\lambda_2=\frac{9}{R_H}$

ratio of wavelength of series limit of Balmer and Paschen , $\frac{\lambda_1}{\lambda_2}=\frac{4}{9}$